5x5 RGB图像与3x3卷积核的卷积计算示例

首先，我们将 I 和 K 展开为向量形式，以便进行卷积计算。

I 的展开形式为： I = [I11, I12, I13, I14, I15, I21, I22, I23, I24, I25, I31, I32, I33, I34, I35, I41, I42, I43, I44, I45, I51, I52, I53, I54, I55]

K 的展开形式为： K = [-1, -1, -1, -1, -1, -1, -1, -1, -1]

接下来，我们将 I 和 K 进行卷积计算。由于 stride=1，我们可以将 K 滑动步长为 1 地在 I 上进行卷积。

第一步，将 K 的第一个元素与 I 的第一个元素进行点乘： conv1 = I11 * (-1) + I12 * (-1) + I21 * (-1) + I22 * (-1) + I23 * (-1) + I31 * (-1) + I32 * (-1) + I41 * (-1) + I42 * (-1) = -1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 = -9

第二步，将 K 的第二个元素与 I 的第二个元素进行点乘： conv2 = I12 * (-1) + I13 * (-1) + I22 * (-1) + I23 * (-1) + I24 * (-1) + I32 * (-1) + I33 * (-1) + I42 * (-1) + I43 * (-1) = -1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 = -9

以此类推，我们可以计算出所有的卷积结果：

conv1 = -9 conv2 = -9 conv3 = -9 conv4 = -9 conv5 = -9 conv6 = -9 conv7 = -9 conv8 = -9 conv9 = -9 conv10 = -9 conv11 = -9 conv12 = -9 conv13 = -9 conv14 = -9 conv15 = -9 conv16 = -9 conv17 = -9 conv18 = -9 conv19 = -9 conv20 = -9 conv21 = -9 conv22 = -9 conv23 = -9 conv24 = -9 conv25 = -9

最后，我们将卷积结果加上偏置 b = 1：

conv1 = -9 + 1 = -8 conv2 = -9 + 1 = -8 conv3 = -9 + 1 = -8 conv4 = -9 + 1 = -8 conv5 = -9 + 1 = -8 conv6 = -9 + 1 = -8 conv7 = -9 + 1 = -8 conv8 = -9 + 1 = -8 conv9 = -9 + 1 = -8 conv10 = -9 + 1 = -8 conv11 = -9 + 1 = -8 conv12 = -9 + 1 = -8 conv13 = -9 + 1 = -8 conv14 = -9 + 1 = -8 conv15 = -9 + 1 = -8 conv16 = -9 + 1 = -8 conv17 = -9 + 1 = -8 conv18 = -9 + 1 = -8 conv19 = -9 + 1 = -8 conv20 = -9 + 1 = -8 conv21 = -9 + 1 = -8 conv22 = -9 + 1 = -8 conv23 = -9 + 1 = -8 conv24 = -9 + 1 = -8 conv25 = -9 + 1 = -8

因此，卷积结果为： [-8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8]