The filter with matrix is a technique to process image based on mathematical calculation.
The basic procedure is as follows:


Original image.

Smoothed

Matrix={1,1,1, 1,1,1, 1,1,1}, n=9

Enedged

Matrix={0,-1,0, -1,5,-1, 0,-1,0}, n=1

Embossed

Matrix={0,0,0, -2,0,-2, 0,0,0}, n=4

Conversion from Color to Grayscale

GRAY=(BLUE*28+77*RED+GREEN*151)/256