5514 lines
163 KiB
HTML
5514 lines
163 KiB
HTML
|
||
<!doctype html>
|
||
<html lang="zh" class="no-js">
|
||
<head>
|
||
|
||
<meta charset="utf-8">
|
||
<meta name="viewport" content="width=device-width,initial-scale=1">
|
||
|
||
<meta name="description" content="一本开源的直觉优先教科书，从零开始覆盖数学、计算机科学和人工智能（中文翻译版）。">
|
||
|
||
|
||
<meta name="author" content="Henry Ndubuaku (flykhan 译)">
|
||
|
||
|
||
<link rel="canonical" href="https://flykhan.github.io/maths-cs-ai-compendium-zh/chapter%2008%3A%20computer%20vision/01.%20image%20fundamentals/">
|
||
|
||
|
||
<link rel="prev" href="../../chapter%2007%3A%20computational%20linguistics/05.%20advanced%20text%20generation/">
|
||
|
||
|
||
<link rel="next" href="../02.%20convolutional%20networks/">
|
||
|
||
|
||
|
||
|
||
|
||
<link rel="icon" href="../../assets/images/favicon.png">
|
||
<meta name="generator" content="mkdocs-1.6.1, mkdocs-material-9.7.6">
|
||
|
||
|
||
|
||
<title>图像基础 - 数学、计算机科学与 AI 百科全书</title>
|
||
|
||
|
||
|
||
<link rel="stylesheet" href="../../assets/stylesheets/main.484c7ddc.min.css">
|
||
|
||
|
||
<link rel="stylesheet" href="../../assets/stylesheets/palette.ab4e12ef.min.css">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
|
||
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Roboto:300,300i,400,400i,700,700i%7CRoboto+Mono:400,400i,700,700i&display=fallback">
|
||
<style>:root{--md-text-font:"Roboto";--md-code-font:"Roboto Mono"}</style>
|
||
|
||
|
||
|
||
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,_)=>(e<<5)-e+_.charCodeAt(0)),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script>
|
||
|
||
|
||
|
||
|
||
|
||
</head>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="slate" data-md-color-accent="indigo">
|
||
|
||
|
||
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
|
||
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
|
||
<label class="md-overlay" for="__drawer"></label>
|
||
<div data-md-component="skip">
|
||
|
||
|
||
<a href="#_1" class="md-skip">
|
||
跳转至
|
||
</a>
|
||
|
||
</div>
|
||
<div data-md-component="announce">
|
||
|
||
</div>
|
||
|
||
|
||
|
||
|
||
<header class="md-header" data-md-component="header">
|
||
<nav class="md-header__inner md-grid" aria-label="页眉">
|
||
<a href="../.." title="数学、计算机科学与 AI 百科全书" class="md-header__button md-logo" aria-label="数学、计算机科学与 AI 百科全书" data-md-component="logo">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54"/></svg>
|
||
|
||
</a>
|
||
<label class="md-header__button md-icon" for="__drawer">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg>
|
||
</label>
|
||
<div class="md-header__title" data-md-component="header-title">
|
||
<div class="md-header__ellipsis">
|
||
<div class="md-header__topic">
|
||
<span class="md-ellipsis">
|
||
数学、计算机科学与 AI 百科全书
|
||
</span>
|
||
</div>
|
||
<div class="md-header__topic" data-md-component="header-topic">
|
||
<span class="md-ellipsis">
|
||
|
||
图像基础
|
||
|
||
</span>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
<form class="md-header__option" data-md-component="palette">
|
||
|
||
|
||
|
||
|
||
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="slate" data-md-color-accent="indigo" aria-label="切换到深色模式" type="radio" name="__palette" id="__palette_0">
|
||
|
||
<label class="md-header__button md-icon" title="切换到深色模式" for="__palette_1" hidden>
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a4 4 0 0 0-4 4 4 4 0 0 0 4 4 4 4 0 0 0 4-4 4 4 0 0 0-4-4m0 10a6 6 0 0 1-6-6 6 6 0 0 1 6-6 6 6 0 0 1 6 6 6 6 0 0 1-6 6m8-9.31V4h-4.69L12 .69 8.69 4H4v4.69L.69 12 4 15.31V20h4.69L12 23.31 15.31 20H20v-4.69L23.31 12z"/></svg>
|
||
</label>
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="slate" data-md-color-accent="indigo" aria-label="切换到浅色模式" type="radio" name="__palette" id="__palette_1">
|
||
|
||
<label class="md-header__button md-icon" title="切换到浅色模式" for="__palette_0" hidden>
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 18c-.89 0-1.74-.2-2.5-.55C11.56 16.5 13 14.42 13 12s-1.44-4.5-3.5-5.45C10.26 6.2 11.11 6 12 6a6 6 0 0 1 6 6 6 6 0 0 1-6 6m8-9.31V4h-4.69L12 .69 8.69 4H4v4.69L.69 12 4 15.31V20h4.69L12 23.31 15.31 20H20v-4.69L23.31 12z"/></svg>
|
||
</label>
|
||
|
||
|
||
</form>
|
||
|
||
|
||
|
||
<script>var palette=__md_get("__palette");if(palette&&palette.color){if("(prefers-color-scheme)"===palette.color.media){var media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']");palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent")}for(var[key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-header__button md-icon" for="__search">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
|
||
</label>
|
||
<div class="md-search" data-md-component="search" role="dialog">
|
||
<label class="md-search__overlay" for="__search"></label>
|
||
<div class="md-search__inner" role="search">
|
||
<form class="md-search__form" name="search">
|
||
<input type="text" class="md-search__input" name="query" aria-label="搜索" placeholder="搜索" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
|
||
<label class="md-search__icon md-icon" for="__search">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
|
||
</label>
|
||
<nav class="md-search__options" aria-label="查找">
|
||
|
||
<button type="reset" class="md-search__icon md-icon" title="清空当前内容" aria-label="清空当前内容" tabindex="-1">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
|
||
</button>
|
||
</nav>
|
||
|
||
<div class="md-search__suggest" data-md-component="search-suggest"></div>
|
||
|
||
</form>
|
||
<div class="md-search__output">
|
||
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
|
||
<div class="md-search-result" data-md-component="search-result">
|
||
<div class="md-search-result__meta">
|
||
正在初始化搜索引擎
|
||
</div>
|
||
<ol class="md-search-result__list" role="presentation"></ol>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-header__source">
|
||
<a href="https://github.com/flykhan/maths-cs-ai-compendium-zh" title="前往仓库" class="md-source" data-md-component="source">
|
||
<div class="md-source__icon md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M439.6 236.1 244 40.5c-5.4-5.5-12.8-8.5-20.4-8.5s-15 3-20.4 8.4L162.5 81l51.5 51.5c27.1-9.1 52.7 16.8 43.4 43.7l49.7 49.7c34.2-11.8 61.2 31 35.5 56.7-26.5 26.5-70.2-2.9-56-37.3L240.3 199v121.9c25.3 12.5 22.3 41.8 9.1 55-6.4 6.4-15.2 10.1-24.3 10.1s-17.8-3.6-24.3-10.1c-17.6-17.6-11.1-46.9 11.2-56v-123c-20.8-8.5-24.6-30.7-18.6-45L142.6 101 8.5 235.1C3 240.6 0 247.9 0 255.5s3 15 8.5 20.4l195.6 195.7c5.4 5.4 12.7 8.4 20.4 8.4s15-3 20.4-8.4l194.7-194.7c5.4-5.4 8.4-12.8 8.4-20.4s-3-15-8.4-20.4"/></svg>
|
||
</div>
|
||
<div class="md-source__repository">
|
||
flykhan/maths-cs-ai-compendium-zh
|
||
</div>
|
||
</a>
|
||
</div>
|
||
|
||
</nav>
|
||
|
||
</header>
|
||
|
||
<div class="md-container" data-md-component="container">
|
||
|
||
|
||
|
||
|
||
|
||
<nav class="md-tabs" aria-label="标签" data-md-component="tabs">
|
||
<div class="md-grid">
|
||
<ul class="md-tabs__list">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../.." class="md-tabs__link">
|
||
|
||
|
||
|
||
|
||
|
||
首页
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2001%3A%20vectors/01.%20vector%20spaces/" class="md-tabs__link">
|
||
|
||
|
||
|
||
向量
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2002%3A%20matrices/01.%20matrix%20properties/" class="md-tabs__link">
|
||
|
||
|
||
|
||
矩阵
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2003%3A%20calculus/01.%20differential%20calculus/" class="md-tabs__link">
|
||
|
||
|
||
|
||
微积分
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2004%3A%20statistics/01.%20fundamentals/" class="md-tabs__link">
|
||
|
||
|
||
|
||
统计学
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2005%3A%20probability/01.%20counting/" class="md-tabs__link">
|
||
|
||
|
||
|
||
概率论
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/01.%20classical%20machine%20learning/" class="md-tabs__link">
|
||
|
||
|
||
|
||
机器学习
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/01.%20linguistic%20foundations/" class="md-tabs__link">
|
||
|
||
|
||
|
||
计算语言学
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item md-tabs__item--active">
|
||
<a href="./" class="md-tabs__link">
|
||
|
||
|
||
|
||
计算机视觉
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/01.%20digital%20signal%20processing/" class="md-tabs__link">
|
||
|
||
|
||
|
||
音频与语音
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/01.%20multimodal%20representations/" class="md-tabs__link">
|
||
|
||
|
||
|
||
多模态学习
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/01.%20perception/" class="md-tabs__link">
|
||
|
||
|
||
|
||
自主系统
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/01.%20geometric%20deep%20learning/" class="md-tabs__link">
|
||
|
||
|
||
|
||
图神经网络
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/01.%20discrete%20maths/" class="md-tabs__link">
|
||
|
||
|
||
|
||
计算机与操作系统
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/00.%20foundations/" class="md-tabs__link">
|
||
|
||
|
||
|
||
数据结构与算法
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/01.%20linux%20and%20CMD/" class="md-tabs__link">
|
||
|
||
|
||
|
||
生产级软件工程
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/00.%20why%20C%2B%2B%20and%20how%20ML%20frameworks%20work/" class="md-tabs__link">
|
||
|
||
|
||
|
||
SIMD 与 GPU 编程
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2017%3A%20AI%20inference/01.%20quantisation/" class="md-tabs__link">
|
||
|
||
|
||
|
||
AI 推理
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2018%3A%20ML%20systems%20design/01.%20systems%20design%20fundamentals/" class="md-tabs__link">
|
||
|
||
|
||
|
||
ML 系统设计
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/01.%20AI%20for%20finance/" class="md-tabs__link">
|
||
|
||
|
||
|
||
应用 AI
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/01.%20quantum%20machine%20learning/" class="md-tabs__link">
|
||
|
||
|
||
|
||
前沿 AI
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</div>
|
||
</nav>
|
||
|
||
|
||
|
||
<main class="md-main" data-md-component="main">
|
||
<div class="md-main__inner md-grid">
|
||
|
||
|
||
|
||
<div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
|
||
<div class="md-sidebar__scrollwrap">
|
||
<div class="md-sidebar__inner">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--primary md-nav--lifted" aria-label="导航栏" data-md-level="0">
|
||
<label class="md-nav__title" for="__drawer">
|
||
<a href="../.." title="数学、计算机科学与 AI 百科全书" class="md-nav__button md-logo" aria-label="数学、计算机科学与 AI 百科全书" data-md-component="logo">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54"/></svg>
