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ELEC 317 Midterm Test (Spring 1998) Apr. 17. 1998.
1. An image x is passed into a system with transfer function T and the output image is y. Let T(i,j; x) represent the output at location (i,j) when the input is x. That is , y(i,j)=T(i,j; x).
a.
(5%) What is the property of T if it is linear?

b.
(5%) What is the property of T if it is shift invariant?


Assume that T is the FIR filter [3 3 3;3 3 3;3 3 3] such that
11
yi j) =3 xi + k, jl)

(, ( + k = C1 l = C1
c.
(10%) Show that this filter is linear.

d.
(10%) Show that this filter is shift invariant.

e.
(10%) Is this a high-pass filter or a low-pass filter? Why?


2. Comparison between averaging filter and median filter
a. (10%) Apply the 3x3 averaging filter f to the 3x3 image a. What is the output?
f= [1 1 1; 1 1 1; 1 1 1]/9;
a=[21 110 24; 22 23 24; 23 21 23];

Assume a(0,i)=a(1,i), a(4,i)=a(3,i), a(i,0)=a(i,1), a(i,4)=a(i,3) for all i.
b.
(10%) Apply a 3x3 median filter to the same image in part (a). What is the output?

c.
(10%) Both the averaging filter and the median filter can enhance a noisy image. What is the advantage and disadvantage of the averaging filter?

d.
(10%) What is the advantage and disadvantage of median filter?


3. Matlab programming
a. (10%) Write a Matlab routine to apply the 2-dimensional FIR filter, filt, to the image x, and then subsample the filtered image by a factor of 2:1 and return the final image.
function y=myfilter(x, filt) Do not worry about edge effects. Here x and filt are matrices of unknown size.
b. (10%) Write a Matlab routine to return the bitwise AND of the 0th and 4rd bit planes of an
image.
function y=bit0and4(x)