EE5356 Digital Image Processing

Instructor: Dr. K.R. Rao

Spring 2012, Test 2

Tuesday, 3April 2012

2:00 – 3:20 PM (1 hour and 20 minutes)

(CLOSED BOOK, CLOSED NOTES)

INSTRUCTIONS:

1. Closed books and closed notes.

2. Please show all the steps in your works.

4. You can work problems in any order.

At the end please rearrange in the correct order.

5. Please print your name and student ID.

6. No cheating, no talking.

Name______

Student ID ______

  1. Show that the formula for extracting the nth bit of a pixel is

Where

u is a pixel value of an image

ki is either 0 or 1

i =1,2, … … , B

B is the number of quantization bits for each pixel. [points20]

  1. Write the purpose of using spatial averaging. In the 3X3 window in figure 1, fill up the weights for spatial averaging for a) equal weighting

b) 5 point unequal weighting

Figure 1: 3X3 window

[points10]

  1. The 2D- DFT of an image is given by

Where is the magnitude spectrum .

Write the equation for Root filter output . What is the effect of αrooting.

Figure 2: Root Filtering operation

[points 8]

  1. Explain contrast stretching operation clearly. Draw the contrast stretching transformation diagram for dark region stretch. [points 12]
  2. 2D (NXN) DFT of x(m,n) is XF (k,l)

Where k,l = 0,1,2 … … N-1

and 2D (NXN) DFT of [(-1)(m+n)x(m,n)] isXF (k-N/2,l-N/2).


Figure 3: Baseband spectrum for XF(k,l)

Baseband spectrum for XF(k,l) is shown in figure 3. Show all the steps to map

XF (k-N/2,l-N/2).Region A, B, C, D in figure 3 are LPF.

Figure 4: Baseband spectrum for XF(k,l)

Baseband spectrum for XF(k,l) is shown in figure 4. Show all the steps to map XF (k-N/2,l-N/2). Shaded regions in figure 4 are BPF. [points 20]

  1. Write‘T’ for true and ‘F’ for false [points 18]

a) Median filtering performs well for images with binary noise.

b) Median filtering performs well for images with Gaussian noise.

c) Unsharp masking technique is used for enhancing the edges of an image.

d)

Figure 5: Filtering operation

Suppose the cutoff frequencies of LPF1 and LPF2 in figure 5 arefc1and fc2 respectively.

If fc1fc2,the system will act as a BP filter.

e) The KL transform coefficients are correlated and have nonzero mean.

f) Inverse Gaussian filter is good for restoring images blurred by atmospheric turbulence.

  1. Describe clearly different histogram modeling techniques (equalization and specification) . [points 12]