|
||
|
||
</a>
|
||
数学、计算机科学与 AI 百科全书
|
||
</label>
|
||
|
||
<div class="md-nav__source">
|
||
<a href="https://github.com/flykhan/maths-cs-ai-compendium-zh" title="前往仓库" class="md-source" data-md-component="source">
|
||
<div class="md-source__icon md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M439.6 236.1 244 40.5c-5.4-5.5-12.8-8.5-20.4-8.5s-15 3-20.4 8.4L162.5 81l51.5 51.5c27.1-9.1 52.7 16.8 43.4 43.7l49.7 49.7c34.2-11.8 61.2 31 35.5 56.7-26.5 26.5-70.2-2.9-56-37.3L240.3 199v121.9c25.3 12.5 22.3 41.8 9.1 55-6.4 6.4-15.2 10.1-24.3 10.1s-17.8-3.6-24.3-10.1c-17.6-17.6-11.1-46.9 11.2-56v-123c-20.8-8.5-24.6-30.7-18.6-45L142.6 101 8.5 235.1C3 240.6 0 247.9 0 255.5s3 15 8.5 20.4l195.6 195.7c5.4 5.4 12.7 8.4 20.4 8.4s15-3 20.4-8.4l194.7-194.7c5.4-5.4 8.4-12.8 8.4-20.4s-3-15-8.4-20.4"/></svg>
|
||
</div>
|
||
<div class="md-source__repository">
|
||
flykhan/maths-cs-ai-compendium-zh
|
||
</div>
|
||
</a>
|
||
</div>
|
||
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../.." class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
首页
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_2" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_2" id="__nav_2_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
向量
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_2">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
向量
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2001%3A%20vectors/01.%20vector%20spaces/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
向量空间
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2001%3A%20vectors/02.%20vector%20properties/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
向量性质
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2001%3A%20vectors/03.%20norms%20and%20metrics/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
范数与度量
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2001%3A%20vectors/04.%20products/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
向量积
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2001%3A%20vectors/05.%20basis%20and%20duality/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
基与对偶性
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_3" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
矩阵
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_3">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
矩阵
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2002%3A%20matrices/01.%20matrix%20properties/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
矩阵性质
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2002%3A%20matrices/02.%20matrix%20types/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
矩阵类型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2002%3A%20matrices/03.%20operations/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
矩阵运算
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2002%3A%20matrices/04.%20linear%20transformations/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
线性变换
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2002%3A%20matrices/05.%20decompositions/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
矩阵分解
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_4" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
微积分
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_4">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
微积分
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2003%3A%20calculus/01.%20differential%20calculus/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
微分
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2003%3A%20calculus/02.%20integral%20calculus/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
积分
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2003%3A%20calculus/03.%20multivariate%20calculus/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
多元微积分
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2003%3A%20calculus/04.%20function%20approximation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
函数逼近
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2003%3A%20calculus/05.%20optimisation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
优化
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_5" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_5" id="__nav_5_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
统计学
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_5">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
统计学
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2004%3A%20statistics/01.%20fundamentals/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2004%3A%20statistics/02.%20measures/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
统计量
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2004%3A%20statistics/03.%20sampling/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
抽样
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2004%3A%20statistics/04.%20hypothesis%20testing/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
假设检验
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2004%3A%20statistics/05.%20inference/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
推断
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_6" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
概率论
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_6">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
概率论
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2005%3A%20probability/01.%20counting/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
计数
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2005%3A%20probability/02.%20probability%20concepts/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
概率概念
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2005%3A%20probability/03.%20distributions/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
分布
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2005%3A%20probability/04.%20bayesian/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
贝叶斯
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2005%3A%20probability/05.%20information%20theory/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
信息论
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_7" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_7" id="__nav_7_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
机器学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_7">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
机器学习
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/01.%20classical%20machine%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
经典机器学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/02.%20gradient%20machine%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
梯度机器学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/03.%20deep%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
深度学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/04.%20reinforcement%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
强化学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/05.%20distributed%20deep%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
分布式深度学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_8" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
计算语言学
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_8">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
计算语言学
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/01.%20linguistic%20foundations/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
语言学基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/02.%20text%20processing%20and%20classic%20NLP/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
文本处理与经典 NLP
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/03.%20embeddings%20and%20sequence%20models/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
嵌入与序列模型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/04.%20transformers%20and%20language%20models/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Transformer 与语言模型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/05.%20advanced%20text%20generation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
高级文本生成
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" checked>
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
计算机视觉
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="true">
|
||
<label class="md-nav__title" for="__nav_9">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
计算机视觉
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active">
|
||
|
||
<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link md-nav__link--active" for="__toc">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图像基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<a href="./" class="md-nav__link md-nav__link--active">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图像基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="目录">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
目录
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#colab-notebook" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
编码任务（使用 CoLab 或 notebook）
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../02.%20convolutional%20networks/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
卷积网络
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../03.%20object%20detection%20and%20segmentation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
目标检测与分割
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../04.%20vision%20transformers%20and%20generation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ViT 与生成模型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../05.%20video%20and%203D%20vision/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
视频与 3D 视觉
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_10" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
音频与语音
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_10">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
音频与语音
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/01.%20digital%20signal%20processing/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
数字信号处理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/02.%20automatic%20speech%20recognition/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
自动语音识别
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/03.%20text%20to%20speech%20and%20voice/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
语音合成
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/04.%20speaker%20and%20audio%20analysis/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
