本文详细介绍了卷积神经网络中的感受野概念，包括其定义、计算方法以及在图像分类、目标检测和语义分割等任务中的作用。感受野的大小影响网络对全局和局部特征的捕捉能力，较大的感受野对应更全局的特征，较小的感受野则关注细节。此外，还探讨了有效感受野的概念，它通常小于理论感受野，并且在计算时要考虑像素的使用频率。最后，提供了计算感受野的代码示例，如AlexNet和VGG16的网络结构。
一、定义
- 卷积神经网络输出特征图上的像素点
在原始图像上所能看到区域的大小，输出特征会受感受野区域内的像素点的影响
在卷积神经网络中,感受野(Receptive Field)是指特征图上的某个点能看到的输入图像的区域,即特征图上的点是由输入图像中感受野大小区域的计算得到的
- 图像的空间联系是局部的，就像人是通过一个
局部的感受野去感受外界图像一样，每一个神经元都不需要对全局图像做感受，每个神经元只感受局部的图像区域，然后在更高层，将这些感受不同局部的神经元综合起来就可以得到全局的信息了
图来自[1]
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.[1]
二、计算
卷积层(conv)和池化层(pooling)都会影响感受野,而激活函数层通常对于感受野没有影响,当前层的步长并不影响当前层的感受野,感受野和填补(padding)没有关系, 计算当层感受野的公式如下:
其中,
表示当前层的感受野, 
表示上一层的感受野, 
表示卷积核的大小,例如3*3的卷积核,则 
表示之前所有层的步长的乘积(不包括本层),公式如下:
下面来练练手,以AlexNet举个例子
AlexNet(图来自[1])
我的一部分计算过程:
感受野计算的是否正确可使用 此链接：Receptive Field Calculator 提供的工具进行验证
tf 官方感受野计算代码
三、作用
感受野的值可以用来大致判断每一层的抽象层次：
感受野越大表示其能接触到的原始图像范围就越大，也意味着可能蕴含更为 全局、语义层次更高的特征
感受野越小则表示其所包含的特征越趋向于 局部和细节
辅助网络的设计：
一般任务：要求感受野越大越好，如图像分类中最后卷积层的感受野要大于输入图像，网络深度越深感受野越大性能越好
目标检测：设置 anchor 要严格对应感受野，anchor 太大或偏离感受野都会严重影响检测性能
语义分割：要求输出像素的感受野足够的大，确保做出决策时没有忽略重要信息，一般也是越深越好
多个小卷积代替一个大卷积层，在 加深网络深度（增强了网络容量和复杂度）的同时减少参数的个数：
小卷积核（如 ）通过多层叠加可取得与大卷积核（如
）同等规模的感受野
多层小卷积核和大卷积核具有同等感受野及减少参数的直观理解
四、拓展：有效感受野
- 实际上，上述的计算是理论感受野，而特征的有效感受野是
远小于理论感受野的- 且越靠近感受野
中心的值被使用次数越多，靠近边缘的值使用次数越少
通常上述公式求取的感受野通常很大,而实际的有效感受野(Effective Receptive Field)往往小于理论感受野,因为输入层中边缘点的使用次数明显比中间点要少,因此作出的贡献不同,所以经过多层的卷积堆叠后,输入层对于特征图点做出的贡献分布呈高斯分布形状
在使用Anchor作为强先验区域的物体检测算法中,如Faster RCNN和SSD,如何设置Anchor的大小,都应该考虑感受野,尤其是有效感受野,过大或过小都不好,来自[2]
2、感受野和 anchor 的关系
经典目标检测和最新目标跟踪中，都用到了 RPN(region proposal network)，anchor 是 RPN 的基础，感受野 是 anchor 的基础
目标检测中，anchor 大小及比例的设置应该跟该层特征的 有效感受野相匹配，anchor 比有效感受野大太多不好，小太多也不好
Equal-proportion interval principle: 感受野的大小设置为步长的 n（4） 倍
五、代码实现
# -*- coding: utf-8 -*-
"""
@File : compute_receptive_field.py
@Version : 1.0
"""
import numpy as np
# 需指定每层的 kernel_size, stride, pad, dilation, channel_num
net_struct = {
'vgg16': {'net': [[3, 1, 1, 1, 64], [3, 1, 1, 1, 64], [2, 2, 0, 1, 64], [3, 1, 1, 1, 128], [3, 1, 1, 1, 128],
[2, 2, 0, 1, 128],
[3, 1, 1, 1, 256], [3, 1, 1, 1, 256], [3, 1, 1, 1, 256], [2, 2, 0, 1, 256], [3, 1, 1, 1, 512],
[3, 1, 1, 1, 512],
[3, 1, 1, 1, 512], [2, 2, 0, 1, 512], [3, 1, 1, 1, 512], [3, 1, 1, 1, 512], [3, 1, 1, 1, 512],
[2, 2, 0, 1, 512]],
'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']},
'vgg16_ssd': {'net': [[3, 1, 1, 1, 64], [3, 1, 1, 1, 64], [2, 2, 0, 1, 64], [3, 1, 1, 1, 128], [3, 1, 1, 1, 128],
[2, 2, 0, 1, 128], [3, 1, 1, 1, 256], [3, 1, 1, 1, 256], [3, 1, 1, 1, 256], [2, 2, 0, 1, 256],
[3, 1, 1, 1, 512], [3, 1, 1, 1, 512], [3, 1, 1, 1, 512], [2, 2, 0, 1, 512], [3, 1, 1, 1, 512],
[3, 1, 1, 1, 512], [3, 1, 1, 1, 512], [3, 1, 1, 1, 512], [3, 1, 6, 6, 1024], [1, 1, 0, 1, 1024],
[1, 1, 0, 1, 256], [3, 2, 1, 1, 512], [1, 1, 0, 1, 128], [3, 2, 1, 1, 256], [1, 1, 0, 1, 128],
[3, 1, 0, 1, 256], [1, 1, 0, 1, 128], [3, 1, 0, 1, 256]],
'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',
