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QuestionBelow is the matrix of a 3x3 monochrome image:s = [[2, 1, 3], [4, 0, 2], [1, 5, 6]]And 2x2 weights:w = [[-1, -2], [1, 2]]Use the formula to determine the result of a two-dimensional convolution operation:

Question

QuestionBelow is the matrix of a 3x3 monochrome image:s = [[2, 1, 3], [4, 0, 2], [1, 5, 6]]And 2x2 weights:w = [[-1, -2], [1, 2]]Use the formula to determine the result of a two-dimensional convolution operation:

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Solution

To perform a two-dimensional convolution operation, we slide the 2x2 weights matrix over the 3x3 image matrix and multiply the overlapping values together, then sum them up.

Here's how to do it step by step:

  1. First, we align the top left corner of the weights matrix with the top left corner of the image matrix. The overlapping values are 2, 1, 4, and 0. We multiply each of these by the corresponding value in the weights matrix and sum them up:

    (-12) + (-21) + (14) + (20) = -2 - 2 + 4 + 0 = 0

  2. Next, we slide the weights matrix one step to the right. The overlapping values are now 1, 3, 0, and 2. We repeat the multiplication and summation process:

    (-11) + (-23) + (10) + (22) = -1 - 6 + 0 + 4 = -3

  3. We then slide the weights matrix one step down and to the left. The overlapping values are now 4, 0, 1, and 5. We repeat the multiplication and summation process:

    (-14) + (-20) + (11) + (25) = -4 - 0 + 1 + 10 = 7

  4. Finally, we slide the weights matrix one step to the right. The overlapping values are now 0, 2, 5, and 6. We repeat the multiplication and summation process:

    (-10) + (-22) + (15) + (26) = - 0 - 4 + 5 + 12 = 13

So, the result of the two-dimensional convolution operation is a new 2x2 matrix:

[[0, -3], [7, 13]]

This problem has been solved

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