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多模态学习
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统计学
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抽样
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推断
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概率论
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计数
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</a>
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概率概念
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分布
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</span>
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</a>
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贝叶斯
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</span>
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</a>
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信息论
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</span>
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机器学习
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</span>
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<span class="md-nav__icon md-icon"></span>
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机器学习
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经典机器学习
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梯度机器学习
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</span>
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</a>
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深度学习
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</span>
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</a>
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强化学习
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</span>
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</a>
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分布式深度学习
|
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</span>
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|
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|
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|
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</a>
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计算语言学
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<span class="md-nav__icon md-icon"></span>
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计算语言学
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语言学基础
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</a>
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嵌入与序列模型
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</span>
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</a>
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Transformer 与语言模型
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</span>
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|
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</a>
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<span class="md-ellipsis">
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高级文本生成
|
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|
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|
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|
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</span>
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|
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|
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|
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</a>
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计算机视觉
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计算机视觉
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图像基础
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</span>
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</a>
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter%2008%3A%20computer%20vision/02.%20convolutional%20networks/" class="md-nav__link">
|
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<span class="md-ellipsis">
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卷积网络
|
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|
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|
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</span>
|
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|
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|
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</a>
|
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</li>
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<li class="md-nav__item">
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<a href="../../chapter%2008%3A%20computer%20vision/03.%20object%20detection%20and%20segmentation/" class="md-nav__link">
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|
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<span class="md-ellipsis">
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目标检测与分割
|
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|
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|
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</span>
|
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|
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|
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|
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter%2008%3A%20computer%20vision/04.%20vision%20transformers%20and%20generation/" class="md-nav__link">
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<span class="md-ellipsis">
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ViT 与生成模型
|
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</span>
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|
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter%2008%3A%20computer%20vision/05.%20video%20and%203D%20vision/" class="md-nav__link">
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<span class="md-ellipsis">
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视频与 3D 视觉
|
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|
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|
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|
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</span>
|
||
|
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|
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|
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</a>
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</nav>
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<span class="md-ellipsis">
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音频与语音
