Let us consider an example to prove that Original – LPF Image = HPF Image Consider an image f(x,y)

f(x,y)=

We will do zero padding and then convolve the image with a standard 3 X 3 low pass and a high pass mask.

Step 1: Zero padding the original image

Zero padding is done to make the image a 5 X 5 image so that convolution can be done easily.

Step 2: Apply Low pass mask to this image

Low pass mask $h_1(x,y( =(1/9) $

$g1(x,y) = f(x,y)*h_(x,y) = $

Step 3 : Apply High pass mask to the image

High pass mask h2(x,y) = (1/9).

$g2(x,y) = f(x,y)*h2(x,y) = $

Step 4 : High pass = Original – Low Pass