Question

I’m writing a program that allows to preform the SuperResolution algorithm. In the book, on the way of restoration, they uses the discrete Laplacian operator. I must somehow multiply the matrix (my image) by this Laplacian operator. So, i have to represent this operator as a matrix, but i cant imagine HOW?

The text from the book:

The Laplacian is a second-derivative term, but for discrete data, it
can be approximated by a single convolution with a mask of form:

The operator preforms this convolution as matrix multiplication. It has the form like below (blank represents zeroes).

P.S. sorry for my English! 🙂

Answer 1

You just need to apply the 3×3 convolution kernel to your image, e.g. in pseudo-code:

for i = 1 to M - 1
    for j = 1 to N - 1
        img_out[i][j] = 4 * img[i][j] - img[i-1][j] - img[i+1][j] - img[i][j-1] - img[i][j+1]

where img is the input image, M is the number of rows, N is the number of cols, img_out is the convolved output image.

Note that the border pixels in img_out are undefined.