Description

5/5 - (2 votes)

Q1. a. Find the convolution of  ( ,  ) given by

 

  1. 3

 

  1. 5

With  ( ,  ) given by

 

  • 2

 

  • 1

 

Origin is at top leftmost element for both. [2]

 

  1. 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 3×3 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 4×4 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 4×4, the mean is 1 and variance is 3/2. Consider the 2×2 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   , .