=========================preview======================
(ELEC317)midterm2b.pdf
======================================================
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.