[作业/人工智能]作业5 - CNN卷积、池化、激活测试

手工实现

测试程序

import numpy as np

x = np.array([[-1, -1, -1, -1, -1, -1, -1, -1, -1],
              [-1, 1, -1, -1, -1, -1, -1, 1, -1],
              [-1, -1, 1, -1, -1, -1, 1, -1, -1],
              [-1, -1, -1, 1, -1, 1, -1, -1, -1],
              [-1, -1, -1, -1, 1, -1, -1, -1, -1],
              [-1, -1, -1, 1, -1, 1, -1, -1, -1],
              [-1, -1, 1, -1, -1, -1, 1, -1, -1],
              [-1, 1, -1, -1, -1, -1, -1, 1, -1],
              [-1, -1, -1, -1, -1, -1, -1, -1, -1]])
print("x=\n", x)
# 初始化 三个 卷积核
Kernel = [[0 for i in range(0, 3)] for j in range(0, 3)]
Kernel[0] = np.array([[1, -1, -1],
                      [-1, 1, -1],
                      [-1, -1, 1]])
Kernel[1] = np.array([[1, -1, 1],
                      [-1, 1, -1],
                      [1, -1, 1]])
Kernel[2] = np.array([[-1, -1, 1],
                      [-1, 1, -1],
                      [1, -1, -1]])

# --------------- 卷积  ---------------
stride = 1  # 步长
feature_map_h = 7  # 特征图的高
feature_map_w = 7  # 特征图的宽
feature_map = [0 for i in range(0, 3)]  # 初始化3个特征图
for i in range(0, 3):
    feature_map[i] = np.zeros((feature_map_h, feature_map_w))  # 初始化特征图
for h in range(feature_map_h):  # 向下滑动,得到卷积后的固定行
    for w in range(feature_map_w):  # 向右滑动,得到卷积后的固定行的列
        v_start = h * stride  # 滑动窗口的起始行(高)
        v_end = v_start + 3  # 滑动窗口的结束行(高)
        h_start = w * stride  # 滑动窗口的起始列(宽)
        h_end = h_start + 3  # 滑动窗口的结束列(宽)
        window = x[v_start:v_end, h_start:h_end]  # 从图切出一个滑动窗口
        for i in range(0, 3):
            feature_map[i][h, w] = np.divide(np.sum(np.multiply(window, Kernel[i][:, :])), 9)
print("feature_map:\n", np.around(feature_map, decimals=2))

# --------------- 池化  ---------------
pooling_stride = 2  # 步长
pooling_h = 4  # 特征图的高
pooling_w = 4  # 特征图的宽
feature_map_pad_0 = [[0 for i in range(0, 8)] for j in range(0, 8)]
for i in range(0, 3):  # 特征图 补 0 ,行 列 都要加 1 (因为上一层是奇数,池化窗口用的偶数)
    feature_map_pad_0[i] = np.pad(feature_map[i], ((0, 1), (0, 1)), 'constant', constant_values=(0, 0))
# print("feature_map_pad_0 0:\n", np.around(feature_map_pad_0[0], decimals=2))

pooling = [0 for i in range(0, 3)]
for i in range(0, 3):
    pooling[i] = np.zeros((pooling_h, pooling_w))  # 初始化特征图
for h in range(pooling_h):  # 向下滑动,得到卷积后的固定行
    for w in range(pooling_w):  # 向右滑动,得到卷积后的固定行的列
        v_start = h * pooling_stride  # 滑动窗口的起始行(高)
        v_end = v_start + 2  # 滑动窗口的结束行(高)
        h_start = w * pooling_stride  # 滑动窗口的起始列(宽)
        h_end = h_start + 2  # 滑动窗口的结束列(宽)
        for i in range(0, 3):
            pooling[i][h, w] = np.max(feature_map_pad_0[i][v_start:v_end, h_start:h_end])
print("pooling:\n", np.around(pooling[0], decimals=2))
print("pooling:\n", np.around(pooling[1], decimals=2))
print("pooling:\n", np.around(pooling[2], decimals=2))