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</span>
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<span class="md-nav__icon md-icon"></span>
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<span class="md-nav__icon md-icon"></span>
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音频与语音
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter%2009%3A%20audio%20and%20speech/01.%20digital%20signal%20processing/" class="md-nav__link">
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<span class="md-ellipsis">
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数字信号处理
|
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter%2009%3A%20audio%20and%20speech/02.%20automatic%20speech%20recognition/" class="md-nav__link">
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<span class="md-ellipsis">
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自动语音识别
|
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|
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|
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|
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</span>
|
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|
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|
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|
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</a>
|
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</li>
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<li class="md-nav__item">
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<a href="../../chapter%2009%3A%20audio%20and%20speech/03.%20text%20to%20speech%20and%20voice/" class="md-nav__link">
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|
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|
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<span class="md-ellipsis">
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语音合成
|
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|
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|
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|
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</span>
|
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|
||
|
||
|
||
</a>
|
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</li>
|
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<li class="md-nav__item">
|
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<a href="../../chapter%2009%3A%20audio%20and%20speech/04.%20speaker%20and%20audio%20analysis/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
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说话人与音频分析
|
||
|
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|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter%2009%3A%20audio%20and%20speech/05.%20source%20separation%20and%20noise/" class="md-nav__link">
|
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|
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|
||
|
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<span class="md-ellipsis">
|
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|
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|
||
源分离与降噪
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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|
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</ul>
|
||
</nav>
|
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|
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</li>
|
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|
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|
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|
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|
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|
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|
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|
||
|
||
|
||
|
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_11" >
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<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
多模态学习
|
||
|
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|
||
|
||
</span>
|
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|
||
|
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|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_11">
|
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<span class="md-nav__icon md-icon"></span>
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多模态学习
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|
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|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
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<a href="../../chapter%2010%3A%20multimodal%20learning/01.%20multimodal%20representations/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
多模态表征
|
||
|
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|
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|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter%2010%3A%20multimodal%20learning/02.%20vision%20language%20models/" class="md-nav__link">
|
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|
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<span class="md-ellipsis">
|
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|
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|
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视觉语言模型
|
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|
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|
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|
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</span>
|
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|
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|
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|
||
</a>
|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter%2010%3A%20multimodal%20learning/03.%20image%20and%20video%20tokenisation/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
图像与视频 Token 化
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter%2010%3A%20multimodal%20learning/04.%20cross-modal%20generation/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
跨模态生成
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter%2010%3A%20multimodal%20learning/05.%20unified%20multimodal%20architectures/" class="md-nav__link">
|
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|
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|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
统一多模态架构
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