说话人与音频分析
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/05.%20source%20separation%20and%20noise/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
源分离与降噪
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_11" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
多模态学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
多模态学习
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/01.%20multimodal%20representations/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
多模态表征
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/02.%20vision%20language%20models/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
视觉语言模型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/03.%20image%20and%20video%20tokenisation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图像与视频 Token 化
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/04.%20cross-modal%20generation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
跨模态生成
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/05.%20unified%20multimodal%20architectures/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
统一多模态架构
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_12" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
自主系统
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_12">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
自主系统
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/01.%20perception/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
感知
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/02.%20robot%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
机器人学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/03.%20vision-language-action%20models/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
视觉-语言-动作模型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/04.%20self-driving/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
自动驾驶
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/05.%20space%20and%20extreme%20robotics/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
太空与极端机器人
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_13" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_13" id="__nav_13_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图神经网络
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_13">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
图神经网络
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/01.%20geometric%20deep%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
几何深度学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/02.%20graph%20theory/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图论
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/03.%20graph%20neural%20networks/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图神经网络
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/04.%20graph%20attention%20networks/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图注意力网络
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/05.%203d%20graph%20networks/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
3D 图网络
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_14" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_14" id="__nav_14_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
计算机与操作系统
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_14">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
计算机与操作系统
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/01.%20discrete%20maths/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
离散数学
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/02.%20computer%20architecture/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
计算机体系结构
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/03.%20operating%20systems/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
操作系统
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/04.%20concurrency%20and%20parallelism/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
并发与并行
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/05.%20programming%20languages/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
编程语言
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_15" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_15" id="__nav_15_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
数据结构与算法
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_15">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
数据结构与算法
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/00.%20foundations/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/01.%20arrays%20and%20hashing/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
数组与哈希
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/02.%20linked%20lists%2C%20stacks%2C%20and%20queues/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
链表、栈与队列
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/03.%20trees/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
树
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/04.%20graphs/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/05.%20sorting%20and%20search/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
排序与搜索
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_16" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_16" id="__nav_16_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
生产级软件工程
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_16">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
生产级软件工程
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/01.%20linux%20and%20CMD/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Linux 与命令行
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/02.%20git%20and%20repository%20management/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Git 与仓库管理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/03.%20codebase%20design/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
代码设计
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/04.%20testing%20and%20quality%20assurance/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
测试与质量保障
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/05.%20deployment%20and%20devops/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
部署与 DevOps
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_17" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_17" id="__nav_17_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
SIMD 与 GPU 编程
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_17">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
SIMD 与 GPU 编程
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/00.%20why%20C%2B%2B%20and%20how%20ML%20frameworks%20work/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
为什么是 C++ 及 ML 框架原理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/01.%20hardware%20fundamentals/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
硬件基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/02.%20ARM%20and%20NEON/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ARM 与 NEON
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/03.%20x86%20and%20AVX/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
x86 与 AVX
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/04.%20GPU%20architecture%20and%20CUDA/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
GPU 架构与 CUDA
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/05.%20triton%2C%20TPUs%20and%20pallax/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Triton、TPU 与 Pallas
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/06.%20RISC-V%20and%20embedded%20systems/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
RISC-V 与嵌入式系统
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/07.%20vulkan%20compute%20and%20cross-platform%20GPU/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Vulkan Compute 与跨平台 GPU
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_18" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_18" id="__nav_18_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
AI 推理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_18">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
AI 推理
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2017%3A%20AI%20inference/01.%20quantisation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
量化
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2017%3A%20AI%20inference/02.%20efficient%20architectures/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
高效架构
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2017%3A%20AI%20inference/03.%20serving%20and%20batching/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
服务与批处理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2017%3A%20AI%20inference/04.%20edge%20inference/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
边缘推理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2017%3A%20AI%20inference/05.%20scaling%20and%20deployment/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
扩缩与部署
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_19" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_19" id="__nav_19_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ML 系统设计
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_19">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
ML 系统设计
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2018%3A%20ML%20systems%20design/01.%20systems%20design%20fundamentals/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
系统设计基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2018%3A%20ML%20systems%20design/02.%20cloud%20computing/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
云计算
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2018%3A%20ML%20systems%20design/03.%20large%20scale%20infrastructure/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
大规模基础设施
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2018%3A%20ML%20systems%20design/04.%20ML%20systems%20design/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ML 系统设计
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2018%3A%20ML%20systems%20design/05.%20ML%20design%20examples/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ML 设计案例
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_20" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_20" id="__nav_20_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
应用 AI
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_20_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_20">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
应用 AI