'fc6', 'fc7', 'conv6_1', 'conv6_2', 'conv7_1', 'conv7_2', 'conv8_1', 'conv8_2', 'conv9_1',
'conv9_2']}
}
# 输出特征图大小的计算（down-top calculation）
def out_from_in(img_size_f, net_p, net_n, layer_len):
total_stride = 1
in_size = img_size_f
for layer in range(layer_len):
k_size, stride, pad, dilation, _ = net_p[layer]
net_name = net_n[layer]
if 'pool' in net_name:
out_size = np.ceil(1.0 * (in_size + 2 * pad - dilation * (k_size - 1) - 1) / stride).astype(np.int32) + 1
else:
out_size = np.floor(1.0 * (in_size + 2 * pad - dilation * (k_size - 1) - 1) / stride).astype(np.int32) + 1
in_size = out_size
total_stride = total_stride * stride
return out_size, total_stride
# 输出特征图上每个像素感受野的计算（top-down calculation）
def in_from_out(net_p, layer_len):
RF = 1
for layer in reversed(range(layer_len)):
k_size, stride, pad, dilation, _ = net_p[layer]
RF = ((RF - 1) * stride) + dilation * (k_size - 1) + 1
return RF
if __name__ == '__main__':
img_size = 300
print("layer output sizes given image = %dx%d" % (img_size, img_size))
for net in net_struct.keys():
print('************net structrue name is %s**************' % net)
for i in range(len(net_struct[net]['net'])):
p = out_from_in(img_size, net_struct[net]['net'], net_struct[net]['name'], i + 1)
rf = in_from_out(net_struct[net]['net'], i + 1)
print(
"layer_name = {:<8} output_size = {:<4} total_stride = {:<3} output_channel = {:<4} rf_size = {:<4}".format(
net_struct[net]['name'][i], p[0], p[1], net_struct[net]['net'][i][4], rf)
)
# vgg16 输出结果如下
layer output sizes given image = 300x300
************net structrue name is vgg16**************
layer_name = conv1_1 output_size = 300 total_stride = 1 output_channel = 64 rf_size = 3
layer_name = conv1_2 output_size = 300 total_stride = 1 output_channel = 64 rf_size = 5
layer_name = pool1 output_size = 150 total_stride = 2 output_channel = 64 rf_size = 6
layer_name = conv2_1 output_size = 150 total_stride = 2 output_channel = 128 rf_size = 10
layer_name = conv2_2 output_size = 150 total_stride = 2 output_channel = 128 rf_size = 14
layer_name = pool2 output_size = 75 total_stride = 4 output_channel = 128 rf_size = 16
layer_name = conv3_1 output_size = 75 total_stride = 4 output_channel = 256 rf_size = 24
layer_name = conv3_2 output_size = 75 total_stride = 4 output_channel = 256 rf_size = 32
layer_name = conv3_3 output_size = 75 total_stride = 4 output_channel = 256 rf_size = 40
layer_name = pool3 output_size = 38 total_stride = 8 output_channel = 256 rf_size = 44
layer_name = conv4_1 output_size = 38 total_stride = 8 output_channel = 512 rf_size = 60
layer_name = conv4_2 output_size = 38 total_stride = 8 output_channel = 512 rf_size = 76
layer_name = conv4_3 output_size = 38 total_stride = 8 output_channel = 512 rf_size = 92
layer_name = pool4 output_size = 19 total_stride = 16 output_channel = 512 rf_size = 100
layer_name = conv5_1 output_size = 19 total_stride = 16 output_channel = 512 rf_size = 132
layer_name = conv5_2 output_size = 19 total_stride = 16 output_channel = 512 rf_size = 164
