# 3.1 目标定位（Object localization）

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/0107af10b33fcb955cc3c588dfb78d49.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/0107af10b33fcb955cc3c588dfb78d49.png)

定位分类问题：不仅要用算法判断图片中是不是一辆汽车，还要在图片中标记出它的位置，用边框或红色方框把汽车圈起来，“定位”的意思是判断汽车在图片中的具体位置

定位分类问题通常只有一个较大的对象位于图片中间位置，对它进行识别和定位。对象检测问题中图片可以含有多个对象，甚至单张图片中会有多个不同分类的对象

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/d4a47c2041807f891c0a606d246330c5.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/d4a47c2041807f891c0a606d246330c5.png)

构建汽车自动驾驶系统，对象可能包括以下几类：行人、汽车、摩托车和背景

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/6461ff27c00dff4205688de4cf9d8803.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/6461ff27c00dff4205688de4cf9d8803.png)

定位图片中汽车的位置：让神经网络输出一个边界框，标记为$$b\_{x}$$,$$b\_{y}$$,$$b\_{h}$$和$$b\_{w}$$，是被检测对象的边界框的参数化表示

红色方框的中心点表示为($$b\_{x}$$,$$b\_{y}$$)，边界框的高度为$$b\_{h}$$，宽度为$$b\_{w}$$。训练集不仅包含神经网络要预测的对象分类标签，还要包含表示边界框的这四个数字，接着采用监督学习算法，输出一个分类标签，还有四个参数值，从而给出检测对象的边框位置

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/21b37dcb413e7c86464f88484796420c.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/21b37dcb413e7c86464f88484796420c.png)

如何为监督学习任务定义目标标签 $$y$$：

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/02d85ab36285cd21b5df4d1c253df57e.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/02d85ab36285cd21b5df4d1c253df57e.png)

目标标签$$y$$的定义：$$y= \begin{bmatrix} p\_{c} \ b\_{x} \ b\_{y}\ b\_{h}\ b\_{w} \ c\_{1}\ c\_{2}\ c\_{3} \end{bmatrix}$$

$$p\_{c}$$表示是否含有对象，如果对象属于前三类（行人、汽车、摩托车），则$$p\_{c}= 1$$，如果是背景，则$$p\_{c} =0$$。$$p\_{c}$$表示被检测对象属于某一分类的概率，背景分类除外

如果检测到对象，就输出被检测对象的边界框参数$$b\_{x}$$、$$b\_{y}$$、$$b\_{h}$$和$$b\_{w}$$。$$p\_{c}=1$$，同时输出$$c\_{1}$$、$$c\_{2}$$和$$c\_{3}$$，表示该对象属于行人，汽车还是摩托车

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/fd37e4750b64a07cc1f29880c9b97261.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/fd37e4750b64a07cc1f29880c9b97261.png)

如果图片中没有检测对象:

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/131239883224f03709ddc66d9481c3c7.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/131239883224f03709ddc66d9481c3c7.png)

$$p\_{c} =0$$，$$y$$的其它参数全部写成问号，表示“毫无意义”的参数

神经网络的损失函数，如果采用平方误差策略：

$$
L\left(\hat{y},y \right) = \left( \hat{y\_1} - y\_{1} \right)^{2} + \left(\hat{y\_2} - y\_{2}\right)^{2} + \ldots+\left( \hat{y\_8} - y\_{8}\right)^{2}
$$

损失值等于每个元素相应差值的平方和

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/d50ae3ee809da4c728837fee2d055f00.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/d50ae3ee809da4c728837fee2d055f00.png)

如果图片中存在定位对象，$$y\_{1} =p\_{c}=1$$，损失值是不同元素的平方和

$$y\_{1}= p\_{c} = 0$$，损失值是$$\left(\hat{y\_1} - y\_{1}\right)^{2}$$，只需要关注神经网络输出$$p\_{c}$$的准确度

这里用平方误差简化了描述过程。实际应用中可以不对$$c\_{1}$$、$$c\_{2}$$、$$c\_{3}$$和**softmax**激活函数应用对数损失函数，并输出其中一个元素值，通常做法是对边界框坐标应用平方差，对$$p\_{c}$$应用逻辑回归函数，甚至采用平方预测误差


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