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/01.%20AI%20for%20finance/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
AI 金融
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/02.%20protein%20design/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
蛋白质设计
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/03.%20drug%20discovery/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
药物发现
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/04.%20agentic%20systems/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
智能体系统
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/05.%20healthcare/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
医疗健康
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_21" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_21" id="__nav_21_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
前沿 AI
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_21_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_21">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
前沿 AI
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/01.%20quantum%20machine%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
量子机器学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/02.%20neuromorphic%20computing/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
神经形态计算
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/03.%20datacentres%20in%20space/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
太空数据中心
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/04.%20decentralised%20AI/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
去中心化 AI
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/05.%20brain%20machine%20interfaces/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
脑机接口
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
|
||
<div class="md-sidebar__scrollwrap">
|
||
<div class="md-sidebar__inner">
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="目录">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
目录
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#colab-notebook" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
编码任务（使用 CoLab 或 notebook）
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-content" data-md-component="content">
|
||
|
||
<article class="md-content__inner md-typeset">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<h1 id="_1">图像基础<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
|
||
<p><em>图像基础解释数字图像在被任何模型处理之前如何表示、形成和预处理。本文涵盖像素、色彩空间（RGB、HSV、YCbCr、LAB）、针孔相机模型、卷积、边缘检测（Sobel、Canny）、直方图以及特征描述子（SIFT、ORB），是底层视觉的工具包。</em></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>数字图像</strong>是一个二维数字网格。网格中的每个单元格是一个<strong>像素</strong>（图像元素），其值表示强度或颜色。灰度图像是一个单一的二维矩阵，其中每个像素包含一个亮度值，对于 8 位图像，通常范围从 0（黑色）到 255（白色）。</p>
|
||
</li>
|
||
<li>
|
||
<p>彩色图像将此扩展到三个通道。在 <strong>RGB</strong> 色彩空间中，每个像素存储三个值：红色、绿色和蓝色的强度。</p>
|
||
</li>
|
||
<li>
|
||
<p>彩色图像是一个形状为 (高度, 宽度, 3) 的三维张量（矩阵）。以不同强度混合这三个通道可以产生完整的可见光谱。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="彩色图像分解为红、绿、蓝三个通道，每个通道显示为灰度强度图" src="../../images/rgb_channels.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>位深度</strong>决定每个通道可以表示的离散强度级别数量。</p>
|
||
</li>
|
||
<li>
|
||
<p>8 位图像每个通道有 <span class="arithmatex">\(2^8 = 256\)</span> 个级别，总共 <span class="arithmatex">\(256^3 \approx 1670\)</span> 万种可能的颜色。16 位图像每个通道有 65,536 个级别，用于医学成像和高动态范围摄影等对精细强度差异敏感的场景。</p>
|
||
</li>
|
||
<li>
|
||
<p>RGB 便于显示，但其他色彩空间更适合不同的任务。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>HSV</strong>（色调、饱和度、明度）将颜色信息与亮度分离。色调是纯色（在色环上 0-360 度），饱和度是颜色的鲜艳程度（0 = 灰色，1 = 纯色），明度是亮度。HSV 适合基于颜色的分割，因为你可以仅根据色调设定阈值，而无需考虑光照条件。在 HSV 中检测"红色物体"比在 RGB 中容易得多。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>YCbCr</strong> 将亮度（Y，感知亮度）与色度（Cb、Cr，颜色差异信号）分离。这是 JPEG 压缩和视频编解码器中使用的色彩空间。人眼对亮度比对颜色更敏感，因此色度可以以较低分辨率存储（色度子采样）而几乎不产生感知损失。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>LAB</strong>（CIELAB）的设计目标是使两种颜色之间的数值距离对应于感知差异。在 LAB 空间中相等的步长对人眼观察者来说看起来也是相等的。L 通道是明度，A 从绿色到红色，B 从蓝色到黄色。当需要感知均匀的颜色比较时，使用 LAB。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>图像形成</strong>描述三维场景如何变成二维图像。最简单的模型是<strong>针孔相机</strong>：来自场景的光线通过一个小孔投射到其后的传感器平面上。世界坐标系中的点 <span class="arithmatex">\((X, Y, Z)\)</span> 投影到像素坐标 <span class="arithmatex">\((u, v)\)</span>：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[
|
||
\begin{bmatrix} u \\ v \\ 1 \end{bmatrix} = \frac{1}{Z} \begin{bmatrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} X \\ Y \\ Z \end{bmatrix}
|
||
\]</div>
|
||
<ul>
|
||
<li>这个 3x3 矩阵是<strong>内参矩阵</strong> <span class="arithmatex">\(K\)</span>。它编码了相机的内部属性：焦距 <span class="arithmatex">\(f_x, f_y\)</span>（透镜会聚光线的强度）和主点 <span class="arithmatex">\((c_x, c_y)\)</span>（光轴与传感器的交点，通常靠近图像中心）。对于给定的相机和镜头组合，这些参数是固定的。</li>
|
||
</ul>
|
||
<p><img alt="针孔相机模型：三维点通过光学中心投影到图像平面上，标注了焦距和主点" src="../../images/pinhole_camera.svg" /></p>
|
||
<ul>
|
||
<li><strong>外参</strong>描述相机在世界中的位置：一个旋转矩阵 <span class="arithmatex">\(R\)</span>（3x3，来自第 02 章）和一个平移向量 <span class="arithmatex">\(t\)</span>（3x1）。它们共同将世界坐标转换为相机坐标。完整的投影是：</li>
|
||
</ul>
|
||
<div class="arithmatex">\[\mathbf{p} = K [R \mid t] \mathbf{P}\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>其中 <span class="arithmatex">\(\mathbf{P} = [X, Y, Z, 1]^T\)</span> 是齐次坐标下的三维点，<span class="arithmatex">\(\mathbf{p} = [u, v, 1]^T\)</span> 是投影后的像素。<span class="arithmatex">\([R \mid t]\)</span> 矩阵是 3x4，将旋转和平移并排放置。这全是第 02 章中的线性代数。</p>
|
||
</li>
|
||
<li>
|
||
<p>真实镜头会引入<strong>畸变</strong>。</p>
|
||
<ul>
|
||
<li><strong>径向畸变</strong>使直线弯曲成曲线（桶形畸变使图像向外凸出；枕形畸变使其向内收缩）。
|
||
<strong>切向畸变</strong>源于镜头未与传感器完全平行。</li>
|
||
</ul>
|
||
</li>
|
||
<li>
|
||
<p>相机标定通过拍摄已知图案（如棋盘格）的图像来估计内参和畸变系数，然后校正（去畸变）图像。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>空间滤波</strong>是经典图像处理的基础。一个<strong>滤波器</strong>（或卷积核）是一个小矩阵（通常为 3x3 或 5x5），它在图像上滑动。在每个位置，滤波器的值与重叠的图像块逐元素相乘并求和，产生一个输出像素。这就是<strong>二维卷积</strong>，与驱动 CNN（文件 02）的运算相同，但这里的滤波器权重是手工设计而非学习得到的。</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[(\text{图像} * K)[i,j] = \sum_{m} \sum_{n} \text{图像}[i+m, j+n] \cdot K[m, n]\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>这是第 06 章中一维卷积的二维扩展。滤波器决定了该运算检测的内容：不同的滤波器检测不同的特征。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>模糊</strong>通过对相邻像素取平均来平滑图像。<strong>盒式滤波器</strong>对所有相邻像素赋予相同的权重。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>高斯滤波器</strong>通过二维高斯函数（第 05 章）对相邻像素加权，给相邻像素更大的权重，给远处的像素更小的权重。高斯模糊是最常见的平滑操作，由 <span class="arithmatex">\(\sigma\)</span> 参数化：<span class="arithmatex">\(\sigma\)</span> 越大，平滑程度越高。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>中值滤波</strong>用邻域的中值代替每个像素，而非加权平均。它在去除椒盐噪声（随机的黑白像素）方面特别有效，同时保留边缘，因为中值对异常值具有鲁棒性（如第 04 章所讨论的）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>边缘检测</strong>识别像素强度急剧变化的边界。边缘承载了图像中的大部分结构信息；仅凭边缘就可以识别物体。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>Sobel 算子</strong>使用两个 3x3 滤波器来估计水平方向和垂直方向的梯度：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[
|
||
G_x = \begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{bmatrix}, \quad G_y = \begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{bmatrix}
|
||
\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>将图像与 <span class="arithmatex">\(G_x\)</span> 卷积得到水平梯度（对垂直边缘响应强烈），与 <span class="arithmatex">\(G_y\)</span> 卷积得到垂直梯度（对水平边缘响应强烈）。</p>
|
||
</li>
|
||
<li>
|
||
<p>梯度幅值 <span class="arithmatex">\(\sqrt{G_x^2 + G_y^2}\)</span> 和方向 <span class="arithmatex">\(\arctan(G_y / G_x)\)</span> 共同描述每个像素处的边缘强度和方向。这是第 03 章中梯度在图像域的对应概念。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="原始图像、Sobel 水平梯度、Sobel 垂直梯度和组合边缘幅值" src="../../images/sobel_edges.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>Canny 边缘检测器</strong>是边缘检测的黄金标准。它包含四个步骤：</p>
|
||
<ol>
|
||
<li>使用高斯滤波器平滑图像以减少噪声</li>
|
||
<li>计算梯度幅值和方向（使用 Sobel）</li>
|
||
<li><strong>非极大值抑制</strong>：仅保留沿梯度方向为局部最大值的像素，细化边缘</li>
|
||
<li><strong>滞后阈值处理</strong>：使用两个阈值（高阈值和低阈值）。高于高阈值的像素是确定边缘。介于两个阈值之间的像素仅当连接到确定边缘时才被视为边缘。低于低阈值的像素被舍弃。</li>
|
||
</ol>
|
||
</li>
|
||
<li>
|
||
<p>Canny 中的双阈值使其比单阈值更鲁棒：强边缘始终被保留，弱边缘仅当属于连续边缘结构时才被保留。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>频域</strong>分析揭示了在空间域难以看到的模式。<strong>二维傅里叶变换</strong>（扩展自第 03 章的一维版本）将图像分解为不同频率和方向的正弦模式之和：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[F(u, v) = \sum_{x=0}^{M-1} \sum_{y=0}^{N-1} f(x, y) \cdot e^{-j2\pi(ux/M + vy/N)}\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>低频对应平滑、缓慢变化的区域（天空、墙壁）。高频对应锐利变化（边缘、纹理、噪声）。<strong>幅度谱</strong>显示每个频率上存在多少能量，<strong>相位谱</strong>编码了空间排列信息。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>低通滤波</strong>去除高频，从而平滑图像（相当于空间域的高斯模糊）。<strong>高通滤波</strong>去除低频，从而强调边缘和细节。<strong>带通滤波</strong>只保留一定范围的频率，用于纹理分析。</p>
|
||
</li>
|
||
<li>
|
||
<p>在实践中，对于大尺寸滤波器，频域滤波可能比空间卷积更快，因为空间域中的卷积等价于频域中的逐元素乘法（<strong>卷积定理</strong>）。这直接联系到第 03 章中的傅里叶变换性质。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>直方图</strong>总结像素强度的分布。直方图统计每个强度值有多少像素（对于 8 位图像为 0-255）。这是第 04 章中的频率分布应用于像素值。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="图像及其强度直方图：暗图像的直方图偏左，亮图像的直方图偏右" src="../../images/image_histogram.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p>暗图像的直方图集中在左侧（低值）。亮图像的直方图集中在右侧。低对比度图像的直方图狭窄。高对比度图像的直方图宽而分散。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>直方图均衡化</strong>将直方图拉伸以覆盖整个强度范围，从而改善对比度。其思路是找到一个映射，使像素强度的累积分布函数（CDF）近似为线性。这是第 04 章中 CDF 概念的直接应用。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>Otsu 方法</strong>自动找到将图像分割为前景和背景的最佳阈值。它尝试每个可能的阈值，并选择使类内方差最小（或等价地，使类间方差最大）的阈值。这是第 04 章中方差概念应用于像素强度群体的体现。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>特征提取</strong>识别图像中可用于匹配、识别和三维重建的独特点或区域。好的特征应具有可重复性（在不同视角下能被再次找到）、独特性（可与其他特征区分）和计算高效性。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>角点检测</strong>寻找图像强度在多个方向上显著变化的点。平滑区域在任何方向上的变化都很小。边缘在一个方向上有变化。角点在至少两个方向上都有变化，使其在局部是唯一的，因此是可靠的标志点。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>Harris 角点检测器</strong>分析每个像素处的<strong>结构张量</strong>（也称为二阶矩矩阵）：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[
|
||
M = \sum_{(x,y) \in W} w(x,y) \begin{bmatrix} I_x^2 & I_x I_y \\ I_x I_y & I_y^2 \end{bmatrix}
|
||
\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>其中 <span class="arithmatex">\(I_x\)</span> 和 <span class="arithmatex">\(I_y\)</span> 是图像梯度（使用 Sobel 计算），<span class="arithmatex">\(W\)</span> 是局部窗口，<span class="arithmatex">\(w\)</span> 是高斯加权函数。<span class="arithmatex">\(M\)</span> 的特征值（来自第 02 章）告诉你特征的类型：</p>
|
||
<ul>
|
||
<li>两个特征值都很小：平坦区域（无特征）</li>
|
||
<li>一个很大，一个很小：边缘</li>
|
||
<li>两个都很大：角点</li>
|
||
</ul>
|
||
</li>
|
||
<li>
|
||
