ECE 6532 Digital Image Processing Assignment 1 Due date: Friday ...

ECE 6532 Digital Image Processing
Assignment 1
Due date: Wednesday, September 11
General guidelines
Please submit your answers electronically as a pdf file. Electronic submissions are due at 5 pm on the
specified date (email to tolga@sci.utah.edu). Matlab functions you create must be emailed, printouts of
the functions will not be accepted. All materials should be sent in one email with the subject ECE6962
Assignment. Make sure to put your name on all written and electronic submissions.
MATLAB question guidelines:
• Name the .m files with the same name as the function. For instance, if the question asks you to create
a function named IntensityTransform1, it should be saved in a file named IntensityTransform1.m. If
you write other subfunctions that are used by the main function IntensityTransform1, they should also
be included in the same .m file after the main function.
• You are not allowed to use any functions from the MATLAB Image Processing Toolbox or any other
toolboxes in your methods. Only functions that are part of the basic MATLAB package may be used.
QUESTIONS
1. Let f be an image with the histogram
p f (z) =
{ 2
255 2 z z ∈ [0, 255]
0 otherwise
Let g be the image that is the result of applying gamma correction s = 1
255 r2 to f. Find the histogram
for g. Assume that both images are continuous valued.
2. Give an intensity transformation function for linearly spreading the intensities of any given image so
the lowest intensity is 0 and the highest is 255.
3. Problem 3.7 from textbook. Assume that the image intensities are continuous valued.
4. Let f(x, y) and g(x, y) be two images with histograms p f and p g , respectively. Let
h(x, y) = 0.5 (f(x, y) + g(x, y)) .
Is the histogram of the image h(x, y) always the average of the histograms p f and p g ? Justify your
answer.
5. Problem 3.11 from textbook.
6. Implement the intensity transform T (r) shown in the figure below as a MATLAB function. Name your
MATLAB function IntensityTransform1.

Your function should take as input an image and 4 parameters r1, r2, s1 and s2. You can assume the
following:
• The input image will be stored in a matrix of type uint8.
• The input image will have intensities in the range r ∈ [0, 255].
• 0 ≤ r1 < r2 ≤ 255 and 0 ≤ s1 ≤ s2 ≤ 255
The output should be the image with the transformed intensities s. The output image should be of
type uint8.
Hint: It is a good idea to convert the input image to type double at the start of your function and
to convert the output image back to type uint8 at the end.
7. For this question you will implement a locally adaptive intensity transform. Name your function
IntensityTransform2. It should take as input an image and two parameters a and b. Divide the image
into a × a blocks starting from coordinates (0, 0). Notice that some blocks at the right and bottom
edges of the image might be smaller than a × a, this is OK.
In each block compute the mean intensity µ and the standard deviation σ. The transform for a given
block will be defined as
(r − µ)b
s = T (r) = 128 + (1)
σ
Also clamp the output s given by this transformation to the range [0, 255]. In other words, if s as
defined above falls below 0 set it to 0. If it exceeds 255, set it to 255. Create an output image such
that each of the blocks are transformed in this way.
Try your method on the image tem2.pgm with the following sets of parameters:
• a = 128, b = 100
• a = 16, b = 100
• a = 128, b = 10.
Answer the following questions:
a) What effect do you observe when by changing a?
b) What effect do you observe when by changing b?
c) From your observations, briefly discuss what in your opinion is an advantage and a disadvantage
of this method as opposed to the one implemented in IntensityTransform1.