Q1. a. Find the convolution of ( , ) given by
3
5
With ( , ) given by
2
1
Origin is at top leftmost element for both.
[2]
b. Write a program to compute this convolution and verify if both the results are in consensus. You can use built in
functions. Refer to the lecture notes.
[2]
Q2. Find the response of a 3x3 median filter on ( , ) given by
3
4
1
8
6
6
5
4
3
Assume zero padding at the borders. The first output should correspond to the response of the filter with center at
element 3 at top left. Similarly last response should be at bottom right 3.
[2]
Q3. a. Perform histogram equalization (HE). Assume bit depth to be 2.
[1]
r
p(r)
z
p(z)
0
0.8
1
0.3
1
0.2
2
0.7
Give the output pixel values.
b. Write a code to perform HE for part a. You can refer to the lecture notes.
[2]
Q4. In a local/adaptive processing for a 4x4 image given by
[1]
3
3
0
0
3
3
0
1
1
0
1
0
0
0
0
1
Considering the global image to be 4x4, the mean is 1 and variance is 3/2. Consider the 2x2 local window in red color. Compute its mean and variance. Suppose you want to enhance the intensity in this region, and use constraints
<
2
< 2
, K 0, C 0
( , ) =
{
( , )
When the constraints are satisfied
( , )
ℎ
,
, 2
, 2
,
( , ) , ( , ) , 1
Find , .
