CENG 466 Fundamentals of Image Processing
Jan 2011,
Final Exam 180 Minutes
Consider the following 3 bits/pixel image
3
2
5
6
5
7
1
2
2
0
4
0
6
2
1
4
a) Find a pyramid representation of the image at all levels by using the averaging filter
0.5
0.5
b) Find a nonlinear transformation T to stretch the gray values [0, 7] to [0, 11] interval.
c) Plot the streched image and its histogram, you obtained in part b.
Consider the following signature function, where the origin is taken at the center of mass:
a) Find the shape, corresponding to the above signature function
b) Represent this shape by the Medial Axis Transform.
c) Represent this shape by a 4-directional chain code.
3. Consider a database, with binary images of size 64x64. The images consists of one pixel wide
vertical and horizantal stripes. Some samples are given below:
a) Develop a segmentation algorithm to extract the object boundaries. Plot the output of your
algorithm for the second image using polygon representation.
b) Design a similarity metric based on co-occurence matrices for representing each region
i) What is the position operators you suggest for each region.
ii) Find the co-occurence matrix for a 4x4 matrix for each position operator you suggested.
Consider the 3 bits/pixel 4x4 image represented by bit planes as follows
1 0
0 0
0 0
0 0
0 0
0 0
1 0
0 0
Most Significant bit
1
0
0
0
1
1
1
0
1 0
1 1
1 1
1 1
Second bit
1 0 0 0
0 1 1 0
0 1 1 0
0 0 0 1
Least Significant bit
a) Plot this image indicating each gray level by an integer.
b) Develop a color quantization algorithm of this image to reduce the image to 2 bits/pixels.
Plot the output image.
c) Develop an algoritm to down-sample this image to a size of 2x2.
d) Find the Fourier Transform of the most significant bit in the downsampled2x2 image.