python实现卷积运算

article/2025/10/23 10:27:00

一、卷积定义与朴素计算方法：

图1 卷积定义与计算方法

二、 Python代码实现

结合伪代码实现python代码如下（因为我是先写的代码，后才发现上面的伪代码，所以循环次序略有不同）：

import torch.nn as nn
import torchdef myConv2d(images, in_channels, out_channels, kernel_size, stride, padding, weights=None, bias=None):if weights is None:weights = torch.rand(out_channels, in_channels, kernel_size[0], kernel_size[1])if bias is None:bias = torch.zeros(out_channels)n, c, w, h = images.shape# 给原始图片加上padding# new_image = torch.zeros(n, c, w + 2 * padding, h + 2 * padding)images = images.clone()images = torch.cat((torch.zeros(n, c, padding, h), images), 2)images = torch.cat((images, torch.zeros(n, c, padding, h)), 2)images = torch.cat((torch.zeros(n, c, w + 2 * padding, padding), images), 3)images = torch.cat((images, torch.zeros(n, c, w + 2 * padding, padding)), 3)n, c, w, h = images.shapeoutput = []# 循环batch_sizefor i, im in enumerate(images):imout = []# 循环feature map count, 也就是输出通道数for j in range(out_channels):feature_map = []row = 0# 下面两层循环为使用kernel滑动窗口遍历输入图片while row + kernel_size[0] <= h:row_feat_map = []col = 0while col + kernel_size[1] <= w:# 卷积计算每个点的值，此处为了方便理解定义了channels,其实可以直接定义point=0，然后进行累加，最后再加上偏置channels = [0 for x in range(c)]for ch in range(c):for y in range(kernel_size[0]):for x in range(kernel_size[1]):channels[ch] += im[ch][row + y][col + x] * weights[j][ch][y][x]point = sum(channels) + bias[j]row_feat_map.append(point)col += stride[1]feature_map.append(row_feat_map)row += stride[0]imout.append(feature_map)output.append(imout)return torch.Tensor(output)if __name__ == "__main__":# 测试参数image_w, image_h = 7,7in_channels = 1out_channels = 1kernel_size = (2, 3)stride = (2,3)padding = 1# 输入图片与网络权重image = torch.rand(1, in_channels, image_w, image_h)weights = torch.rand(out_channels, in_channels, kernel_size[0], kernel_size[1])bias = torch.ones(out_channels)# pytorch运算结果net = nn.Conv2d(in_channels, out_channels, kernel_size=kernel_size, stride=stride, padding=padding, bias=True)net.weight = nn.Parameter(weights)net.bias = nn.Parameter(bias)net.eval()output = net(image)print(output)# 自己实现的结果output = myConv2d(image, in_channels, out_channels, kernel_size=kernel_size, stride=stride, padding=padding, weights=weights, bias=bias)print(output)

三、卷积运算图示

下图展示了padding=1, stride=(1,1), 不使用偏置bias的情况下，使用3*3的卷积核在的两个通道的5*5图片上的计算过程，其中卷积核权重为[[1,0,1], [-1,1,0], [0,-1,0]].