# --------------- 激活  ---------------
def relu(x):
    return (abs(x) + x) / 2


relu_map_h = 7  # 特征图的高
relu_map_w = 7  # 特征图的宽
relu_map = [0 for i in range(0, 3)]  # 初始化3个特征图
for i in range(0, 3):
    relu_map[i] = np.zeros((relu_map_h, relu_map_w))  # 初始化特征图

for i in range(0, 3):
    relu_map[i] = relu(feature_map[i])

print("relu map :\n", np.around(relu_map[0], decimals=2))
print("relu map :\n", np.around(relu_map[1], decimals=2))
print("relu map :\n", np.around(relu_map[2], decimals=2))

输出

# 模拟一个原图像
x=
 [[-1 -1 -1 -1 -1 -1 -1 -1 -1]
 [-1  1 -1 -1 -1 -1 -1  1 -1]
 [-1 -1  1 -1 -1 -1  1 -1 -1]
 [-1 -1 -1  1 -1  1 -1 -1 -1]
 [-1 -1 -1 -1  1 -1 -1 -1 -1]
 [-1 -1 -1  1 -1  1 -1 -1 -1]
 [-1 -1  1 -1 -1 -1  1 -1 -1]
 [-1  1 -1 -1 -1 -1 -1  1 -1]
 [-1 -1 -1 -1 -1 -1 -1 -1 -1]]

# 特征图
feature_map:
 [[[ 0.78 -0.11  0.11  0.33  0.56 -0.11  0.33]
  [-0.11  1.   -0.11  0.33 -0.11  0.11 -0.11]
  [ 0.11 -0.11  1.   -0.33  0.11 -0.11  0.56]
  [ 0.33  0.33 -0.33  0.56 -0.33  0.33  0.33]
  [ 0.56 -0.11  0.11 -0.33  1.   -0.11  0.11]
  [-0.11  0.11 -0.11  0.33 -0.11  1.   -0.11]
  [ 0.33 -0.11  0.56  0.33  0.11 -0.11  0.78]]

 [[ 0.33 -0.56  0.11 -0.11  0.11 -0.56  0.33]
  [-0.56  0.56 -0.56  0.33 -0.56  0.56 -0.56]
  [ 0.11 -0.56  0.56 -0.78  0.56 -0.56  0.11]
  [-0.11  0.33 -0.78  1.   -0.78  0.33 -0.11]
  [ 0.11 -0.56  0.56 -0.78  0.56 -0.56  0.11]
  [-0.56  0.56 -0.56  0.33 -0.56  0.56 -0.56]
  [ 0.33 -0.56  0.11 -0.11  0.11 -0.56  0.33]]

 [[ 0.33 -0.11  0.56  0.33  0.11 -0.11  0.78]
  [-0.11  0.11 -0.11  0.33 -0.11  1.   -0.11]
  [ 0.56 -0.11  0.11 -0.33  1.   -0.11  0.11]
  [ 0.33  0.33 -0.33  0.56 -0.33  0.33  0.33]
  [ 0.11 -0.11  1.   -0.33  0.11 -0.11  0.56]
  [-0.11  1.   -0.11  0.33 -0.11  0.11 -0.11]
  [ 0.78 -0.11  0.11  0.33  0.56 -0.11  0.33]]]
  
# 池化层
pooling:
 [[1.   0.33 0.56 0.33]
 [0.33 1.   0.33 0.56]
 [0.56 0.33 1.   0.11]
 [0.33 0.56 0.11 0.78]]
pooling:
 [[0.56 0.33 0.56 0.33]
 [0.33 1.   0.56 0.11]
 [0.56 0.56 0.56 0.11]
 [0.33 0.11 0.11 0.33]]
pooling:
 [[0.33 0.56 1.   0.78]
 [0.56 0.56 1.   0.33]
 [1.   1.   0.11 0.56]
 [0.78 0.33 0.56 0.33]]
 
