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

f(x,y)= enter image description here

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.

enter image description here

Step 2: Apply Low pass mask to this image

Low pass mask h1(x,y(=(1/9)

g1(x,y)=f(x,y)h(x,y)= enter image description here

Step 3 : Apply High pass mask to the image

High pass mask h2(x,y) = (1/9). enter image description here

g2(x,y)=f(x,y)h2(x,y)= enter image description here

Step 4 : High pass = Original – Low Pass

enter image description here

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