5x5 RGB图像卷积计算示例 - 步幅为1，无填充 - 常规

为了将I用三个独立的5 x 5矩阵表示，我们可以将RGB图像拆分为三个单独的通道矩阵。

假设I的红色通道为R，绿色通道为G，蓝色通道为B。

将I表示为三个独立的5 x 5矩阵如下：

R = [[R11, R12, R13, R14, R15], [R21, R22, R23, R24, R25], [R31, R32, R33, R34, R35], [R41, R42, R43, R44, R45], [R51, R52, R53, R54, R55]]

G = [[G11, G12, G13, G14, G15], [G21, G22, G23, G24, G25], [G31, G32, G33, G34, G35], [G41, G42, G43, G44, G45], [G51, G52, G53, G54, G55]]

B = [[B11, B12, B13, B14, B15], [B21, B22, B23, B24, B25], [B31, B32, B33, B34, B35], [B41, B42, B43, B44, B45], [B51, B52, B53, B54, B55]]

接下来，我们将计算I与K的卷积，其中K是一个3 x 3的卷积核，所有权重都等于-1。卷积的步幅stride为1，没有应用填充。

对于每个通道矩阵，我们将K应用于它，然后将结果相加，并加上偏置项b。

对于红色通道R的计算过程如下：

R_conv = [[(-1 * R11) + (-1 * R12) + (-1 * R13) + (-1 * R21) + (-1 * R22) + (-1 * R23) + (-1 * R31) + (-1 * R32) + (-1 * R33) + 1, (-1 * R12) + (-1 * R13) + (-1 * R14) + (-1 * R22) + (-1 * R23) + (-1 * R24) + (-1 * R32) + (-1 * R33) + (-1 * R34) + 1, (-1 * R13) + (-1 * R14) + (-1 * R15) + (-1 * R23) + (-1 * R24) + (-1 * R25) + (-1 * R33) + (-1 * R34) + (-1 * R35) + 1, (-1 * R21) + (-1 * R22) + (-1 * R23) + (-1 * R31) + (-1 * R32) + (-1 * R33) + (-1 * R41) + (-1 * R42) + (-1 * R43) + 1, (-1 * R22) + (-1 * R23) + (-1 * R24) + (-1 * R32) + (-1 * R33) + (-1 * R34) + (-1 * R42) + (-1 * R43) + (-1 * R44) + 1], [(-1 * R12) + (-1 * R13) + (-1 * R14) + (-1 * R22) + (-1 * R23) + (-1 * R24) + (-1 * R32) + (-1 * R33) + (-1 * R34) + 1, (-1 * R13) + (-1 * R14) + (-1 * R15) + (-1 * R23) + (-1 * R24) + (-1 * R25) + (-1 * R33) + (-1 * R34) + (-1 * R35) + 1, (-1 * R14) + (-1 * R15) + (-1 * R21) + (-1 * R24) + (-1 * R25) + (-1 * R31) + (-1 * R34) + (-1 * R35) + (-1 * R41) + 1, (-1 * R23) + (-1 * R24) + (-1 * R25) + (-1 * R32) + (-1 * R33) + (-1 * R34) + (-1 * R42) + (-1 * R43) + (-1 * R44) + 1, (-1 * R24) + (-1 * R25) + (-1 * R31) + (-1 * R34) + (-1 * R35) + (-1 * R41) + (-1 * R43) + (-1 * R44) + (-1 * R45) + 1], [(-1 * R13) + (-1 * R14) + (-1 * R15) + (-1 * R23) + (-1 * R24) + (-1 * R25) + (-1 * R33) + (-1 * R34) + (-1 * R35) + 1, (-1 * R14) + (-1 * R15) + (-1 * R21) + (-1 * R24) + (-1 * R25) + (-1 * R31) + (-1 * R34) + (-1 * R35) + (-1 * R41) + 1, (-1 * R15) + (-1 * R21) + (-1 * R22) + (-1 * R25) + (-1 * R31) + (-1 * R32) + (-1 * R35) + (-1 * R41) + (-1 * R42) + 1, (-1 * R24) + (-1 * R25) + (-1 * R31) + (-1 * R34) + (-1 * R35) + (-1 * R41) + (-1 * R43) + (-1 * R44) + (-1 * R45) + 1, (-1 * R25) + (-1 * R31) + (-1 * R32) + (-1 * R35) + (-1 * R41) + (-1 * R42) + (-1 * R45) + (-1 * R51) + (-1 * R52) + 1], [(-1 * R21) + (-1 * R22) + (-1 * R23) + (-1 * R31) + (-1 * R32) + (-1 * R33) + (-1 * R41) + (-1 * R42) + (-1 * R43) + 1, (-1 * R22) + (-1 * R23) + (-1 * R24) + (-1 * R32) + (-1 * R33) + (-1 * R34) + (-1 * R42) + (-1 * R43) + (-1 * R44) + 1, (-1 * R23) + (-1 * R24) + (-1 * R25) + (-1 * R33) + (-1 * R34) + (-1 * R35) + (-1 * R43) + (-1 * R44) + (-1 * R45) + 1, (-1 * R32) + (-1 * R33) + (-1 * R34) + (-1 * R42) + (-1 * R43) + (-1 * R44) + (-1 * R52) + (-1 * R53) + (-1 * R54) + 1, (-1 * R33) + (-1 * R34) + (-1 * R35) + (-1 * R43) + (-1 * R44) + (-1 * R45) + (-1 * R53) + (-1 * R54) + (-1 * R55) + 1]]

对于绿色通道G和蓝色通道B的计算过程与红色通道R类似。

最后，将三个通道矩阵R_conv，G_conv和B_conv组合成一个RGB图像矩阵I_conv。

I_conv = [[R_conv[0][0], G_conv[0][0], B_conv[0][0]], [R_conv[0][1], G_conv[0][1], B_conv[0][1]], [R_conv[0][2], G_conv[0][2], B_conv[0][2]], [R_conv[0][3], G_conv[0][3], B_conv[0][3]], [R_conv[0][4], G_conv[0][4], B_conv[0][4]], [R_conv[1][0], G_conv[1][0], B_conv[1][0]], [R_conv[1][1], G_conv[1][1], B_conv[1][1]], [R_conv[1][2], G_conv[1][2], B_conv[1][2]], [R_conv[1][3], G_conv[1][3], B_conv[1][3]], [R_conv[1][4], G_conv[1][4], B_conv[1][4]], [R_conv[2][0], G_conv[2][0], B_conv[2][0]], [R_conv[2][1], G_conv[2][1], B_conv[2][1]], [R_conv[2][2], G_conv[2][2], B_conv[2][2]], [R_conv[2][3], G_conv[2][3], B_conv[2][3]], [R_conv[2][4], G_conv[2][4], B_conv[2][4]], [R_conv[3][0], G_conv[3][0], B_conv[3][0]], [R_conv[3][1], G_conv[3][1], B_conv[3][1]], [R_conv[3][2], G_conv[3][2], B_conv[3][2]], [R_conv[3][3], G_conv[3][3], B_conv[3][3]], [R_conv[3][4], G_conv[3][4], B_conv[3][4]], [R_conv[4][0], G_conv[4][0], B_conv[4][0]], [R_conv[4][1], G_conv[4][1], B_conv[4][1]], [R_conv[4][2], G_conv[4][2], B_conv[4][2]], [R_conv[4][3], G_conv[4][3], B_conv[4][3]], [R_conv[4][4], G_conv[4][4], B_conv[4][4]]]