# RELU图
relu map :
 [[0.78 0.   0.11 0.33 0.56 0.   0.33]
 [0.   1.   0.   0.33 0.   0.11 0.  ]
 [0.11 0.   1.   0.   0.11 0.   0.56]
 [0.33 0.33 0.   0.56 0.   0.33 0.33]
 [0.56 0.   0.11 0.   1.   0.   0.11]
 [0.   0.11 0.   0.33 0.   1.   0.  ]
 [0.33 0.   0.56 0.33 0.11 0.   0.78]]
relu map :
 [[0.33 0.   0.11 0.   0.11 0.   0.33]
 [0.   0.56 0.   0.33 0.   0.56 0.  ]
 [0.11 0.   0.56 0.   0.56 0.   0.11]
 [0.   0.33 0.   1.   0.   0.33 0.  ]
 [0.11 0.   0.56 0.   0.56 0.   0.11]
 [0.   0.56 0.   0.33 0.   0.56 0.  ]
 [0.33 0.   0.11 0.   0.11 0.   0.33]]
relu map :
 [[0.33 0.   0.56 0.33 0.11 0.   0.78]
 [0.   0.11 0.   0.33 0.   1.   0.  ]
 [0.56 0.   0.11 0.   1.   0.   0.11]
 [0.33 0.33 0.   0.56 0.   0.33 0.33]
 [0.11 0.   1.   0.   0.11 0.   0.56]
 [0.   1.   0.   0.33 0.   0.11 0.  ]
 [0.78 0.   0.11 0.33 0.56 0.   0.33]]

用Pytorch实现

测试程序

# https://blog.csdn.net/qq_26369907/article/details/88366147
# https://zhuanlan.zhihu.com/p/405242579
import numpy as np
import torch
import torch.nn as nn

x = torch.tensor([[[[-1, -1, -1, -1, -1, -1, -1, -1, -1],
                    [-1, 1, -1, -1, -1, -1, -1, 1, -1],
                    [-1, -1, 1, -1, -1, -1, 1, -1, -1],
                    [-1, -1, -1, 1, -1, 1, -1, -1, -1],
                    [-1, -1, -1, -1, 1, -1, -1, -1, -1],
                    [-1, -1, -1, 1, -1, 1, -1, -1, -1],
                    [-1, -1, 1, -1, -1, -1, 1, -1, -1],
                    [-1, 1, -1, -1, -1, -1, -1, 1, -1],
                    [-1, -1, -1, -1, -1, -1, -1, -1, -1]]]], dtype=torch.float)
print(x.shape)
print(x)

print("--------------- 卷积  ---------------")
conv1 = nn.Conv2d(1, 1, (3, 3), 1)  # in_channel , out_channel , kennel_size , stride
conv1.weight.data = torch.Tensor([[[[1, -1, -1],
                                    [-1, 1, -1],
                                    [-1, -1, 1]]
                                   ]])
conv2 = nn.Conv2d(1, 1, (3, 3), 1)  # in_channel , out_channel , kennel_size , stride
conv2.weight.data = torch.Tensor([[[[1, -1, 1],
                                    [-1, 1, -1],
                                    [1, -1, 1]]
                                   ]])
conv3 = nn.Conv2d(1, 1, (3, 3), 1)  # in_channel , out_channel , kennel_size , stride
conv3.weight.data = torch.Tensor([[[[-1, -1, 1],
                                    [-1, 1, -1],
                                    [1, -1, -1]]
                                   ]])

feature_map1 = conv1(x)
feature_map2 = conv2(x)
feature_map3 = conv3(x)

print(feature_map1 / 9)
print(feature_map2 / 9)
print(feature_map3 / 9)

print("--------------- 池化  ---------------")
max_pool = nn.MaxPool2d(2, padding=0, stride=2)  # Pooling
zeroPad = nn.ZeroPad2d(padding=(0, 1, 0, 1))  # pad 0 , Left Right Up Down

feature_map_pad_0_1 = zeroPad(feature_map1)
feature_pool_1 = max_pool(feature_map_pad_0_1)
feature_map_pad_0_2 = zeroPad(feature_map2)
feature_pool_2 = max_pool(feature_map_pad_0_2)
feature_map_pad_0_3 = zeroPad(feature_map3)
feature_pool_3 = max_pool(feature_map_pad_0_3)

print(feature_pool_1.size())
print(feature_pool_1 / 9)
print(feature_pool_2 / 9)
print(feature_pool_3 / 9)

print("--------------- 激活  ---------------")
activation_function = nn.ReLU()

feature_relu1 = activation_function(feature_map1)
feature_relu2 = activation_function(feature_map2)
feature_relu3 = activation_function(feature_map3)
print(feature_relu1 / 9)
print(feature_relu2 / 9)
print(feature_relu3 / 9)

