Part 1: Theoretical Concepts

problem 1: Given the following:

1    2    1    1    2    0
0    1    5    1    0    1
1    6    7    6    1    2

a) Draw the histogram of the original image.

b) find out the equalized image with eight possible gray levels. Show each step carefully.

• Draw the histogram of the equalized image.
• Show the equalized image.

problem 2: The given figure describes:

a) a 3-bit image of size 5-by-5 image in the square, with x and y coordinates specified,

b) a Laplacian filter.

find out the following:

a) The output of correlation of h= [1 1 0] and the first row. Assume the first row as 1-D image.

b) The output of convolution of h = [1 1 0] at (0,0). Assume the first row as 1-D image.

c) The output of a 3 × 3 mean filter at (2,2).

d) The output of a 3 × 3 median filter at (2,2).

e) The output of the 3 × 3 Laplacian filter shown above at (2,2).

Part 2: You must submit your matlab code as a .m matlab function well commented. Also you must submit all figures and relevant images as part of your work.

problem 3: Read the ‘Cameraman.tif’  image file into MATLAB and then display the image in a MATLAB figure window.    
                                
a) Apply a 3-by-3  average filter (A) in spatial domain on the original image and then display the filtered image.                            
b) Apply a 3-by-3 Laplacian filter (B) in spatial domain on the original image and then display the filtered image.                           
c) Based on the output images obtained from the above two filters, what you can deduce about the function for the two filters: (A) and  (B).                   

d) prepare the sequence of Matlab commands that can be applied to the original image and the results from (b) to implement the ‘Unsharp Masking’. What  you can deduce about the function of this process?