19图像卷积

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import torch
from torch import nn
from d2l import torch as d2l

def corr2d(X, K):  #@save
    """计算二维互相关运算"""
    h, w = K.shape
    Y = torch.zeros((X.shape[0] - h + 1, X.shape[1] - w + 1))
    for i in range(Y.shape[0]):
        for j in range(Y.shape[1]):
            Y[i, j] = (X[i:i + h, j:j + w] * K).sum()
    return Y

X = torch.tensor([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]])
K = torch.tensor([[0.0, 1.0], [2.0, 3.0]])
print('Y_corr2d = ', corr2d(X, K))

# 卷积层
class Conv2D(nn.Module):
    def __init__(self, kernel_size):
        super().__init__()
        self.weight = nn.Parameter(torch.rand(kernel_size))
        self.bias = nn.Parameter(torch.zeros(1))

    def forward(self, x):
        print('bias.shape = ', self.bias.shape)
        print(self.weight.sum())
        return corr2d(x, self.weight) + self.bias
# X = torch.tensor([[1.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 1.0]])
# co = Conv2D((2, 2))
# print('Y_Conv2D = ', co(X))

# 通过找到像素变化的位置，来检测图像中不同颜色的边缘。
# 构造一个像素的黑白图像。中间四列为黑色（0），其余像素为白色（1）。
X = torch.ones((6, 8))
X[:, 2:6] = 0
"""
tensor([[1., 1., 0., 0., 0., 0., 1., 1.],
        [1., 1., 0., 0., 0., 0., 1., 1.],
        [1., 1., 0., 0., 0., 0., 1., 1.],
        [1., 1., 0., 0., 0., 0., 1., 1.],
        [1., 1., 0., 0., 0., 0., 1., 1.],
        [1., 1., 0., 0., 0., 0., 1., 1.]])
"""
K = torch.tensor([[1.0, -1.0]])
Y = corr2d(X, K)
"""
tensor([[ 0.,  1.,  0.,  0.,  0., -1.,  0.],
        [ 0.,  1.,  0.,  0.,  0., -1.,  0.],
        [ 0.,  1.,  0.,  0.,  0., -1.,  0.],
        [ 0.,  1.,  0.,  0.,  0., -1.,  0.],
        [ 0.,  1.,  0.,  0.,  0., -1.,  0.],
        [ 0.,  1.,  0.,  0.,  0., -1.,  0.]])
"""
# 卷积核K只可以检测垂直边缘
# print(corr2d(X.t(), K))
"""
tensor([[0., 0., 0., 0., 0.],
        [0., 0., 0., 0., 0.],
        [0., 0., 0., 0., 0.],
        [0., 0., 0., 0., 0.],
        [0., 0., 0., 0., 0.],
        [0., 0., 0., 0., 0.],
        [0., 0., 0., 0., 0.],
        [0., 0., 0., 0., 0.]])
"""

# 学习由X生成Y的卷积核
conv2d = nn.Conv2d(1, 1, kernel_size=(1, 2), bias=False)
# 这个二维卷积层使用四维输入和输出格式（批量大小、通道、高度、宽度），
# 其中批量大小和通道数都为1
X = X.reshape((1, 1, 6, 8))
Y = Y.reshape((1, 1, 6, 7))
lr = 3e-2
for i in range(10):
    Y_hat = conv2d(X)
    l = (Y_hat - Y) ** 2
    conv2d.zero_grad()
    l.sum().backward()
    conv2d.weight.data[:] -= lr * conv2d.weight.grad
    if (i + 1) % 2 == 0:
        print(f'batch {i + 1}, loss {l.sum():.3f}')

"""
batch 2, loss 5.354
batch 4, loss 1.616
batch 6, loss 0.565
batch 8, loss 0.215
batch 10, loss 0.085
"""
# 卷积核的权重张量
# print(conv2d.weight.data.reshape((1, 2)))
"""tensor([[ 1.0287, -0.9564]])"""