<p>Harris 不显式计算特征值，而是使用角点响应函数：<span class="arithmatex">\(R = \det(M) - k \cdot (\text{tr}(M))^2\)</span>，其中 <span class="arithmatex">\(\det(M) = \lambda_1 \lambda_2\)</span> 且 <span class="arithmatex">\(\text{tr}(M) = \lambda_1 + \lambda_2\)</span>（均来自第 02 章）。<span class="arithmatex">\(R\)</span> 为正且较大时表示角点。常数 <span class="arithmatex">\(k\)</span> 通常为 0.04-0.06。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>Shi-Tomasi</strong> 检测器将其简化为 <span class="arithmatex">\(R = \min(\lambda_1, \lambda_2)\)</span>，直接检查较小的特征值是否足够大。这在实际中稍微更稳定。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>斑点检测</strong>寻找与周围环境不同的区域。与角点（属于点特征）不同，斑点具有特征尺寸。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>SIFT</strong>（尺度不变特征变换，Lowe，2004）在多个尺度上检测斑点，并构建对旋转、尺度具有不变性，对光照变化具有部分不变性的描述子。它的工作原理是：</p>
|
||
<ol>
|
||
<li>使用逐渐增大 <span class="arithmatex">\(\sigma\)</span> 的高斯模糊构建<strong>尺度空间</strong>（见下文）</li>
|
||
<li>在尺度间的 Gaussian 差分（DoG）中寻找极值点</li>
|
||
<li>精炼关键点位置，去除低对比度点和边缘响应</li>
|
||
<li>基于局部梯度方向分配主方向</li>
|
||
<li>从关键点周围 16x16 块中的梯度直方图构建 128 维描述子</li>
|
||
</ol>
|
||
</li>
|
||
<li>
|
||
<p><strong>SURF</strong>（加速稳健特征）使用盒式滤波器和积分图像近似 SIFT 以实现更快的计算。<strong>ORB</strong>（定向 FAST 和旋转 BRIEF）是一个快速、开源的替代方案，它将 FAST 角点检测器与 BRIEF 二进制描述子结合，并增加了旋转不变性。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>HOG</strong>（方向梯度直方图）描述子将图像划分为小单元格，计算每个单元格内梯度方向的直方图，并在单元格块间进行归一化。HOG 捕捉边缘方向的分布，这对物体形状具有高度信息量。在深度学习之前，HOG + SVM（第 06 章）是行人检测和物体识别的主流方法。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>图像金字塔</strong>以多种分辨率表示图像。</p>
|
||
<ul>
|
||
<li><strong>高斯金字塔</strong>通过重复模糊和下采样（分辨率减半）构建。每一层都是原始图像的粗略版本。</li>
|
||
<li><strong>拉普拉斯金字塔</strong>存储连续高斯层之间的差异，捕捉每一步下采样丢失的细节。拉普拉斯金字塔是可逆的：你可以从中重建原始图像。</li>
|
||
</ul>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="高斯金字塔：原始图像为全分辨率，然后每层逐步缩小为一半分辨率" src="../../images/image_pyramid.svg" /></p>
|
||
<ul>
|
||
<li><strong>尺度空间</strong>形式化了物体存在于不同尺度这一概念。一棵树是一个大斑点；树上的一片叶子是一个小斑点。要同时检测两者，你需要跨尺度搜索。图像的尺度空间是通过将图像与逐渐增大 <span class="arithmatex">\(\sigma\)</span> 的高斯函数卷积得到的图像族：</li>
|
||
</ul>
|
||
<div class="arithmatex">\[L(x, y, \sigma) = G(x, y, \sigma) * I(x, y)\]</div>
|
||
<ul>
|
||
<li>其中 <span class="arithmatex">\(G\)</span> 是标准差为 <span class="arithmatex">\(\sigma\)</span> 的二维高斯函数。跨多个尺度持续存在的特征更有可能是有意义的结构而非噪声。尺度空间是 SIFT 的理论基础，也是贯穿现代计算机视觉的多尺度处理的基础，包括目标检测中的特征金字塔网络（文件 03）。</li>
|
||
</ul>
|
||
<h2 id="colab-notebook">编码任务（使用 CoLab 或 notebook）<a class="headerlink" href="#colab-notebook" title="Permanent link">¶</a></h2>
|
||
<ol>
|
||
<li>
|
||
<p>加载图像，将其转换为不同的色彩空间（RGB、HSV、LAB），并可视化各个通道。观察颜色信息在不同空间中的分布差异。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="kn">from</span><span class="w"> </span><span class="nn">PIL</span><span class="w"> </span><span class="kn">import</span> <span class="n">Image</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="c1"># Create a synthetic test image with distinct colours</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">H</span><span class="p">,</span> <span class="n">W</span> <span class="o">=</span> <span class="mi">128</span><span class="p">,</span> <span class="mi">256</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">img</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">H</span><span class="p">,</span> <span class="n">W</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">)</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">img</span><span class="p">[:,</span> <span class="p">:</span><span class="mi">64</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">255</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">50</span><span class="p">]</span> <span class="c1"># red</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">img</span><span class="p">[:,</span> <span class="mi">64</span><span class="p">:</span><span class="mi">128</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">50</span><span class="p">,</span> <span class="mi">255</span><span class="p">,</span> <span class="mi">50</span><span class="p">]</span> <span class="c1"># green</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="n">img</span><span class="p">[:,</span> <span class="mi">128</span><span class="p">:</span><span class="mi">192</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">50</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">255</span><span class="p">]</span> <span class="c1"># blue</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="n">img</span><span class="p">[:,</span> <span class="mi">192</span><span class="p">:]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">255</span><span class="p">,</span> <span class="mi">255</span><span class="p">,</span> <span class="mi">50</span><span class="p">]</span> <span class="c1"># yellow</span>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="c1"># Add a brightness gradient</span>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">H</span><span class="p">):</span>
|
||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a> <span class="n">scale</span> <span class="o">=</span> <span class="mf">0.3</span> <span class="o">+</span> <span class="mf">0.7</span> <span class="o">*</span> <span class="n">y</span> <span class="o">/</span> <span class="n">H</span>
|
||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a> <span class="n">img</span><span class="p">[</span><span class="n">y</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">img</span><span class="p">[</span><span class="n">y</span><span class="p">]</span> <span class="o">*</span> <span class="n">scale</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">)</span>
|
||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>
|
||
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="n">img_jnp</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> <span class="o">/</span> <span class="mf">255.0</span>
|
||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>
|
||
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># Manual RGB to HSV conversion</span>
|
||
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">rgb_to_hsv</span><span class="p">(</span><span class="n">rgb</span><span class="p">):</span>
|
||
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a> <span class="n">r</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">rgb</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">rgb</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">rgb</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>
|
||
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a> <span class="n">maxc</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">rgb</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a> <span class="n">minc</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">rgb</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a> <span class="n">diff</span> <span class="o">=</span> <span class="n">maxc</span> <span class="o">-</span> <span class="n">minc</span> <span class="o">+</span> <span class="mf">1e-7</span>
|
||
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>
|
||
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a> <span class="c1"># Hue</span>
|
||
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a> <span class="n">h</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">maxc</span> <span class="o">==</span> <span class="n">minc</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a> <span class="n">jnp</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">maxc</span> <span class="o">==</span> <span class="n">r</span><span class="p">,</span> <span class="mi">60</span> <span class="o">*</span> <span class="p">((</span><span class="n">g</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span> <span class="o">/</span> <span class="n">diff</span> <span class="o">%</span> <span class="mi">6</span><span class="p">),</span>
|
||
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a> <span class="n">jnp</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">maxc</span> <span class="o">==</span> <span class="n">g</span><span class="p">,</span> <span class="mi">60</span> <span class="o">*</span> <span class="p">((</span><span class="n">b</span> <span class="o">-</span> <span class="n">r</span><span class="p">)</span> <span class="o">/</span> <span class="n">diff</span> <span class="o">+</span> <span class="mi">2</span><span class="p">),</span>
|
||
<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a> <span class="mi">60</span> <span class="o">*</span> <span class="p">((</span><span class="n">r</span> <span class="o">-</span> <span class="n">g</span><span class="p">)</span> <span class="o">/</span> <span class="n">diff</span> <span class="o">+</span> <span class="mi">4</span><span class="p">))))</span>
|
||
<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a> <span class="n">s</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">maxc</span> <span class="o"><</span> <span class="mf">1e-7</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="n">diff</span> <span class="o">/</span> <span class="n">maxc</span><span class="p">)</span>
|
||
<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a> <span class="n">v</span> <span class="o">=</span> <span class="n">maxc</span>
|
||
<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a> <span class="k">return</span> <span class="n">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">([</span><span class="n">h</span> <span class="o">/</span> <span class="mi">360</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">v</span><span class="p">],</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>
|
||
<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a><span class="n">hsv</span> <span class="o">=</span> <span class="n">rgb_to_hsv</span><span class="p">(</span><span class="n">img_jnp</span><span class="p">)</span>
|
||
<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>
|
||
<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a><span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
|
||
<a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a><span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="p">(</span><span class="n">ch</span><span class="p">,</span> <span class="n">name</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">zip</span><span class="p">([</span><span class="n">img_jnp</span><span class="p">[</span><span class="o">...</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="n">img_jnp</span><span class="p">[</span><span class="o">...</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="n">img_jnp</span><span class="p">[</span><span class="o">...</span><span class="p">,</span><span class="mi">2</span><span class="p">]],</span>
|
||