输出结果

torch.Size([1, 1, 9, 9])
tensor([[[[-1., -1., -1., -1., -1., -1., -1., -1., -1.],
          [-1.,  1., -1., -1., -1., -1., -1.,  1., -1.],
          [-1., -1.,  1., -1., -1., -1.,  1., -1., -1.],
          [-1., -1., -1.,  1., -1.,  1., -1., -1., -1.],
          [-1., -1., -1., -1.,  1., -1., -1., -1., -1.],
          [-1., -1., -1.,  1., -1.,  1., -1., -1., -1.],
          [-1., -1.,  1., -1., -1., -1.,  1., -1., -1.],
          [-1.,  1., -1., -1., -1., -1., -1.,  1., -1.],
          [-1., -1., -1., -1., -1., -1., -1., -1., -1.]]]])
--------------- 卷积  ---------------
tensor([[[[ 0.8108, -0.0780,  0.1442,  0.3664,  0.5886, -0.0780,  0.3664],
          [-0.0780,  1.0331, -0.0780,  0.3664, -0.0780,  0.1442, -0.0780],
          [ 0.1442, -0.0780,  1.0331, -0.3003,  0.1442, -0.0780,  0.5886],
          [ 0.3664,  0.3664, -0.3003,  0.5886, -0.3003,  0.3664,  0.3664],
          [ 0.5886, -0.0780,  0.1442, -0.3003,  1.0331, -0.0780,  0.1442],
          [-0.0780,  0.1442, -0.0780,  0.3664, -0.0780,  1.0331, -0.0780],
          [ 0.3664, -0.0780,  0.5886,  0.3664,  0.1442, -0.0780,  0.8108]]]],
       grad_fn=<DivBackward0>)
tensor([[[[ 0.3433, -0.5455,  0.1211, -0.1011,  0.1211, -0.5455,  0.3433],
          [-0.5455,  0.5656, -0.5455,  0.3433, -0.5455,  0.5656, -0.5455],
          [ 0.1211, -0.5455,  0.5656, -0.7678,  0.5656, -0.5455,  0.1211],
          [-0.1011,  0.3433, -0.7678,  1.0100, -0.7678,  0.3433, -0.1011],
          [ 0.1211, -0.5455,  0.5656, -0.7678,  0.5656, -0.5455,  0.1211],
          [-0.5455,  0.5656, -0.5455,  0.3433, -0.5455,  0.5656, -0.5455],
          [ 0.3433, -0.5455,  0.1211, -0.1011,  0.1211, -0.5455,  0.3433]]]],
       grad_fn=<DivBackward0>)
tensor([[[[ 0.3269, -0.1176,  0.5491,  0.3269,  0.1047, -0.1176,  0.7713],
          [-0.1176,  0.1047, -0.1176,  0.3269, -0.1176,  0.9936, -0.1176],
          [ 0.5491, -0.1176,  0.1047, -0.3398,  0.9936, -0.1176,  0.1047],
          [ 0.3269,  0.3269, -0.3398,  0.5491, -0.3398,  0.3269,  0.3269],
          [ 0.1047, -0.1176,  0.9936, -0.3398,  0.1047, -0.1176,  0.5491],
          [-0.1176,  0.9936, -0.1176,  0.3269, -0.1176,  0.1047, -0.1176],
          [ 0.7713, -0.1176,  0.1047,  0.3269,  0.5491, -0.1176,  0.3269]]]],
       grad_fn=<DivBackward0>)