||
|
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|
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|
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|
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</ul>
|
||
</nav>
|
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|
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</li>
|
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|
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|
||
|
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|
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|
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|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
|
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|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" checked>
|
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<label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
自主系统
|
||
|
||
|
||
|
||
</span>
|
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|
||
|
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|
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<span class="md-nav__icon md-icon"></span>
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</label>
|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="true">
|
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<label class="md-nav__title" for="__nav_12">
|
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<span class="md-nav__icon md-icon"></span>
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|
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|
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自主系统
|
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|
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|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item md-nav__item--active">
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<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
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<label class="md-nav__link md-nav__link--active" for="__toc">
|
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<span class="md-ellipsis">
|
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|
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感知
|
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</span>
|
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|
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<span class="md-nav__icon md-icon"></span>
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</label>
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<a href="./" class="md-nav__link md-nav__link--active">
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<span class="md-ellipsis">
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感知
|
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|
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|
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|
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</span>
|
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|
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|
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|
||
</a>
|
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|
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|
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|
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<nav class="md-nav md-nav--secondary" aria-label="目录">
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<label class="md-nav__title" for="__toc">
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<span class="md-nav__icon md-icon"></span>
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目录
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</label>
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<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
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|
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<li class="md-nav__item">
|
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<a href="#_2" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
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传感器模态
|
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|
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</span>
|
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</a>
|
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|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="#_3" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
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传感器标定
|
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|
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</span>
|
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</a>
|
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|
||
</li>
|
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|
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<li class="md-nav__item">
|
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<a href="#_4" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
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传感器融合
|
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|
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</span>
|
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</a>
|
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|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="#3d" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
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3D目标检测
|
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|
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</span>
|
||
</a>
|
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|
||
</li>
|
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|
||
<li class="md-nav__item">
|
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<a href="#_5" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
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深度估计
|
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|
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</span>
|
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</a>
|
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|
||
</li>
|
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|
||
<li class="md-nav__item">
|
||
<a href="#_6" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
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|
