2D Convolution (Valid)

Problem

Compute the valid-mode 2D convolution of an image with a kernel.

out[i][j] = sum over (a, b) of image[i + a][j + b] * kernel[kh - 1 - a][kw - 1 - b], so the kernel is flipped 180 degrees relative to cross-correlation. The output shape is (H - kh + 1) x (W - kw + 1).

Hint

Same sliding-window code as correlation, but read the kernel backwards.

Test cases

case 1

in: [[[1,2,3],[4,5,6],[7,8,9]],[[1,0],[0,0]]]

expected: [[5,6],[8,9]]

case 2

in: [[[1,2,3],[4,5,6],[7,8,9]],[[0,0,0],[0,1,0],[0,0,0]]]

expected: [[5]]

case 3

in: [[[1,2,3],[4,5,6],[7,8,9]],[[1,2],[3,4]]]

expected: [[23,33],[53,63]]

case 4

in: [[[1,2,3],[4,5,6]],[[1,1],[1,1]]]

expected: [[12,16]]

Starter codePython

def convolve2d(image, kernel):
    # Your code here
    pass

4 test cases · run your code against them in the editor