--------------- 池化  ---------------
torch.Size([1, 1, 4, 4])
tensor([[[[1.0331, 0.3664, 0.5886, 0.3664],
          [0.3664, 1.0331, 0.3664, 0.5886],
          [0.5886, 0.3664, 1.0331, 0.1442],
          [0.3664, 0.5886, 0.1442, 0.8108]]]], grad_fn=<DivBackward0>)
tensor([[[[0.5656, 0.3433, 0.5656, 0.3433],
          [0.3433, 1.0100, 0.5656, 0.1211],
          [0.5656, 0.5656, 0.5656, 0.1211],
          [0.3433, 0.1211, 0.1211, 0.3433]]]], grad_fn=<DivBackward0>)
tensor([[[[0.3269, 0.5491, 0.9936, 0.7713],
          [0.5491, 0.5491, 0.9936, 0.3269],
          [0.9936, 0.9936, 0.1047, 0.5491],
          [0.7713, 0.3269, 0.5491, 0.3269]]]], grad_fn=<DivBackward0>)
--------------- 激活  ---------------
tensor([[[[0.8108, 0.0000, 0.1442, 0.3664, 0.5886, 0.0000, 0.3664],
          [0.0000, 1.0331, 0.0000, 0.3664, 0.0000, 0.1442, 0.0000],
          [0.1442, 0.0000, 1.0331, 0.0000, 0.1442, 0.0000, 0.5886],
          [0.3664, 0.3664, 0.0000, 0.5886, 0.0000, 0.3664, 0.3664],
          [0.5886, 0.0000, 0.1442, 0.0000, 1.0331, 0.0000, 0.1442],
          [0.0000, 0.1442, 0.0000, 0.3664, 0.0000, 1.0331, 0.0000],
          [0.3664, 0.0000, 0.5886, 0.3664, 0.1442, 0.0000, 0.8108]]]],
       grad_fn=<DivBackward0>)
tensor([[[[0.3433, 0.0000, 0.1211, 0.0000, 0.1211, 0.0000, 0.3433],
          [0.0000, 0.5656, 0.0000, 0.3433, 0.0000, 0.5656, 0.0000],
          [0.1211, 0.0000, 0.5656, 0.0000, 0.5656, 0.0000, 0.1211],
          [0.0000, 0.3433, 0.0000, 1.0100, 0.0000, 0.3433, 0.0000],
          [0.1211, 0.0000, 0.5656, 0.0000, 0.5656, 0.0000, 0.1211],
          [0.0000, 0.5656, 0.0000, 0.3433, 0.0000, 0.5656, 0.0000],
          [0.3433, 0.0000, 0.1211, 0.0000, 0.1211, 0.0000, 0.3433]]]],
       grad_fn=<DivBackward0>)
tensor([[[[0.3269, 0.0000, 0.5491, 0.3269, 0.1047, 0.0000, 0.7713],
          [0.0000, 0.1047, 0.0000, 0.3269, 0.0000, 0.9936, 0.0000],
          [0.5491, 0.0000, 0.1047, 0.0000, 0.9936, 0.0000, 0.1047],
          [0.3269, 0.3269, 0.0000, 0.5491, 0.0000, 0.3269, 0.3269],
          [0.1047, 0.0000, 0.9936, 0.0000, 0.1047, 0.0000, 0.5491],
          [0.0000, 0.9936, 0.0000, 0.3269, 0.0000, 0.1047, 0.0000],
          [0.7713, 0.0000, 0.1047, 0.3269, 0.5491, 0.0000, 0.3269]]]],
       grad_fn=<DivBackward0>)