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占据网络
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
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|
||
<li class="md-nav__item">
|
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<a href="#_7" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
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|
||
车道检测与道路拓扑
|
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|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_8" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
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|
||
语义建图
|
||
|
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</span>
|
||
</a>
|
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|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="#colabnotebook" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
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|
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编程任务（使用CoLab或notebook）
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
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|
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</nav>
|
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|
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</li>
|
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|
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|
||
|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../02.%20robot%20learning/" class="md-nav__link">
|
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|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
机器人学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
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|
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|
||
|
||
|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../03.%20vision-language-action%20models/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
视觉-语言-动作模型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../04.%20self-driving/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
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|
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|
||
自动驾驶
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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AI 推理
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量化
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服务与批处理
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边缘推理
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ML 系统设计
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ML 设计案例
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应用 AI
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AI 金融
|
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</a>
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蛋白质设计
|
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|
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药物发现
|
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|
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|
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|
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</span>
|
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|
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|
||
|
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</a>
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智能体系统
|
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|
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|
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|
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</span>
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|
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|
||
|
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</a>
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医疗健康
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</span>
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前沿 AI
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传感器模态
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传感器标定
|
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传感器融合
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3D目标检测
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深度估计
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占据网络
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车道检测与道路拓扑
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编程任务（使用CoLab或notebook）
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<article class="md-content__inner md-typeset">
|
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||
|
||
|
||
|
||
|
||
|
||
<h1 id="_1">感知<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
|
||
<p><em>感知是自主系统感知和解释物理世界的方式。本章涵盖传感器模态、标定、传感器融合、3D目标检测、深度估计、占据网络、车道检测和语义建图——这是每个机器人、无人机和自动驾驶汽车赖以构建的感知基础。</em></p>
|
||
<ul>
|
||
<li>
|
||
<p>对人类而言，感知世界毫不费力：你看到一辆车驶近，听到引擎声，感受到脚下的地面，瞬间在脑海中构建出周围环境的心智模型。自主系统也必须做到同样的事，但它使用的是电子传感器和算法，而非眼睛和耳朵。</p>
|
||
</li>
|
||
<li>
|
||
<p>根本性挑战在于：传感器提供的是原始数字（像素强度、点云、信号反射），系统必须将这些数字转化为结构化的理解："前方12米处有一个行人，以1.5米/秒的速度向左移动。"这就是感知问题。</p>
|
||
</li>
|
||
<li>
|
||
<p>下游的所有任务（预测、规划、控制）都依赖于感知。一个拥有完美规划器但感知能力差的自动驾驶汽车仍然会撞车。感知是瓶颈。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_2">传感器模态<a class="headerlink" href="#_2" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>自主系统使用多种传感器类型，各有其优势与失效模式。没有哪种传感器能单独胜任。</li>
|
||
</ul>
|
||
<p><img alt="传感器比较：相机、LiDAR、雷达和IMU在分辨率、深度、天气鲁棒性、速度测量和成本方面的评分" src="../../images/sensor_comparison.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>相机</strong>以高分辨率捕获密集的颜色信息。单张图像包含数百万像素，每个像素记录RGB值（如我们在第8章所见）。相机价格低廉、重量轻，提供丰富的纹理和颜色信息，这对识别标牌、检测交通信号灯和识别物体至关重要。</p>
|
||
</li>
|
||
<li>
|
||
<p>相机类型包括<strong>单目</strong>（单个镜头，无原生深度）、<strong>立体</strong>（两个镜头相隔一个基线，通过视差计算深度，详见第8章）和<strong>鱼眼</strong>（超宽视场角，180°以上，具有严重径向畸变，用于环绕视图泊车系统）。</p>
|
||
</li>
|
||
<li>
|
||
<p>相机的主要弱点是投影过程中丢失深度信息。3D场景通过针孔相机模型映射到2D图像平面（回顾第8章的内参矩阵<span class="arithmatex">\(K\)</span>）：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[\\begin{bmatrix} u \\\\ v \\\\ 1 \\end{bmatrix} = \\frac{1}{Z} K \\begin{bmatrix} X \\\\ Y \\\\ Z \\end{bmatrix}\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>除以<span class="arithmatex">\(Z\)</span>的过程丢弃了绝对深度。两个不同大小、不同距离的物体可能产生完全相同的投影。从单张图像恢复深度是病态问题，这就是为什么需要立体相机或学习型单目深度模型。</p>
|
||
</li>
|
||
<li>
|
||
<p>相机在恶劣条件下也会受到影响：直射阳光产生眩光，黑暗降低信号，雨雾散射光线。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>LiDAR</strong>（光探测与测距）发射激光脉冲并测量每个脉冲返回的时间。由于光速已知（<span class="arithmatex">\(c \\approx 3 \\times 10^8\)</span> m/s），每个反射点的距离为：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[d = \\frac{c \\cdot \\Delta t}{2}\]</div>
