PyTorch笔记 - Convolution卷积运算的原理 (1)

Convolution：

• 元素：input size、kernel size、stride、padding、group、dilation(膨胀)

• 计算方法：F.conv2d、input展开+矩阵相乘、kernel展开+矩阵相乘

• 用途：局部建模、下采样

• 卷积与互相关

Transpose Convolution：

• 计算方法：F.conv_transpose2d、kernel转置+矩阵相乘
• 用途：上采样

PyTorch Conv2D：

• torch.nn.Conv2d
• torch.nn.functional.conv2d

Conv2D的参数：

• in_channels(输入通道), out_channels(输出通道), kernel_size(卷积核)
• stride=1(步长), padding=0(填充), dilation=1(膨胀)

卷积和信号互相关类似，对于一张图像，卷积核沿着图像的不同区域，滑动相乘

Input Feature Map，特征图，4x4

Kernel，卷积核，3x3

stride=1，padding=0

Z字型移动，从左到右，从上到下

bias是标量，卷积之后的再加上标量

二维卷积源码：

import torch
import torch.nn as nn
import torch.nn.functional as F

in_channels = 1
out_channels = 1
kernel_size = 3  # 可以是标量，也可以是元组
batch_size = 1  
bias = False
input_size = (batch_size, in_channels, 4, 4)  # 卷积的输入是4维，需要batch_size

# 初始化卷积
conv_layer = torch.nn.Conv2d(in_channels, out_channels, kernel_size, bias=bias)
# 卷积输入
input_feature_map = torch.randn(input_size)
# 卷积操作
output_feature_map = conv_layer(input_feature_map)
print(f'[Info] input_feature_map: \n{input_feature_map}') # 1x1x4x4
print(f'[Info] conv_layer.weight(kernel): \n{conv_layer.weight}') # 1x1x3x3
print(f'[Info] output_feature_map: \n{output_feature_map}')  # 1x1x2x2
# 输出公式: O=(I-K+2P)/S+1

output_feature_map_ = F.conv2d(input_feature_map, conv_layer.weight)
# F.conv2d和conv_layer的区别，在于传入kernel
print(f'[Info] output_feature_map_: \n{output_feature_map_}')  # 1x1x2x2