<a id="__codelineno-0-41" name="__codelineno-0-41" href="#__codelineno-0-41"></a> <span class="p">[</span><span class="s1">'Red'</span><span class="p">,</span> <span class="s1">'Green'</span><span class="p">,</span> <span class="s1">'Blue'</span><span class="p">])):</span>
|
||
<a id="__codelineno-0-42" name="__codelineno-0-42" href="#__codelineno-0-42"></a> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">ch</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-0-43" name="__codelineno-0-43" href="#__codelineno-0-43"></a> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s1">'RGB: </span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="s1">'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
|
||
<a id="__codelineno-0-44" name="__codelineno-0-44" href="#__codelineno-0-44"></a>
|
||
<a id="__codelineno-0-45" name="__codelineno-0-45" href="#__codelineno-0-45"></a><span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="p">(</span><span class="n">ch</span><span class="p">,</span> <span class="n">name</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">zip</span><span class="p">([</span><span class="n">hsv</span><span class="p">[</span><span class="o">...</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="n">hsv</span><span class="p">[</span><span class="o">...</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="n">hsv</span><span class="p">[</span><span class="o">...</span><span class="p">,</span><span class="mi">2</span><span class="p">]],</span>
|
||
<a id="__codelineno-0-46" name="__codelineno-0-46" href="#__codelineno-0-46"></a> <span class="p">[</span><span class="s1">'Hue'</span><span class="p">,</span> <span class="s1">'Saturation'</span><span class="p">,</span> <span class="s1">'Value'</span><span class="p">])):</span>
|
||
<a id="__codelineno-0-47" name="__codelineno-0-47" href="#__codelineno-0-47"></a> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">ch</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-0-48" name="__codelineno-0-48" href="#__codelineno-0-48"></a> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s1">'HSV: </span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="s1">'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
|
||
<a id="__codelineno-0-49" name="__codelineno-0-49" href="#__codelineno-0-49"></a>
|
||
<a id="__codelineno-0-50" name="__codelineno-0-50" href="#__codelineno-0-50"></a><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s1">'RGB vs HSV Channels'</span><span class="p">)</span>
|
||
<a id="__codelineno-0-51" name="__codelineno-0-51" href="#__codelineno-0-51"></a><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">();</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>使用二维卷积从头实现 Sobel 边缘检测和高斯模糊。将其应用于图像并比较结果。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">conv2d</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="n">kernel</span><span class="p">):</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="sd">"""2D convolution (valid mode) from scratch."""</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a> <span class="n">H</span><span class="p">,</span> <span class="n">W</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a> <span class="n">kH</span><span class="p">,</span> <span class="n">kW</span> <span class="o">=</span> <span class="n">kernel</span><span class="o">.</span><span class="n">shape</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a> <span class="n">out_h</span><span class="p">,</span> <span class="n">out_w</span> <span class="o">=</span> <span class="n">H</span> <span class="o">-</span> <span class="n">kH</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">W</span> <span class="o">-</span> <span class="n">kW</span> <span class="o">+</span> <span class="mi">1</span>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a> <span class="n">output</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">out_h</span><span class="p">,</span> <span class="n">out_w</span><span class="p">))</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">out_h</span><span class="p">):</span>
|
||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">out_w</span><span class="p">):</span>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a> <span class="n">patch</span> <span class="o">=</span> <span class="n">image</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">kH</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span><span class="n">j</span><span class="o">+</span><span class="n">kW</span><span class="p">]</span>
|
||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a> <span class="n">output</span> <span class="o">=</span> <span class="n">output</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">patch</span> <span class="o">*</span> <span class="n">kernel</span><span class="p">))</span>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a> <span class="k">return</span> <span class="n">output</span>
|
||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
|
||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="c1"># Create a test image: white rectangle on dark background</span>
|
||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="n">img</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">64</span><span class="p">,</span> <span class="mi">64</span><span class="p">))</span>
|
||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">img</span> <span class="o">=</span> <span class="n">img</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="mi">15</span><span class="p">:</span><span class="mi">50</span><span class="p">,</span> <span class="mi">20</span><span class="p">:</span><span class="mi">45</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)</span>
|
||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="c1"># Add some noise</span>
|
||
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="n">key</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
|
||
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="n">img</span> <span class="o">=</span> <span class="n">img</span> <span class="o">+</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">img</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="o">*</span> <span class="mf">0.05</span>
|
||
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a>
|
||
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="c1"># Sobel filters</span>
|
||
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="n">sobel_x</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
|
||
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="n">sobel_y</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">]],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
|
||
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>
|
||
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="c1"># Gaussian blur kernel (5x5, sigma=1)</span>
|
||
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="n">ax</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
|
||
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">ax</span><span class="p">)</span>
|
||
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="n">gaussian</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">xx</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">yy</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="mf">1.0</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span>
|
||
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="n">gaussian</span> <span class="o">=</span> <span class="n">gaussian</span> <span class="o">/</span> <span class="n">gaussian</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
|
||
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a>
|
||
<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="c1"># Apply filters</span>
|
||
<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="n">gx</span> <span class="o">=</span> <span class="n">conv2d</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">sobel_x</span><span class="p">)</span>
|
||
<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="n">gy</span> <span class="o">=</span> <span class="n">conv2d</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">sobel_y</span><span class="p">)</span>
|
||
<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="n">edges</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">gx</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">gy</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
|
||
<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="n">blurred</span> <span class="o">=</span> <span class="n">conv2d</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">gaussian</span><span class="p">)</span>
|
||
<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a>
|
||
<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a><span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
|
||
<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="k">for</span> <span class="n">ax</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="n">title</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">axes</span><span class="p">,</span>
|
||
<a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a> <span class="p">[</span><span class="n">img</span><span class="p">,</span> <span class="n">edges</span><span class="p">,</span> <span class="n">blurred</span><span class="p">,</span> <span class="n">gx</span><span class="p">],</span>
|
||
<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a> <span class="p">[</span><span class="s1">'Original'</span><span class="p">,</span> <span class="s1">'Edge Magnitude'</span><span class="p">,</span> <span class="s1">'Gaussian Blur'</span><span class="p">,</span> <span class="s1">'Horizontal Gradient'</span><span class="p">]):</span>
|
||
<a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a> <span class="n">ax</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">)</span>
|
||
<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a> <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">);</span> <span class="n">ax</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
|
||