|
||
<p><img alt="LiDAR飞行时间：激光脉冲从物体上弹回，距离由往返时间计算得出" src="../../images/lidar_time_of_flight.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p>因子2考虑了往返行程（去程和回程）。通过将激光扫过场景，LiDAR构建了一个<strong>点云</strong>：一组3D坐标<span class="arithmatex">\((x, y, z)\)</span>，通常带有强度（反射率）值。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>旋转式LiDAR</strong>（如Velodyne）旋转激光阵列360°以提供完整的环视视图。典型设备每秒生成超过30万个点，覆盖64-128个垂直通道。结果是场景的稀疏但几何精度高的3D表示。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>固态LiDAR</strong>没有运动部件，使用光学相控阵或MEMS镜面。这使得它们更便宜、更紧凑、更可靠，但通常视场角较窄（120° vs 360°）。</p>
|
||
</li>
|
||
<li>
|
||
<p>LiDAR提供精确的深度，但生成的是稀疏数据（"像素"数量远少于相机），没有颜色信息，且价格昂贵。在大雨、雪或灰尘中，粒子会散射激光脉冲，其性能也会下降。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>雷达</strong>（无线电探测与测距）基于与LiDAR相同的飞行时间原理，但使用无线电波（毫米波，汽车领域通常为77 GHz）。无线电波穿透雨、雾、尘和雪的能力远优于光，使雷达成为最耐天气的传感器。</p>
|
||
</li>
|
||
<li>
|
||
<p>雷达还能通过<strong>多普勒效应</strong>直接测量<strong>速度</strong>。当物体向传感器移动时，反射波被压缩（频率升高）；当远离时，反射波被拉伸（频率降低）。速度公式为：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[v = \\frac{\\Delta f \\cdot c}{2 f_0}\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>其中<span class="arithmatex">\(\\Delta f\)</span>是频移，<span class="arithmatex">\(f_0\)</span>是发射频率。这提供了瞬时径向速度，无需任何跟踪或帧间计算。</p>
|
||
</li>
|
||
<li>
|
||
<p>折中是分辨率：雷达的角分辨率远低于相机或LiDAR，难以区分邻近物体或检测精细细节。但它在任何天气条件下都能出色地探测远距离（200米以上）的车辆。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>超声波传感器</strong>发射高频声脉冲（40-70 kHz）并测量回波返回时间。它们工作在极短距离（0.2-5米），主要用于泊车辅助。其物理原理与LiDAR相同，只是用声音代替光，因此<span class="arithmatex">\(d = \\frac{v_{\\text{声}} \\cdot \\Delta t}{2}\)</span>，其中<span class="arithmatex">\(v_{\\text{声}} \\approx 343\)</span> m/s。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>IMU</strong>（惯性测量单元）包含加速度计和陀螺仪，分别测量线加速度和角速度。IMU提供高频运动数据（通常200-1000 Hz），填补了较慢传感器更新之间的空白。它们不直接感知环境，而是跟踪机器人自身的运动，因此对航位推算和状态估计至关重要。</p>
|
||
</li>
|
||
<li>
|
||
<p>IMU存在<strong>漂移</strong>问题：小的测量误差随时间累积，导致估计位置偏离真实位置。这就是为什么IMU几乎总是与其他传感器（相机、GPS、LiDAR）融合使用，而非单独使用。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>GNSS</strong>（全球导航卫星系统，包括GPS）通过三角测量来自多颗卫星的信号，提供地球表面的绝对位置。标准GPS精度为2-5米，不足以进行车道级驾驶。<strong>RTK-GPS</strong>（实时动态差分GPS）使用固定基站校正误差，达到厘米级精度，但需要清晰的天空视野和基站基础设施。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_3">传感器标定<a class="headerlink" href="#_3" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p>在传感器协同工作之前，必须进行<strong>标定</strong>：将每个传感器的测量值与共同坐标系关联起来。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>内参标定</strong>确定传感器的内部参数。对于相机，这意味着焦距、主点和畸变系数（如第8章所述）。对于LiDAR，这意味着激光束之间的精确角度偏移。常用的方法是张氏棋盘格标定法，即从多个角度观察已知平面图案，求解内参矩阵。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>外参标定</strong>确定两个传感器之间的刚体变换（旋转<span class="arithmatex">\(R\)</span>和平移<span class="arithmatex">\(\\mathbf{t}\)</span>）。如果相机和LiDAR安装在同一辆车上，外参标定会找到一个<span class="arithmatex">\(4 \\times 4\)</span>变换矩阵，将LiDAR坐标中的点映射到相机坐标：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[\\mathbf{p}_{\\text{相}} = \\begin{bmatrix} R & \\mathbf{t} \\\\ \\mathbf{0}^T & 1 \\end{bmatrix} \\mathbf{p}_{\\text{激}}\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>这是齐次坐标中的仿射变换，正是我们在第2章（线性变换）中研究过的那种。如果这个矩阵出错，LiDAR点将投影到错误的像素上，整个融合流程就会崩溃。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>时间标定</strong>同步传感器时钟。以30 Hz工作的相机和以10 Hz工作的LiDAR在不同时间戳产生数据。如果汽车以30 m/s（高速公路速度）行驶，10毫秒的时间误差对应30厘米的空间误差。硬件触发（共享时钟脉冲）或软件同步（时间戳之间的插值）至关重要。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_4">传感器融合<a class="headerlink" href="#_4" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p>没有哪种传感器能覆盖所有条件。相机看得到颜色和纹理但丢失深度。LiDAR精确测量深度但稀疏且色盲。雷达在任何天气下都能工作但分辨率低。<strong>传感器融合</strong>结合各自的优势，弥补各自的弱点。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>早期融合</strong>（数据级融合）在进行任何处理之前合并原始传感器数据。例如，将LiDAR点投影到相机图像上，创建RGBD表示（每像素的颜色+深度），或者为每个LiDAR点赋予其投影到的相机像素的颜色。这种方式保留了最多的信息，但需要精确的标定，且对未对准非常敏感。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>后期融合</strong>（决策级融合）每个传感器独立运行各自的检测流程，然后合并最终输出（边界框、类别标签、置信度分数）。每个传感器投票，融合模块协调分歧。这种方式更简单、更模块化，但每个流程无法从其他传感器的原始数据中获益。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>中级融合</strong>在中间特征表示层面进行操作。每个传感器的原始数据被编码到学习到的特征空间（使用CNN或transformer），然后特征被合并。这是现代系统的主流方法，因为它让网络学习从每种模态中提取什么。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="BEV融合流程：相机和LiDAR被独立编码，然后投影到共享的鸟瞰图网格" src="../../images/bev_fusion_pipeline.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>BEVFusion</strong>是一种代表性的中级融合架构。它将相机特征和LiDAR特征投影到一个共同的<strong>鸟瞰图（BEV）</strong>表示中，即场景的俯视网格。相机特征通过预测的深度分布被"提升"到3D，然后散布到BEV网格上。LiDAR特征已经是3D的，直接被体素化到同一个网格上。融合后的BEV特征随后由检测头处理。</p>
|
||
</li>
|
||
<li>
|
||
<p>BEV表示之所以强大，是因为它提供了一个统一的、度量尺度的坐标框架，空间推理（距离、尺寸、重叠）在其中变得直观。在相机图像中，一辆近处的自行车和一辆远处的卡车可能占据相同数量的像素。而在BEV中，它们的真实大小和位置一目了然。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="3d">3D目标检测<a class="headerlink" href="#3d" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p>感知的核心任务是在3D空间中检测物体：它们在哪里，有多大，是什么，朝向何方？每次检测得到一个<strong>3D边界框</strong>，包括位置<span class="arithmatex">\((x, y, z)\)</span>、尺寸<span class="arithmatex">\((l, w, h)\)</span>、航向角<span class="arithmatex">\(\\theta\)</span>、类别标签和置信度分数。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>基于LiDAR的检测</strong>直接在点云上操作。挑战在于点云是无序的、不规则的，且密度变化大（近处物体有数千个点，远处物体只有几个）。回顾第8章，PointNet通过共享MLP和置换不变的聚合（最大池化）来处理这一问题。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>PointPillars</strong>通过将地面平面离散化为垂直柱（"pillars"）的网格，将点云转化为结构化表示。每个pillar内的所有点由一个小型PointNet编码为固定大小的特征向量。结果是一个2D伪图像，可以由标准的2D CNN主干网络处理，然后是检测头（如第8章中的SSD架构）。这种方法快速且有效。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>CenterPoint</strong>将物体检测为点而非边界框。它在BEV中预测物体中心的热图，然后在每个峰值处回归边界框属性（尺寸、高度、航向、速度）。这是CenterNet（第8章）的3D类比：无锚点，训练时无需NMS，并通过跨帧关联中心点自然扩展到跟踪。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>纯相机3D检测</strong>必须从2D图像推断深度，这从根本上更难。现代方法如<strong>BEVDet</strong>和<strong>BEVFormer</strong>使用transformer架构将2D图像特征"提升"到3D。BEVFormer使用空间交叉注意力：BEV查询关注投影到每个相机图像上的特定3D参考点，从相关位置提取特征。</p>
|
||
</li>
|
||
<li>
|
||
