MTSC 887 - Image Processing
Digital Image Fundamentals
August 24, 2020
Problem 1 (20 points). Illumination-reflectance modeling
Assume that a flat area with center at (x0, y0) is illuminated by a light
source with intensity distribution
i(x, y) = K · e?[(x?x0)2+(y?y0)2].
Let the reflectance of the area be constant and equal to 4 and let K = 127.
If the digital image is acquired with k bits of intensity resolution, and the
human eye can discent an abrupt change of eight shades of intensity between
adjacent pixels, what value of k will cause visible false contouring?
Problem 2 (20 points). Spatial relationships between pixels
For the below sub-image draw the shortest 4–, 8– and m– path between
pixels m and l and compute the corresponding lengths. Explain if there
does not exit a particular requested path. Solve for i) V = {0, 1} and ii)
Problem 3 (20 points). Image transformations
Show that the forward and inverse Fourier kernels r(x, y, u, v) = e?j2pi(ux/M+vy/N)
and s(x, y, u, v) = 1
MN
ej2pi(ux/M+vy/N) are separable and symmetric.
Programming Assignment 1 (30 points). Image interpolation
Download and unzip test images from blackboard page of the course.
Write a program that will
1. read a grayscale image
2. downsample the image by a factor of i) 2 and ii) 8
3. oversample back up to original resolution
4. compute the squared difference between the image of the previous step
and the original image
5. display all images and differences
6. compute the average squared difference between the two images.
Repeat the above process for i) nearest neighbor and ii) bilinear interpo-
lation. Show your results on 3 of the grayscale test images.
Write your program in function format, i.e. with input and output ar-
guments. One of the input arguments should be the input image filename
so that you can apply your program to any grayscale image. You can use
Matlab’s built-in functions for resampling.
Programming Assignment 2 (30 points). Image quantization
Download and unzip test images from blackboard page of the course.
Write a program that will
1. read a grayscale image
2. quantize pixel intensities to i) 6 and ii) 3 bits of accuracy.
3. compute the absolute difference between the image of previous step and
the original image
2
4. display all images and differences
5. compute the average absolute difference between the two images.
Show your results on 3 of the grayscale test images.
Write your program in function format, i.e. with input and output argu-
ments. One of the input arguments should be the input image filename so
that you can apply your program to any grayscale image. You can not use
Matlab’s built-in functions for quantization.
Programming Assignments Write-up For each programming assign-
ment, you are to turn in a brief report (instructions are posted on blackboard
page of the course). The report will determine the grade for each program-
ming assignment. Be well organized, type your reports and include figure
captions with a short descrption of all figures in the report. Motivation and
initiative are greatly encouraged and will earn extra points.