<a id="__codelineno-1-46" name="__codelineno-1-46" href="#__codelineno-1-46"></a><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">();</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>从头实现直方图均衡化，并将其应用于低对比度灰度图像。比较均衡前后的直方图。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="c1"># Create a low-contrast image (values clustered in a narrow range)</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">key</span> <span class="o">=</span> <span class="nb">__import__</span><span class="p">(</span><span class="s1">'jax'</span><span class="p">)</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">img</span> <span class="o">=</span> <span class="nb">__import__</span><span class="p">(</span><span class="s1">'jax'</span><span class="p">)</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="p">(</span><span class="mi">128</span><span class="p">,</span> <span class="mi">128</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.3</span> <span class="o">+</span> <span class="mf">0.3</span> <span class="c1"># values in [0.3, 0.6]</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">histogram_equalise</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">n_bins</span><span class="o">=</span><span class="mi">256</span><span class="p">):</span>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="sd">"""Histogram equalisation for a grayscale image."""</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a> <span class="c1"># Quantise to bins</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a> <span class="n">bins</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n_bins</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a> <span class="n">hist</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">bins</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a> <span class="c1"># Compute CDF</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a> <span class="n">cdf</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">hist</span><span class="p">)</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a> <span class="n">cdf_normalised</span> <span class="o">=</span> <span class="p">(</span><span class="n">cdf</span> <span class="o">-</span> <span class="n">cdf</span><span class="o">.</span><span class="n">min</span><span class="p">())</span> <span class="o">/</span> <span class="p">(</span><span class="n">cdf</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">-</span> <span class="n">cdf</span><span class="o">.</span><span class="n">min</span><span class="p">())</span>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a> <span class="c1"># Map each pixel through the CDF</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a> <span class="n">indices</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">clip</span><span class="p">((</span><span class="n">img</span> <span class="o">*</span> <span class="n">n_bins</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">int32</span><span class="p">),</span> <span class="mi">0</span><span class="p">,</span> <span class="n">n_bins</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a> <span class="n">equalised</span> <span class="o">=</span> <span class="n">cdf_normalised</span><span class="p">[</span><span class="n">indices</span><span class="p">]</span>
|
||
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a> <span class="k">return</span> <span class="n">equalised</span>
|
||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a>
|
||
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="n">eq_img</span> <span class="o">=</span> <span class="n">histogram_equalise</span><span class="p">(</span><span class="n">img</span><span class="p">)</span>
|
||
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a>
|
||
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
|
||
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">'Original (Low Contrast)'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
|
||
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">eq_img</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">'After Histogram Equalisation'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
|
||
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
|
||
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">img</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">64</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'#3498db'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
|
||
<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">'Histogram Before'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">eq_img</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">64</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'#e74c3c'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
|
||
<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">'Histogram After'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a>
|
||
<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">();</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>从头实现 Harris 角点检测器。在简单图像中检测角点并可视化。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">harris_corners</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">threshold</span><span class="o">=</span><span class="mf">0.01</span><span class="p">):</span>
|
||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="sd">"""Harris corner detection from scratch."""</span>
|
||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a> <span class="c1"># Compute gradients with Sobel</span>
|
||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a> <span class="n">sobel_x</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
|
||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a> <span class="n">sobel_y</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">]],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
|
||
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a>
|
||
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a> <span class="c1"># Pad image for valid convolution to preserve size</span>
|
||
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a> <span class="n">img_pad</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'edge'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a> <span class="n">H</span><span class="p">,</span> <span class="n">W</span> <span class="o">=</span> <span class="n">img</span><span class="o">.</span><span class="n">shape</span>
|
||
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a>
|
||
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a> <span class="n">Ix</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">img</span><span class="p">)</span>
|
||
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a> <span class="n">Iy</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">img</span><span class="p">)</span>
|
||
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">H</span><span class="p">):</span>
|
||
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">W</span><span class="p">):</span>
|
||
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a> <span class="n">patch</span> <span class="o">=</span> <span class="n">img_pad</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="mi">3</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span><span class="n">j</span><span class="o">+</span><span class="mi">3</span><span class="p">]</span>
|
||
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a> <span class="n">Ix</span> <span class="o">=</span> <span class="n">Ix</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">patch</span> <span class="o">*</span> <span class="n">sobel_x</span><span class="p">))</span>
|
||
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a> <span class="n">Iy</span> <span class="o">=</span> <span class="n">Iy</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">patch</span> <span class="o">*</span> <span class="n">sobel_y</span><span class="p">))</span>
|
||
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a>
|
||
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a> <span class="c1"># Structure tensor components</span>
|
||
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a> <span class="n">Ixx</span> <span class="o">=</span> <span class="n">Ix</span> <span class="o">*</span> <span class="n">Ix</span>
|
||
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a> <span class="n">Iyy</span> <span class="o">=</span> <span class="n">Iy</span> <span class="o">*</span> <span class="n">Iy</span>
|
||
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a> <span class="n">Ixy</span> <span class="o">=</span> <span class="n">Ix</span> <span class="o">*</span> <span class="n">Iy</span>
|
||
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a>
|
||
<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a> <span class="c1"># Gaussian smoothing of structure tensor (approximate with window sum)</span>
|
||
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a> <span class="n">w</span> <span class="o">=</span> <span class="mi">3</span> <span class="c1"># window half-size</span>
|
||
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a> <span class="n">R</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">img</span><span class="p">)</span>
|
||
<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a> <span class="n">pad_xx</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">Ixx</span><span class="p">,</span> <span class="n">w</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'constant'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a> <span class="n">pad_yy</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">Iyy</span><span class="p">,</span> <span class="n">w</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'constant'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a> <span class="n">pad_xy</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">Ixy</span><span class="p">,</span> <span class="n">w</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'constant'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a>
|
||
<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">H</span><span class="p">):</span>
|
||
<a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">W</span><span class="p">):</span>
|
||
<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a> <span class="n">sxx</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">pad_xx</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">w</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span><span class="n">j</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">w</span><span class="o">+</span><span class="mi">1</span><span class="p">])</span>
|
||
<a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a> <span class="n">syy</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">pad_yy</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">w</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span><span class="n">j</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">w</span><span class="o">+</span><span class="mi">1</span><span class="p">])</span>
