2-D convolution as a matrix-matrix multiplication

Question

I know that, in the 1D case, the convolution between two vectors, a and b, can be computed as conv(a, b), but also as the product betw

Answer 1

The code shown above doesn't produce the unrolled matrix of the right dimensions. The dimension should be (n-k+1)*(m-k+1), (k)(k). k: filter dimension, n: num rows in input matrix, m: num columns.

def unfold_matrix(X, k):
    n, m = X.shape[0:2]
    xx = zeros(((n - k + 1) * (m - k + 1), k**2))
    row_num = 0
    def make_row(x):
        return x.flatten()

    for i in range(n- k+ 1):
        for j in range(m - k + 1):
            #collect block of m*m elements and convert to row
            xx[row_num,:] = make_row(X[i:i+k, j:j+k])
            row_num = row_num + 1

    return xx

For more details, see my blog post:

http://www.telesens.co/2018/04/09/initializing-weights-for-the-convolutional-and-fully-connected-layers/