版权声明：本文为博主原创文章，未经博主允许不得转载。 https://blog.csdn.net/hajungong007/article/details/86541244
一、概念
- 定义：感受野用来表示网络内部的不同神经元对原图像的感受范围的大小，或者说，convNets(cnn)每一层输出的特征图(feature map)上的像素点在原始图像上映射的区域大小。
- 神经元之所以无法对原始图像的所有信息进行感知，是因为在这些网络结构中普遍使用卷积层和pooling层，在层与层之间均为局部连接。
- 神经元感受野的值越大表示其能接触到的原始图像范围就越大，也意味着它可能蕴含更为全局，语义层次更高的特征；相反，值越小则表示其所包含的特征越趋向局部和细节。因此感受野的值可以用来大致判断每一层的抽象层次。
二、感受野计算
感受野计算时有下面的几个情况需要说明：
- 第一层卷积层的输出特征图像素的感受野的大小等于滤波器的大小。
- 深层卷积层的感受野大小和它之前所有层的滤波器大小和步长有关系。
- 计算感受野大小时，忽略了图像边缘的影响，即不考虑padding的大小，关于这个疑惑大家可以参考此文。
这里的每一个卷积层还有一个strides的概念，这个strides是之前所有层stride的乘积。
即strides（i） = stride(1) * stride(2) * …* stride(i-1)
关于感受野大小的计算采用top to down的方式， 即先计算最深层在前一层上的感受野，然后逐渐传递到第一层，使用的公式可以表示如下：
RF = 1 #待计算的feature map上的感受野大小
for layer in （top layer To down layer）:
RF = ((RF -1)* stride) + fsize
stride 表示卷积的步长； fsize表示卷积层滤波器的大小
用python实现了计算Alexnet zf-5和VGG16网络每层输出feature map的感受野大小，实现代码：
net_struct = {'alexnet': {'net':[[11,4,0],[3,2,0],[5,1,2],[3,2,0],[3,1,1],[3,1,1],[3,1,1],[3,2,0]],
'name':['conv1','pool1','conv2','pool2','conv3','conv4','conv5','pool5']},
'vgg16': {'net':[[3,1,1],[3,1,1],[2,2,0],[3,1,1],[3,1,1],[2,2,0],[3,1,1],[3,1,1],[3,1,1],
[2,2,0],[3,1,1],[3,1,1],[3,1,1],[2,2,0],[3,1,1],[3,1,1],[3,1,1],[2,2,0]],
'name':['conv1_1','conv1_2','pool1','conv2_1','conv2_2','pool2','conv3_1','conv3_2',
'conv3_3', 'pool3','conv4_1','conv4_2','conv4_3','pool4','conv5_1','conv5_2','conv5_3','pool5']},
'zf-5':{'net': [[7,2,3],[3,2,1],[5,2,2],[3,2,1],[3,1,1],[3,1,1],[3,1,1]],
'name': ['conv1','pool1','conv2','pool2','conv3','conv4','conv5']},
imsize = 1024
def outFromIn(isz, net, layernum):
totstride = 1
insize = isz
for layer in range(layernum):
fsize, stride, pad = net[layer]
outsize = (insize - fsize + 2*pad) / stride + 1
insize = outsize
totstride = totstride * stride
return outsize, totstride
def inFromOut(net, layernum):
RF = 1
for layer in reversed(range(layernum)):
fsize, stride, pad = net[layer]
RF = ((RF -1)* stride) + fsize
return RF
if __name__ == '__main__':
print ("layer output sizes given image = %dx%d" % (imsize, imsize))
for net in net_struct.keys():
print ('************net structrue name is %s**************'% net)
#ipdb.set_trace()
for i in range(len(net_struct[net]['net'])):
p = outFromIn(imsize,net_struct[net]['net'], i+1)
rf = inFromOut(net_struct[net]['net'], i+1)
print ("Layer Name = %s, Output size = %3d, Stride = %3d, RF size = %3d" % (net_struct[net]['name'][i], p[0], p[1], rf))
代码输出：
layer output sizes given image = 1024x1024
************net structrue name is alexnet**************
Layer Name = conv1, Output size = 254, Stride = 4, RF size = 11
Layer Name = pool1, Output size = 126, Stride = 8, RF size = 19
Layer Name = conv2, Output size = 126, Stride = 8, RF size = 51
Layer Name = pool2, Output size = 62, Stride = 16, RF size = 67
Layer Name = conv3, Output size = 62, Stride = 16, RF size = 99
Layer Name = conv4, Output size = 62, Stride = 16, RF size = 131
Layer Name = conv5, Output size = 62, Stride = 16, RF size = 163
Layer Name = pool5, Output size = 30, Stride = 32, RF size = 195
************net structrue name is vgg16**************
Layer Name = conv1_1, Output size = 1024, Stride = 1, RF size = 3
Layer Name = conv1_2, Output size = 1024, Stride = 1, RF size = 5
Layer Name = pool1, Output size = 512, Stride = 2, RF size = 6
Layer Name = conv2_1, Output size = 512, Stride = 2, RF size = 10
Layer Name = conv2_2, Output size = 512, Stride = 2, RF size = 14
Layer Name = pool2, Output size = 256, Stride = 4, RF size = 16
Layer Name = conv3_1, Output size = 256, Stride = 4, RF size = 24
Layer Name = conv3_2, Output size = 256, Stride = 4, RF size = 32
Layer Name = conv3_3, Output size = 256, Stride = 4, RF size = 40
Layer Name = pool3, Output size = 128, Stride = 8, RF size = 44
Layer Name = conv4_1, Output size = 128, Stride = 8, RF size = 60
Layer Name = conv4_2, Output size = 128, Stride = 8, RF size = 76
Layer Name = conv4_3, Output size = 128, Stride = 8, RF size = 92
Layer Name = pool4, Output size = 64, Stride = 16, RF size = 100
Layer Name = conv5_1, Output size = 64, Stride = 16, RF size = 132
Layer Name = conv5_2, Output size = 64, Stride = 16, RF size = 164
Layer Name = conv5_3, Output size = 64, Stride = 16, RF size = 196
Layer Name = pool5, Output size = 32, Stride = 32, RF size = 212
************net structrue name is zf-5**************
Layer Name = conv1, Output size = 512, Stride = 2, RF size = 7
Layer Name = pool1, Output size = 256, Stride = 4, RF size = 11
Layer Name = conv2, Output size = 128, Stride = 8, RF size = 27
Layer Name = pool2, Output size = 64, Stride = 16, RF size = 43
Layer Name = conv3, Output size = 64, Stride = 16, RF size = 75
Layer Name = conv4, Output size = 64, Stride = 16, RF size = 107
Layer Name = conv5, Output size = 64, Stride = 16, RF size = 139