<p>基于LiDAR和基于相机的3D检测之间的精度差距正在迅速缩小，这得益于更好的深度估计、更大的模型和时间融合（利用多帧累积深度线索，类似立体匹配但跨时间进行）。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_5">深度估计<a class="headerlink" href="#_5" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p>深度估计是为每个像素或点分配距离值的问题。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>立体匹配</strong>使用两个相隔已知基线<span class="arithmatex">\(b\)</span>的相机。同一个3D点在两幅图像中的水平位置略有不同，形成<strong>视差</strong><span class="arithmatex">\(d\)</span>。深度计算公式为（来自第8章）：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[Z = \\frac{f \\cdot b}{d}\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>其中<span class="arithmatex">\(f\)</span>是焦距。挑战在于找到两幅图像之间的正确对应关系，特别是在无纹理区域、遮挡区域和重复图案中。现代立体网络（如RAFT-Stereo）使用带有相关体积的迭代精化方法。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>单目深度估计</strong>从单张图像预测深度。由于这是病态问题（无限多个3D场景可以产生相同的图像），网络必须学习统计先验："地面是平的"、"物体随距离增大而变小"、"纹理梯度表明表面在后退"。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>Depth Anything</strong>（第8章中介绍过）通过在大规模无标注数据集上进行自监督训练，然后在标注数据上进行微调，实现了强大的单目深度估计。关键洞察在于尺度不变损失处理了固有不明确性：模型预测的是相对深度（排序）而非绝对米数。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>LiDAR-相机深度融合</strong>将稀疏的LiDAR深度测量值投影到相机图像上作为监督信号。网络学习"填充"稀疏点之间的空白，生成结合LiDAR精度和相机分辨率的密集深度图。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_6">占据网络<a class="headerlink" href="#_6" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>传统感知输出一个边界框列表，每个检测到的物体一个框。但现实世界中许多事物并不适合用框来整齐地表示：形状不规则的碎片、施工围挡、悬垂的树枝、部分坍塌的墙壁。</li>
|
||
</ul>
|
||
<p><img alt="边界框在不规则形状上浪费空间；占据网格遵循实际几何形状" src="../../images/occupancy_vs_bbox.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>占据网络</strong>将场景表示为密集的3D体素网格。每个体素（一个小立方体空间，例如0.2m × 0.2m × 0.2m）被分类为空闲、占据或未知，并可选择赋予语义标签（道路、人行道、车辆、植被等）。</p>
|
||
</li>
|
||
<li>
|
||
<p>这意味着从以物体为中心的感知（"检测汽车"）转向以场景为中心的感知（"3D空间的哪些部分被占据？"）。优势在于通用性：系统不需要预定义对象类别列表来避免与任意障碍物碰撞。</p>
|
||
</li>
|
||
<li>
|
||
<p>从架构上看，占据网络接收传感器输入（相机、LiDAR或两者），将其编码为3D特征体积，并预测每个体素的标签。3D特征体积通常通过将2D特征提升到3D（类似于BEV构建但扩展到垂直方向）来构建，然后使用3D卷积或稀疏卷积进行处理。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>TPVFormer</strong>（三视角）通过将3D体积分解为三个正交平面（俯视图、前视图、侧视图）来避免完整3D注意力的立方级计算成本。每个平面使用2D注意力，其特征在每个体素处组合。这让人想起SVD如何将矩阵分解为更简单的因子（第2章）：将一个困难的3D问题分解为可管理的2D部分。</p>
|
||
</li>
|
||
<li>
|
||
<p>输出的体素网格直接告诉规划器哪些空间区域是安全的、哪些不是，使其成为感知和规划之间的自然接口。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_7">车道检测与道路拓扑<a class="headerlink" href="#_7" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p>对于在结构化道路上行驶的车辆，理解<strong>车道几何</strong>至关重要。系统必须知道车道在哪里、如何弯曲、在哪里合并和分叉，以及车辆处于哪条车道。</p>
|
||
</li>
|
||
<li>
|
||
<p>经典方法将参数曲线拟合到检测到的车道标线上。常用的模型是三次多项式：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[x(y) = a_0 + a_1 y + a_2 y^2 + a_3 y^3\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>其中<span class="arithmatex">\(y\)</span>是前方纵向距离，<span class="arithmatex">\(x\)</span>是横向偏移。这是多项式近似（回顾第3章的泰勒级数），选择它是因为道路是平滑曲线，很好地由低次多项式描述。系数通过检测到的车道点上的最小二乘回归估计得出。</p>
|
||
</li>
|
||
<li>
|
||
<p>现代方法使用神经网络直接检测车道。<strong>LaneNet</strong>将每条车道视为一个实例，使用嵌入分支对属于同一条车道的像素进行分组，然后进行曲线拟合。<strong>GANet</strong>使用基于图的方法，将车道拓扑表示为有向图，其中节点是车道点，边编码连接关系（哪些车道在交叉口合并、分叉或连接）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>道路拓扑</strong>超越了单个车道曲线，捕获完整结构：车道之间如何连接，哪些车道允许左转，高速公路入口匝道在哪里汇入。这被建模为有向图，交叉口是节点，车道段是带有属性（限速、车道类型、转弯限制）的边。</p>
|
||
</li>
|
||
<li>
|
||
<p>图结构对路线规划至关重要：规划器需要知道的不仅是"车道在哪里"，还有"哪条车道序列能到达目的地"。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_8">语义建图<a class="headerlink" href="#_8" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p>感知并不止于检测单帧中的物体。随着时间的推移，自主系统构建一个<strong>语义地图</strong>：对其环境的持久化、结构化表示，积累来自多次观测的信息。</p>
|
||
</li>
|
||
<li>
|
||
<p>最简单的情况下，语义地图是一个2D网格（<strong>占据网格</strong>），每个单元存储被占据的概率。随着机器人移动并通过传感器扫描，它使用贝叶斯更新来更新这些概率：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[P(\\text{占据} \\mid z_{1:t}) = \\frac{P(z_t \\mid \\text{占据}) \\cdot P(\\text{占据} \\mid z_{1:t-1})}{P(z_t)}\]</div>
|
||
<ul>
|
||
<li>这就是贝叶斯定理的实际应用（来自第5章）：每次新的测量<span class="arithmatex">\(z_t\)</span>更新对每个单元的先验信念。通常使用<strong>对数几率</strong>表示来避免乘以许多小概率带来的数值问题：</li>
|
||
</ul>
|
||
<div class="arithmatex">\[l_t = l_{t-1} + \\log \\frac{P(z_t \\mid \\text{占据})}{P(z_t \\mid \\text{空闲})}\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>对数几率相加等价于概率相乘（回顾<span class="arithmatex">\(\\log(ab) = \\log a + \\log b\)</span>），累加和自然地随时间积累证据。</p>
|
||
</li>
|
||
<li>
|
||
<p>更丰富的地图为每个单元分配语义标签（道路、人行道、建筑、植被），并可扩展到3D。这与占据网络密切相关，但强调持久性和时间聚合而非单帧预测。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>SLAM</strong>（同时定位与建图），在第8章中介绍过，是在构建地图的同时跟踪机器人在地图中的位置的算法。视觉-惯性SLAM融合相机和IMU数据；LiDAR SLAM使用点云配准。感知流程将检测结果和深度估计输入SLAM系统，由后者维护全局地图。</p>
|
||
</li>
|
||
<li>
|
||
<p>现代方法越来越多地使用神经隐式表示（如第8章中的NeRF）来构建可在任何3D点查询的密集、逼真地图。这些神经地图将整个场景的压缩表示存储在网络权重中，支持新视角合成和详细空间查询等任务。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="colabnotebook">编程任务（使用CoLab或notebook）<a class="headerlink" href="#colabnotebook" title="Permanent link">¶</a></h2>
|
||
<ol>
|
||
<li>
|
||
<p>使用投影矩阵将3D LiDAR点投影到2D相机图像上。可视化哪些点落在图像边界内。
|
||
<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>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># 模拟3D LiDAR点（x=向前，y=向左，z=向上）</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="n">rng</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">0</span><span class="p">)</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">points_3d</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">uniform</span><span class="p">(</span><span class="n">rng</span><span class="p">,</span> <span class="p">(</span><span class="mi">200</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="n">minval</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="mi">5</span><span class="p">,</span> <span class="o">-</span><span class="mi">10</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]),</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">maxval</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="mi">50</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">3</span><span class="p">]))</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="c1"># 相机内参矩阵（焦距500，图像中心320x240）</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">K</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="mi">500</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">320</span><span class="p">],</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">500</span><span class="p">,</span> <span class="mi">240</span><span class="p">],</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]])</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"># 外参：LiDAR到相机（单位旋转，小平移）</span>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="n">R</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
|
||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="n">t</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="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">])</span>
|
||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>
|
||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="c1"># 投影：p_cam = K @ (R @ p_lidar + t)</span>
|
||
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="n">p_cam</span> <span class="o">=</span> <span class="p">(</span><span class="n">R</span> <span class="o">@</span> <span class="n">points_3d</span><span class="o">.</span><span class="n">T</span><span class="p">)</span><span class="o">.</span><span class="n">T</span> <span class="o">+</span> <span class="n">t</span>