|
||
<a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a> <span class="n">sxy</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">pad_xy</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">w</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span><span class="n">j</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">w</span><span class="o">+</span><span class="mi">1</span><span class="p">])</span>
|
||
<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a> <span class="n">det</span> <span class="o">=</span> <span class="n">sxx</span> <span class="o">*</span> <span class="n">syy</span> <span class="o">-</span> <span class="n">sxy</span> <span class="o">*</span> <span class="n">sxy</span>
|
||
<a id="__codelineno-3-41" name="__codelineno-3-41" href="#__codelineno-3-41"></a> <span class="n">trace</span> <span class="o">=</span> <span class="n">sxx</span> <span class="o">+</span> <span class="n">syy</span>
|
||
<a id="__codelineno-3-42" name="__codelineno-3-42" href="#__codelineno-3-42"></a> <span class="n">R</span> <span class="o">=</span> <span class="n">R</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">det</span> <span class="o">-</span> <span class="n">k</span> <span class="o">*</span> <span class="n">trace</span> <span class="o">*</span> <span class="n">trace</span><span class="p">)</span>
|
||
<a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></a>
|
||
<a id="__codelineno-3-44" name="__codelineno-3-44" href="#__codelineno-3-44"></a> <span class="c1"># Threshold</span>
|
||
<a id="__codelineno-3-45" name="__codelineno-3-45" href="#__codelineno-3-45"></a> <span class="n">corners</span> <span class="o">=</span> <span class="n">R</span> <span class="o">></span> <span class="n">threshold</span> <span class="o">*</span> <span class="n">R</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
|
||
<a id="__codelineno-3-46" name="__codelineno-3-46" href="#__codelineno-3-46"></a> <span class="k">return</span> <span class="n">R</span><span class="p">,</span> <span class="n">corners</span>
|
||
<a id="__codelineno-3-47" name="__codelineno-3-47" href="#__codelineno-3-47"></a>
|
||
<a id="__codelineno-3-48" name="__codelineno-3-48" href="#__codelineno-3-48"></a><span class="c1"># Test image: checkerboard pattern (lots of corners)</span>
|
||
<a id="__codelineno-3-49" name="__codelineno-3-49" href="#__codelineno-3-49"></a><span class="n">block</span> <span class="o">=</span> <span class="mi">16</span>
|
||
<a id="__codelineno-3-50" name="__codelineno-3-50" href="#__codelineno-3-50"></a><span class="n">n</span> <span class="o">=</span> <span class="mi">4</span>
|
||
<a id="__codelineno-3-51" name="__codelineno-3-51" href="#__codelineno-3-51"></a><span class="n">checker</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">block</span> <span class="o">*</span> <span class="n">n</span><span class="p">,</span> <span class="n">block</span> <span class="o">*</span> <span class="n">n</span><span class="p">))</span>
|
||
<a id="__codelineno-3-52" name="__codelineno-3-52" href="#__codelineno-3-52"></a><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-3-53" name="__codelineno-3-53" href="#__codelineno-3-53"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-3-54" name="__codelineno-3-54" href="#__codelineno-3-54"></a> <span class="k">if</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="n">j</span><span class="p">)</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
||
<a id="__codelineno-3-55" name="__codelineno-3-55" href="#__codelineno-3-55"></a> <span class="n">checker</span> <span class="o">=</span> <span class="n">checker</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">block</span><span class="p">:(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">block</span><span class="p">,</span> <span class="n">j</span><span class="o">*</span><span class="n">block</span><span class="p">:(</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">block</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)</span>
|
||
<a id="__codelineno-3-56" name="__codelineno-3-56" href="#__codelineno-3-56"></a>
|
||
<a id="__codelineno-3-57" name="__codelineno-3-57" href="#__codelineno-3-57"></a><span class="n">R</span><span class="p">,</span> <span class="n">corners</span> <span class="o">=</span> <span class="n">harris_corners</span><span class="p">(</span><span class="n">checker</span><span class="p">)</span>
|
||
<a id="__codelineno-3-58" name="__codelineno-3-58" href="#__codelineno-3-58"></a><span class="n">cy</span><span class="p">,</span> <span class="n">cx</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">corners</span><span class="p">)</span>
|
||
<a id="__codelineno-3-59" name="__codelineno-3-59" href="#__codelineno-3-59"></a>
|
||
<a id="__codelineno-3-60" name="__codelineno-3-60" href="#__codelineno-3-60"></a><span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
|
||
<a id="__codelineno-3-61" name="__codelineno-3-61" href="#__codelineno-3-61"></a><span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">checker</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-62" name="__codelineno-3-62" href="#__codelineno-3-62"></a><span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">'Checkerboard'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-63" name="__codelineno-3-63" href="#__codelineno-3-63"></a><span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">R</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'hot'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-64" name="__codelineno-3-64" href="#__codelineno-3-64"></a><span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">'Harris Response'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-65" name="__codelineno-3-65" href="#__codelineno-3-65"></a><span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">checker</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-66" name="__codelineno-3-66" href="#__codelineno-3-66"></a><span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">cx</span><span class="p">,</span> <span class="n">cy</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'#e74c3c'</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">'x'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-67" name="__codelineno-3-67" href="#__codelineno-3-67"></a><span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s1">'Detected Corners (</span><span class="si">{</span><span class="nb">len</span><span class="p">(</span><span class="n">cx</span><span class="p">)</span><span class="si">}</span><span class="s1">)'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-68" name="__codelineno-3-68" href="#__codelineno-3-68"></a><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">();</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
</ol>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
</article>
|
||
</div>
|
||
|
||
|
||
<script>var target=document.getElementById(location.hash.slice(1));target&&target.name&&(target.checked=target.name.startsWith("__tabbed_"))</script>
|
||
</div>
|
||
|
||
<button type="button" class="md-top md-icon" data-md-component="top" hidden>
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 20h-2V8l-5.5 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8z"/></svg>
|
||
回到页面顶部
|
||
</button>
|
||
|
||
</main>
|
||
|
||
<footer class="md-footer">
|
||
|
||
|
||
|
||
<nav class="md-footer__inner md-grid" aria-label="页脚" >
|
||
|
||
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/05.%20advanced%20text%20generation/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 高级文本生成">
|
||
<div class="md-footer__button md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
|
||
</div>
|
||
<div class="md-footer__title">
|
||
<span class="md-footer__direction">
|
||
上一页
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
高级文本生成
|
||
</div>
|
||
</div>
|
||
</a>
|
||
|
||
|
||
|
||
<a href="../02.%20convolutional%20networks/" class="md-footer__link md-footer__link--next" aria-label="下一页: 卷积网络">
|
||
<div class="md-footer__title">
|
||
<span class="md-footer__direction">
|
||
下一页
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
卷积网络
|
||
</div>
|
||
</div>
|
||
<div class="md-footer__button md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11z"/></svg>
|
||
</div>
|
||
</a>
|
||
|
||
</nav>
|
||
|
||
|
||
<div class="md-footer-meta md-typeset">
|
||
<div class="md-footer-meta__inner md-grid">
|
||
<div class="md-copyright">
|
||
|
||
|
||
Made with
|
||
<a href="https://squidfunk.github.io/mkdocs-material/" target="_blank" rel="noopener">
|
||
Material for MkDocs
|
||
</a>
|
||
|
||
</div>
|
||
|
||
|
||
<div class="md-social">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<a href="https://github.com/flykhan/maths-cs-ai-compendium-zh" target="_blank" rel="noopener" title="github.com" class="md-social__link">
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
|
||
</a>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
</div>
|
||
</footer>
|
||
|
||
</div>
|
||
<div class="md-dialog" data-md-component="dialog">
|
||
<div class="md-dialog__inner md-typeset"></div>
|
||
</div>
|
||
|
||
|
||
|
||
|
||
|
||
<script id="__config" type="application/json">{"annotate": null, "base": "../..", "features": ["navigation.tabs", "navigation.sections", "navigation.expand", "navigation.top", "navigation.footer", "search.suggest", "search.highlight", "content.code.copy", "toc.follow"], "search": "../../assets/javascripts/workers/search.2c215733.min.js", "tags": null, "translations": {"clipboard.copied": "\u5df2\u590d\u5236", "clipboard.copy": "\u590d\u5236", "search.result.more.one": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.more.other": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 # \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.none": "\u6ca1\u6709\u627e\u5230\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.one": "\u627e\u5230 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.other": "# \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.placeholder": "\u952e\u5165\u4ee5\u5f00\u59cb\u641c\u7d22", "search.result.term.missing": "\u7f3a\u5c11", "select.version": "\u9009\u62e9\u5f53\u524d\u7248\u672c"}, "version": null}</script>
|
||
|
||
|
||
<script src="../../assets/javascripts/bundle.79ae519e.min.js"></script>
|
||
|
||
<script src="../../javascripts/mathjax.js"></script>
|
||
|
||
<script src="https://unpkg.com/mathjax@3/es5/tex-mml-chtml.js"></script>
|
||
|
||
|
||
</body>
|
||
</html> |