可视化版本

测试程序

# https://blog.csdn.net/qq_26369907/article/details/88366147
# https://zhuanlan.zhihu.com/p/405242579
import torch
import torch.nn as nn
import matplotlib.pyplot as plt

plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号 #有中文出现的情况,需要u'内容
x = torch.tensor([[[[-1, -1, -1, -1, -1, -1, -1, -1, -1],
                    [-1, 1, -1, -1, -1, -1, -1, 1, -1],
                    [-1, -1, 1, -1, -1, -1, 1, -1, -1],
                    [-1, -1, -1, 1, -1, 1, -1, -1, -1],
                    [-1, -1, -1, -1, 1, -1, -1, -1, -1],
                    [-1, -1, -1, 1, -1, 1, -1, -1, -1],
                    [-1, -1, 1, -1, -1, -1, 1, -1, -1],
                    [-1, 1, -1, -1, -1, -1, -1, 1, -1],
                    [-1, -1, -1, -1, -1, -1, -1, -1, -1]]]], dtype=torch.float)
print(x.shape)
print(x)
img = x.data.squeeze().numpy()  # 将输出转换为图片的格式
plt.imshow(img, cmap='gray')
plt.title('原图')
plt.show()

print("--------------- 卷积  ---------------")
conv1 = nn.Conv2d(1, 1, (3, 3), 1)  # in_channel , out_channel , kennel_size , stride
conv1.weight.data = torch.Tensor([[[[1, -1, -1],
                                    [-1, 1, -1],
                                    [-1, -1, 1]]
                                   ]])
img = conv1.weight.data.squeeze().numpy()  # 将输出转换为图片的格式
plt.imshow(img, cmap='gray')
plt.title('Kernel 1')
plt.show()
conv2 = nn.Conv2d(1, 1, (3, 3), 1)  # in_channel , out_channel , kennel_size , stride
conv2.weight.data = torch.Tensor([[[[1, -1, 1],
                                    [-1, 1, -1],
                                    [1, -1, 1]]
                                   ]])
img = conv2.weight.data.squeeze().numpy()  # 将输出转换为图片的格式
plt.imshow(img, cmap='gray')
plt.title('Kernel 2')
plt.show()
conv3 = nn.Conv2d(1, 1, (3, 3), 1)  # in_channel , out_channel , kennel_size , stride
conv3.weight.data = torch.Tensor([[[[-1, -1, 1],
                                    [-1, 1, -1],
                                    [1, -1, -1]]
                                   ]])
img = conv3.weight.data.squeeze().numpy()  # 将输出转换为图片的格式
plt.imshow(img, cmap='gray')
plt.title('Kernel 3')
plt.show()

feature_map1 = conv1(x)
feature_map2 = conv2(x)
feature_map3 = conv3(x)

print(feature_map1 / 9)
print(feature_map2 / 9)
print(feature_map3 / 9)

img = feature_map1.data.squeeze().numpy()  # 将输出转换为图片的格式
plt.imshow(img, cmap='gray')
plt.title('卷积后的特征图1')
plt.show()

print("--------------- 池化  ---------------")
max_pool = nn.MaxPool2d(2, padding=0, stride=2)  # Pooling
zeroPad = nn.ZeroPad2d(padding=(0, 1, 0, 1))  # pad 0 , Left Right Up Down

feature_map_pad_0_1 = zeroPad(feature_map1)
feature_pool_1 = max_pool(feature_map_pad_0_1)
feature_map_pad_0_2 = zeroPad(feature_map2)
feature_pool_2 = max_pool(feature_map_pad_0_2)
feature_map_pad_0_3 = zeroPad(feature_map3)
feature_pool_3 = max_pool(feature_map_pad_0_3)

print(feature_pool_1.size())
print(feature_pool_1 / 9)
print(feature_pool_2 / 9)
print(feature_pool_3 / 9)
img = feature_pool_1.data.squeeze().numpy()  # 将输出转换为图片的格式
plt.imshow(img, cmap='gray')
plt.title('卷积池化后的特征图1')
plt.show()

print("--------------- 激活  ---------------")
activation_function = nn.ReLU()

feature_relu1 = activation_function(feature_map1)
feature_relu2 = activation_function(feature_map2)
feature_relu3 = activation_function(feature_map3)
print(feature_relu1 / 9)
print(feature_relu2 / 9)
print(feature_relu3 / 9)
img = feature_relu1.data.squeeze().numpy()  # 将输出转换为图片的格式
plt.imshow(img, cmap='gray')
plt.title('卷积 + relu 后的特征图1')
plt.show()

输出结果

原图经过对应的卷积核处理后,其特定的特征会被放大,这也是进行卷积操作的意义所在。
RELU激活函数将输出值转化为大于一的数,保证了梯度的连续性。

原图
[作业/人工智能]作业5 - CNN卷积、池化、激活测试_第1张图片
卷积核
[作业/人工智能]作业5 - CNN卷积、池化、激活测试_第2张图片 [作业/人工智能]作业5 - CNN卷积、池化、激活测试_第3张图片 [作业/人工智能]作业5 - CNN卷积、池化、激活测试_第4张图片
特征图
[作业/人工智能]作业5 - CNN卷积、池化、激活测试_第5张图片 [作业/人工智能]作业5 - CNN卷积、池化、激活测试_第6张图片 [作业/人工智能]作业5 - CNN卷积、池化、激活测试_第7张图片

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