## CS/ECE 545 Homework 3

Complete by Class 4

Gaussian Image

Write a program to create an image having a gaussian intensity. That is, the brightness function should be

where x0 and y0 are the image center locations, A is a constant chosen to produce white at the image center, and s is a scale parameter. Try producing images using various values for s.

Gaussian Transform

Show that when x0=y0=0, the Fourier transform of the gaussian brightness function f(x,y) given above is

Hint: Treat the integration by x and y separately. You may find it helpful to use equation 15.73 of Schaum's Mathematical Handbook,

Median Filtering

Write a program which implements median filtering. Apply it to the images `king1.img` and `king2.img`. Notice, in particular, what happens to the uniform areas of the image (the wall in back). The original image `king.img` is in the image archive.

What happens if you apply median filtering to an image that contains significant small features, such as `galaxy.img` in the image archive? Apply it to the image `galaxy.img` to find out.

3x3 Median Filter Question

Find a solution to the question posed in Class 3.

What to hand in
Hand in to class