ECE-S490 Digital Image Processing
Laboratory 2
Image Filtering
1 Introduction
In this laboratory, you will filter gray scale images using both FIR and IIR filters. We will also use
Matlab to plot various functions. When processing images on a computer, there are usually
special cases that must be properly handled. In particular, all filters will be implemented using
free boundary conditions along edges, and pixels will be clipped to a range of [0, 255].
• Free boundary conditions - In order to understand a free boundary condition, consider an
M x N image denoted by img(i, j) where i = 1,.., M and j = 1,…,N. Some filtering
operations require that you index outside of this valid range. Pixels indexed outside this
range should be considered equal to zero.
• Clipping - Image processing operations will sometimes cause a pixel to exceed the value
255 or go below the value 0. In these cases, you could clip the pixel's value.
y(m, n) = 0 if x(m, n) < 0
y(m, n) = 255 if x(m, n) > 255
y(m, n) = x(m; n) if 0 <= x(m, n) <= 255
2 FIR Low Pass Filter
In this problem, you will analyze and implement a simple low pass filter given by the 9 x 9 point
spread function:
h(m, n) = 1/81 for m, n = -4, …, -1,0,1,…,4
h(m, n) = 0 otherwise
1. Calculate an analytical expression for H(ejµ ; ejν) the DSFT of h(m; n), and use Matlab to plot
the magnitude of the frequency response |H(ejµ ; ejν)| . Make sure to label the axis properly and
plot over the region [ -π ; π] x [ -π ; π] .
2. Load pout.tif image to Matlab by using the command “imread”.
4. Write a Matlab program to perform FIR filtering. Command line arguments should accept an
input image and a FIR filter kernel. Filter pout.tif with the h(m,n) given above.
5. Print out the original and the resulting filtered image.
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