# 1.4 Padding

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/d21e2642815d03b15396f7998ba4459a.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/d21e2642815d03b15396f7998ba4459a.png)

如果有一个$$n\times n$$的图像，用$$f\times f$$的过滤器做卷积，输出的维度就是$$(n-f+1)\times (n-f+1)$$

这样的话会有两个缺点:

* 每次做卷积操作，**输出图片尺寸缩小**
* **原始图片边缘信息对输出贡献得少，输出图片丢失边缘信息**

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/170e076ceaeb70339baa7b25ad5f5e6c.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/170e076ceaeb70339baa7b25ad5f5e6c.png)

> 角落边缘的像素（绿色阴影标记）只被一个输出所触碰或者使用，中间的像素点（红色方框标记）会有许多3×3的区域与之重叠。角落或者边缘区域的像素点在输出中采用较少，丢掉了图像边缘位置的许多信息

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/208104bae9256fba5d8e37e22a9f5408.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/208104bae9256fba5d8e37e22a9f5408.png)

可以在卷积操作之前填充这幅图像。沿着图像边缘再填充一层像素,6×6的图像填充成8×8的图像。就得到了一个尺寸和原始图像6×6的图像。习惯上，可以用0去填充，如果$$p$$是填充的数量，输出也就变成了$$(n+2p-f+1)\times (n+2p-f+1)$$。涂绿的像素点（左边矩阵）影响了输出中的这些格子（右边矩阵）。这样角落或图像边缘的信息发挥的作用较小的这一缺点就被削弱了

选择填充多少像素，通常有两个选择，分别叫做**Valid**卷积和**Same**卷积

**Valid**卷积意味着不填充，如果有一个$$n\times n$$的图像，用一个$$f\times f$$的过滤器卷积，会给一个$$(n-f+1)\times (n-f+1)$$维的输出

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/0663e1a9e477e2737067d9e79194208d.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/0663e1a9e477e2737067d9e79194208d.png)

另一个叫做**Same**卷积，填充后输出大小和输入大小是一样的。由$$n-f+1$$，当填充$$p$$个像素点，$$n$$就变成了$$n+2p$$，公式变为：

$$
n+2p-f+1
$$

即：

$$
p=\frac{f-1}{2}
$$

当$$f$$是一个奇数，只要选择相应的填充尺寸就能确保得到和输入相同尺寸的输出

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/ca5382358f30c1349fff98d1e52366b4.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/ca5382358f30c1349fff98d1e52366b4.png)

计算机视觉中，$$f$$通常是奇数，有两个原因：

* 如果$$f$$是偶数，只能使用一些不对称填充
* 当有一个奇数维过滤器，比如3×3或者5×5的，它就有一个中心点，便于指出过滤器的位置


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