# 1.5 卷积步长（Strided convolutions）

Stride表示filter在原图片中水平方向和垂直方向每次的步进长度。之前默认stride=1。若stride=2，则表示filter每次步进长度为2，即隔一点移动一次

![](https://2314428465-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-Le0cHhI0S0DK8pwlrmD%2F-Le0cKOp1vaxoORIi4ak%2F-Le0cdP8veRmIKmPLINc%2F456import.png?generation=1556953087131866\&alt=media)

用s表示stride长度，p表示padding长度，如果原始图片尺寸为n x n，filter尺寸为f x f，则卷积后的图片尺寸为：

$$
\lfloor\frac{n+2p-f}{s}+1\rfloor\ \times\ \lfloor\frac{n+2p-f}{s}+1\rfloor
$$

真正的卷积运算会先将filter绕其中心旋转180度，然后再将旋转后的filter在原始图片上进行滑动计算。filter旋转如下所示：

![](https://2314428465-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-Le0cHhI0S0DK8pwlrmD%2F-Le0cKOp1vaxoORIi4ak%2F-Le0cdPAWFgzb33uHOr4%2F435import.png?generation=1556953125562001\&alt=media)

相关系数的计算过程则不会对filter进行旋转，而是直接在原始图片上进行滑动计算

目前为止介绍的CNN卷积实际上计算的是相关系数，而不是数学意义上的卷积。为了简化计算，一般把CNN中的这种“相关系数”就称作卷积运算。之所以可以这么等效，是因为滤波器算子一般是水平或垂直对称的，180度旋转影响不大；而且最终滤波器算子需要通过CNN网络梯度下降算法计算得到，旋转部分可以看作是包含在CNN模型算法中。忽略旋转运算可以大大提高CNN网络运算速度，而且不影响模型性能。

卷积运算服从分配律：

$$
(A*B)*C=A*(B*C)
$$


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