layer_name = conv5_3 output_size = 19 total_stride = 16 output_channel = 512 rf_size = 196
layer_name = pool5 output_size = 10 total_stride = 32 output_channel = 512 rf_size = 212
# vgg16_ssd 输出结果如下
************net structrue name is vgg16_ssd**************
layer_name = conv1_1 output_size = 300 total_stride = 1 output_channel = 64 rf_size = 3
layer_name = conv1_2 output_size = 300 total_stride = 1 output_channel = 64 rf_size = 5
layer_name = pool1 output_size = 150 total_stride = 2 output_channel = 64 rf_size = 6
layer_name = conv2_1 output_size = 150 total_stride = 2 output_channel = 128 rf_size = 10
layer_name = conv2_2 output_size = 150 total_stride = 2 output_channel = 128 rf_size = 14
layer_name = pool2 output_size = 75 total_stride = 4 output_channel = 128 rf_size = 16
layer_name = conv3_1 output_size = 75 total_stride = 4 output_channel = 256 rf_size = 24
layer_name = conv3_2 output_size = 75 total_stride = 4 output_channel = 256 rf_size = 32
layer_name = conv3_3 output_size = 75 total_stride = 4 output_channel = 256 rf_size = 40
layer_name = pool3 output_size = 38 total_stride = 8 output_channel = 256 rf_size = 44
layer_name = conv4_1 output_size = 38 total_stride = 8 output_channel = 512 rf_size = 60
layer_name = conv4_2 output_size = 38 total_stride = 8 output_channel = 512 rf_size = 76
layer_name = conv4_3 output_size = 38 total_stride = 8 output_channel = 512 rf_size = 92
layer_name = pool4 output_size = 19 total_stride = 16 output_channel = 512 rf_size = 100
layer_name = conv5_1 output_size = 19 total_stride = 16 output_channel = 512 rf_size = 132
layer_name = conv5_2 output_size = 19 total_stride = 16 output_channel = 512 rf_size = 164
layer_name = conv5_3 output_size = 19 total_stride = 16 output_channel = 512 rf_size = 196
layer_name = pool5 output_size = 19 total_stride = 16 output_channel = 512 rf_size = 228
layer_name = fc6 output_size = 19 total_stride = 16 output_channel = 1024 rf_size = 420
layer_name = fc7 output_size = 19 total_stride = 16 output_channel = 1024 rf_size = 420
layer_name = conv6_1 output_size = 19 total_stride = 16 output_channel = 256 rf_size = 420
layer_name = conv6_2 output_size = 10 total_stride = 32 output_channel = 512 rf_size = 452
layer_name = conv7_1 output_size = 10 total_stride = 32 output_channel = 128 rf_size = 452
layer_name = conv7_2 output_size = 5 total_stride = 64 output_channel = 256 rf_size = 516
layer_name = conv8_1 output_size = 5 total_stride = 64 output_channel = 128 rf_size = 516
layer_name = conv8_2 output_size = 3 total_stride = 64 output_channel = 256 rf_size = 644
layer_name = conv9_1 output_size = 3 total_stride = 64 output_channel = 128 rf_size = 644
layer_name = conv9_2 output_size = 1 total_stride = 64 output_channel = 256 rf_size = 772
reference
目标检测和感受野的总结和想法 - 知乎 (zhihu.com)
1、关于感受野的理解与计算:https://www.jianshu.com/p/9997c6f5c01e
2、书籍《深度学习之PyTorch物体检测实战》
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