|
||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="n">p_img</span> <span class="o">=</span> <span class="p">(</span><span class="n">K</span> <span class="o">@</span> <span class="n">p_cam</span><span class="o">.</span><span class="n">T</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
|
||
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="n">p_img</span> <span class="o">=</span> <span class="n">p_img</span><span class="p">[:,</span> <span class="p">:</span><span class="mi">2</span><span class="p">]</span> <span class="o">/</span> <span class="n">p_img</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="c1"># 除以Z</span>
|
||
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>
|
||
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="c1"># 过滤相机前方且在图像内的点</span>
|
||
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="n">mask</span> <span class="o">=</span> <span class="p">(</span><span class="n">p_cam</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">]</span> <span class="o">></span> <span class="mi">0</span><span class="p">)</span> <span class="o">&</span> <span class="p">(</span><span class="n">p_img</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">></span> <span class="mi">0</span><span class="p">)</span> <span class="o">&</span> <span class="p">(</span><span class="n">p_img</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o"><</span> <span class="mi">640</span><span class="p">)</span> <span class="o">&</span> \
|
||
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a> <span class="p">(</span><span class="n">p_img</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">></span> <span class="mi">0</span><span class="p">)</span> <span class="o">&</span> <span class="p">(</span><span class="n">p_img</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o"><</span> <span class="mi">480</span><span class="p">)</span>
|
||
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a><span class="n">depth</span> <span class="o">=</span> <span class="n">p_cam</span><span class="p">[</span><span class="n">mask</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</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="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
|
||
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">p_img</span><span class="p">[</span><span class="n">mask</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">p_img</span><span class="p">[</span><span class="n">mask</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">depth</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s2">"viridis"</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
|
||
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">label</span><span class="o">=</span><span class="s2">"深度 (米)"</span><span class="p">)</span>
|
||
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">640</span><span class="p">);</span> <span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="mi">480</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"投影到相机图像上的LiDAR点"</span><span class="p">)</span>
|
||
<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"u (像素)"</span><span class="p">);</span> <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"v (像素)"</span><span class="p">)</span>
|
||
<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a><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>使用贝叶斯对数几率更新构建一个简单的2D占据网格。模拟一个距离传感器扫描环境，观察地图的生成过程。
|
||
<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="c1"># 网格设置：50x50个单元，每个0.2米</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">grid_size</span> <span class="o">=</span> <span class="mi">50</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">log_odds</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">grid_size</span><span class="p">,</span> <span class="n">grid_size</span><span class="p">))</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="c1"># 传感器模型：对数几率更新值</span>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">l_occ</span> <span class="o">=</span> <span class="mf">0.85</span> <span class="c1"># 命中意味着占据的置信度</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="n">l_free</span> <span class="o">=</span> <span class="o">-</span><span class="mf">0.4</span> <span class="c1"># 穿过意味着空闲的置信度</span>
|
||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="c1"># 模拟障碍物：从(5,20)到(5,30)的墙（网格坐标）</span>
|
||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="n">wall_y</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="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">)</span>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a>
|
||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="c1"># 机器人在(25, 25)，向外扫描</span>
|
||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="n">robot</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="mi">25</span><span class="p">,</span> <span class="mi">25</span><span class="p">])</span>
|
||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a>
|
||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="k">for</span> <span class="n">angle_deg</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">360</span><span class="p">,</span> <span class="mi">5</span><span class="p">):</span>
|
||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a> <span class="n">angle</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">radians</span><span class="p">(</span><span class="n">angle_deg</span><span class="p">)</span>
|
||
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a> <span class="n">direction</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">jnp</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angle</span><span class="p">),</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angle</span><span class="p">)])</span>
|
||
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a>
|
||
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a> <span class="k">for</span> <span class="n">step</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">25</span><span class="p">):</span>
|
||
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a> <span class="n">cell</span> <span class="o">=</span> <span class="p">(</span><span class="n">robot</span> <span class="o">+</span> <span class="n">direction</span> <span class="o">*</span> <span class="n">step</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">)</span>
|
||
