CNN中的卷积和反卷积

原文链接：https://blog.csdn.net/sinat_29957455/article/details/85558870

前言

卷积和反卷积在CNN中经常被用到，想要彻底搞懂并不是那么容易。本文主要分三个部分来讲解卷积和反卷积，分别包括概念、工作过程、代码示例，其中代码实践部分主结合TensorFlow框架来进行实践。给大家介绍一个卷积过程的可视化工具，这个项目是github上面的一个开源项目。
在这里插入图片描述

卷积和反卷积

卷积(Convolutional)：卷积在图像处理领域被广泛的应用，像滤波、边缘检测、图片锐化等，都是通过不同的卷积核来实现的。在卷积神经网络中通过卷积操作可以提取图片中的特征，低层的卷积层可以提取到图片的一些边缘、线条、角等特征，高层的卷积能够从低层的卷积层中学到更复杂的特征，从而实现到图片的分类和识别。
反卷积：反卷积也被称为转置卷积，反卷积其实就是卷积的逆过程。大家可能对于反卷积的认识有一个误区，以为通过反卷积就可以获取到经过卷积之前的图片，实际上通过反卷积操作并不能还原出卷积之前的图片，只能还原出卷积之前图片的尺寸。那么到底反卷积有什么作用呢？通过反卷积可以用来可视化卷积的过程，反卷积在GAN等领域中有着大量的应用。

工作过程

卷积

在这里插入图片描述
上图展示了一个卷积的过程，其中蓝色的图片(4*4)表示的是进行卷积的图片，阴影的图片(3*3)表示的是卷积核，绿色的图片(2*2)表示是进行卷积计算之后的图片。在卷积操作中有几个比较重要的参数，输入图片的尺寸、步长、卷积核的大小、输出图片的尺寸、填充大小。
下面用一个图来详细介绍这些参数：
在这里插入图片描述
输入图片的尺寸：上图中的蓝色图片(55)，表示的是需要进行卷积操作的图片，在后面的公式中有 $ii i$ $k$ 表示卷积核的尺寸。下图展示的是一个padding为VALID的卷积过程，卷积核始终都是位于输入矩阵内进行移动。
在这里插入图片描述

    x1 = tf.constant(1.0, shape=[1,4,4,3])
    x2 = tf.constant(1.0,shape=[1,6,6,3])
    kernel = tf.constant(1.0,shape=[3,3,3,1])
y1_1 <span class="token operator">=</span> tf<span class="token punctuation">.</span>nn<span class="token punctuation">.</span>conv2d<span class="token punctuation">(</span>x1<span class="token punctuation">,</span>kernel<span class="token punctuation">,</span>strides<span class="token operator">=</span><span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">,</span>padding<span class="token operator">=</span><span class="token string">"SAME"</span><span class="token punctuation">)</span>
y1_2 <span class="token operator">=</span> tf<span class="token punctuation">.</span>nn<span class="token punctuation">.</span>conv2d<span class="token punctuation">(</span>x1<span class="token punctuation">,</span>kernel<span class="token punctuation">,</span>strides<span class="token operator">=</span><span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">,</span>padding<span class="token operator">=</span><span class="token string">"VALID"</span><span class="token punctuation">)</span>
y2_1 <span class="token operator">=</span> tf<span class="token punctuation">.</span>nn<span class="token punctuation">.</span>conv2d<span class="token punctuation">(</span>x2<span class="token punctuation">,</span>kernel<span class="token punctuation">,</span>strides<span class="token operator">=</span><span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">,</span>padding<span class="token operator">=</span><span class="token string">"SAME"</span><span class="token punctuation">)</span>
y2_2 <span class="token operator">=</span> tf<span class="token punctuation">.</span>nn<span class="token punctuation">.</span>conv2d<span class="token punctuation">(</span>x2<span class="token punctuation">,</span>kernel<span class="token punctuation">,</span>strides<span class="token operator">=</span><span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">,</span>padding<span class="token operator">=</span><span class="token string">"VALID"</span><span class="token punctuation">)</span>

sess <span class="token operator">=</span> tf<span class="token punctuation">.</span>InteractiveSession<span class="token punctuation">(</span><span class="token punctuation">)</span>
tf<span class="token punctuation">.</span>global_variables_initializer<span class="token punctuation">(</span><span class="token punctuation">)</span>
x1<span class="token punctuation">,</span>y1_1<span class="token punctuation">,</span>y1_2<span class="token punctuation">,</span>x2<span class="token punctuation">,</span>y2_1<span class="token punctuation">,</span>y2_2 <span class="token operator">=</span> sess<span class="token punctuation">.</span>run<span class="token punctuation">(</span><span class="token punctuation">[</span>x1<span class="token punctuation">,</span>y1_1<span class="token punctuation">,</span>y1_2<span class="token punctuation">,</span>x2<span class="token punctuation">,</span>y2_1<span class="token punctuation">,</span>y2_2<span class="token punctuation">]</span><span class="token punctuation">)</span>
<span class="token keyword">print</span><span class="token punctuation">(</span>x1<span class="token punctuation">.</span>shape<span class="token punctuation">)</span>         <span class="token comment">#(1, 4, 4, 3)</span>
<span class="token keyword">print</span><span class="token punctuation">(</span>y1_1<span class="token punctuation">.</span>shape<span class="token punctuation">)</span>       <span class="token comment">#(1, 2, 2, 1)</span>
<span class="token keyword">print</span><span class="token punctuation">(</span>y1_2<span class="token punctuation">.</span>shape<span class="token punctuation">)</span>       <span class="token comment">#(1, 1, 1, 1)</span>
<span class="token keyword">print</span><span class="token punctuation">(</span>x2<span class="token punctuation">.</span>shape<span class="token punctuation">)</span>         <span class="token comment">#(1, 6, 6, 3)</span>
<span class="token keyword">print</span><span class="token punctuation">(</span>y2_1<span class="token punctuation">.</span>shape<span class="token punctuation">)</span>       <span class="token comment">#(1, 3, 3, 1)</span>
<span class="token keyword">print</span><span class="token punctuation">(</span>y2_2<span class="token punctuation">.</span>shape<span class="token punctuation">)</span>       <span class="token comment">#(1, 2, 2, 1)</span>

