Assume you are given an "image" matrix of size NxM. Reduce the image noise by implementing a mean filter window of size 9 (a 3x3 averaging window). The image matrix will have integer elements from 0 to 255 (to reflect 8 bits of resolution).

The averaging window is a square matrix of odd size where the center element (pixel) is the one that is being operated on. Replace the center pixel with the average of the pixels the matrix window encompasses. This is accomplished for every pixel. The output should be the filtered image matrix. Each average should be rounded to the nearest integer

Note: If the window filter overlaps the edge of an image use zero (0) for missing values

Example:

Operating on the first element of matrix

 [1  2  3  4  5; 6  7  8  9  10; 11 12 13 14 15]

would have the window:

 [0 0 0; 0 1 2; 0 6 7]

this will result in:

 B(1,1) = 2