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a> <span class="n">r</span><span class="p">,</span> <span class="n">c</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">cell</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="nb">int</span><span class="p">(</span><span class="n">cell</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a> <span class="k">if</span> <span class="n">r</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">r</span> <span class="o">>=</span> <span class="n">grid_size</span> <span class="ow">or</span> <span class="n">c</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">c</span> <span class="o">>=</span> <span class="n">grid_size</span><span class="p">:</span>
|
||
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a> <span class="k">break</span>
|
||
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a>
|
||
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a> <span class="c1"># 检查此单元是否为墙</span>
|
||
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a> <span class="n">is_wall</span> <span class="o">=</span> <span class="p">(</span><span class="n">r</span> <span class="o">==</span> <span class="mi">5</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">c</span> <span class="o">>=</span> <span class="mi">20</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">c</span> <span class="o"><</span> <span class="mi">30</span><span class="p">)</span>
|
||
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a> <span class="k">if</span> <span class="n">is_wall</span><span class="p">:</span>
|
||
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a> <span class="n">log_odds</span> <span class="o">=</span> <span class="n">log_odds</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">l_occ</span><span class="p">)</span>
|
||
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a> <span class="k">break</span>
|
||
<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a> <span class="n">log_odds</span> <span class="o">=</span> <span class="n">log_odds</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">l_free</span><span class="p">)</span>
|
||
<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a>
|
||
<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="c1"># 将对数几率转换为概率</span>
|
||
<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="n">prob</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="p">(</span><span class="mf">1.0</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="n">log_odds</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">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">))</span>
|
||
<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">prob</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">origin</span><span class="o">=</span><span class="s2">"lower"</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s2">"RdYlGn_r"</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-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">label</span><span class="o">=</span><span class="s2">"P(被占据)"</span><span class="p">)</span>
|
||
<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="mi">25</span><span class="p">,</span> <span class="mi">25</span><span class="p">,</span> <span class="s2">"b*"</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"机器人"</span><span class="p">)</span>
|
||
<a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a><span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
||
<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"贝叶斯更新生成的2D占据网格"</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">show</span><span class="p">()</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>使用视差从立体图像对计算深度。模拟两个相机视角下的3D点，计算视差并恢复深度。
|
||
<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</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">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-2-3" 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"># 相机参数</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">f</span> <span class="o">=</span> <span class="mf">500.0</span> <span class="c1"># 焦距（像素）</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">b</span> <span class="o">=</span> <span class="mf">0.12</span> <span class="c1"># 基线（米，12厘米）</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="c1"># 已知深度的3D点</span>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">depths_true</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="mf">5.0</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">,</span> <span class="mf">20.0</span><span class="p">,</span> <span class="mf">50.0</span><span class="p">,</span> <span class="mf">100.0</span><span class="p">])</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="c1"># 视差 = f * b / Z</span>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="n">disparities</span> <span class="o">=</span> <span class="n">f</span> <span class="o">*</span> <span class="n">b</span> <span class="o">/</span> <span class="n">depths_true</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"># 从视差恢复深度</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="n">depths_recovered</span> <span class="o">=</span> <span class="n">f</span> <span class="o">*</span> <span class="n">b</span> <span class="o">/</span> <span class="n">disparities</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="k">for</span> <span class="n">z</span><span class="p">,</span> <span class="n">d</span><span class="p">,</span> <span class="n">z_r</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">depths_true</span><span class="p">,</span> <span class="n">disparities</span><span class="p">,</span> <span class="n">depths_recovered</span><span class="p">):</span>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"真实深度: </span><span class="si">{</span><span class="n">z</span><span class="si">:</span><span class="s2">6.1f</span><span class="si">}</span><span class="s2">米 视差: </span><span class="si">{</span><span class="n">d</span><span class="si">:</span><span class="s2">6.2f</span><span class="si">}</span><span class="s2">像素 恢复值: </span><span class="si">{</span><span class="n">z_r</span><span class="si">:</span><span class="s2">6.1f</span><span class="si">}</span><span class="s2">米"</span><span class="p">)</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="c1"># 注意：视差与深度成反比</span>
|
||
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="c1"># 近处物体视差大，远处物体视差小</span>
|
||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="c1"># 这就是为什么立体视觉在近距离最准确</span>
|
||
</code></pre></div></p>
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