下面看一个卷积的计算例子

    x1 = tf.constant([i*0.1 for i in range(16)],shape=
    	[1,4,4,1],dtype=tf.float32)
    kernel = tf.ones(shape=[3,3,1,1],dtype=tf.float32)
    conv1 = tf.nn.conv2d(x1,kernel,strides=
    	[1,1,1,1],padding="VALID")
    sess = tf.InteractiveSession()
    tf.global_variables_initializer()
    conv1 = sess.run(conv1)
    print(conv1)

在这里插入图片描述

将卷积核与输入矩阵对应的位置进行乘加计算即可，对于多维输入矩阵和多维卷积核的卷积计算，将卷积后的结果进行堆叠，作为最终卷积的输出结果。

反卷积

tensorflow提供了tf.nn.conv2d_transpose函数来计算反卷积
功能说明：计算反卷积(转置卷积)

value：4维的tensor，float类型，需要进行反卷积的矩阵
filter：卷积核，参数格式[height，width，output_channels，in_channels]，这里需要注意output_channels和in_channels的顺序
output_shape：一维的Tensor，设置反卷积输出矩阵的shape
strides：反卷积的步长
padding："SAME"和"VALID"两种模式
data_format：和之前卷积参数一样
name：操作的名称

if __name__ == "__main__":
    x1 = tf.constant([4.5,5.4,8.1,9.0],shape=
    	[1,2,2,1],dtype=tf.float32)
    dev_con1 = tf.ones(shape=[3,3,1,1],dtype=tf.float32)
    y1 = tf.nn.conv2d_transpose(x1,dev_con1,output_shape=
    	[1,4,4,1],strides=[1,1,1,1],padding="VALID")
    sess = tf.InteractiveSession()
    tf.global_variables_initializer()
    y1,x1 = sess.run([y1,x1])
    print(y1)
    print(x1)

在这里插入图片描述
需要注意的是，通过反卷积并不能还原卷积之前的矩阵，只能从大小上进行还原，反卷积的本质还是卷积，只是在进行卷积之前，会进行一个自动的padding补0，从而使得输出的矩阵与指定输出矩阵的shape相同。框架本身，会根据你设定的反卷积值来计算输入矩阵的尺寸，如果shape不符合，则会报错。
错误提示：InvalidArgumentError (see above for traceback): Conv2DSlowBackpropInput，这时候需要检查反卷积的参数与输入矩阵之间的shape是否符合。计算规则可以根据padding为SAME还是VALID来计算输入和输出矩阵的shape是否相符合。如上例中，根据反卷积的参数来计算输入矩阵的shape：因为padding是VALID模式，所以我们套用 $ceil((i−k+1)/s)=ceil((4−3+1)/1)=2ceil((i−k+1)/s)=ceil((4−3+1)/1)=2 ceil((i-k+1)/s)=ceil((4-3+1)/1)=2$ $c e i l ((i - k + 1) / s) = c e i l ((4 - 3 + 1) / 1) = 2$ ，而输入矩阵x1的shape刚好是2*2，所以符合。
上面介绍的反卷积的stride是1，接下来看一个stride不为1的例子

    x1 = tf.constant([4.5,5.4,8.1,9.0],shape=
    	[1,2,2,1],dtype=tf.float32)
    dev_con1 = tf.ones(shape=[3,3,1,1],dtype=tf.float32)
    y1 = tf.nn.conv2d_transpose(x1,dev_con1,output_shape=
    	[1,6,6,1],strides=[1,2,2,1],padding="VALID")
    sess = tf.InteractiveSession()
    tf.global_variables_initializer()
    y1,x1 = sess.run([y1,x1])
<span class="token keyword">print</span><span class="token punctuation">(</span>x1<span class="token punctuation">)</span>
<span class="token keyword">print</span><span class="token punctuation">(</span>y1<span class="token punctuation">)</span>

在这里插入图片描述
需要注意的是，在进行反卷积的时候设置的stride并不是指反卷积在进行卷积时候卷积核的移动步长，而是被卷积矩阵填充的padding，仔细观察红色框内可以发现之前输入矩阵之间有一行和一列0的填充。

来源：CSDN

作者：L 学习ing

链接：https://blog.csdn.net/qq_43703185/article/details/104792803

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卷积

反卷积

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