CSCI 510/EENG 510
Image and Multidimensional Signal Processing
Fall 2015
Homework Assignment 5
Due Monday, November 9, 2015
Notes: Please email me your solutions for these problems (in order) as a single Word or PDF document. If you do
a problem on paper by hand, please scan it in and paste it into the document (although I would prefer it typed!).
1. (20 pts) Do Principal Components Analysis (PCA) on the pixels of the RGB image
“pears.png” from the Matlab image processing toolbox and show how it can be represented
with two values per pixel. Give:
a. The 3 eigenvalues and 3 eigenvectors for this image.
b. Show the color RGB image reconstructed from the top two principal components.
c. Plot the reconstructed pixels in RGB space.
2. (20 pts) (This is exercise 6.15 in the Gonzalez and Woods textbook.) Consider the following
image composed of solid color squares. For discussing your answer, choose a gray scale
consisting of eight shades of gray, 0 through 7, where 0 is black and 7 is white. Suppose that
the image is converted to HSI color space.
a. Sketch the hue image and provide the values in the image.
b. Sketch the saturation image and provide the values in the image.
c. Sketch the intensity image and provide the values in the image.
If you cannot assign a specific value to a point in the resulting image, explain why.
Red
Green
Blue
Magenta
Cyan
Yellow
White
Black
3. (20 pts) In class you trained a decision tree to classify two types of shapes (“plus” and
“hearts”), and applied the tree to classify an unknown shape. Another type of classifier is the
“minimum distance” classifier, which chooses the class with the minimum distance to the
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CSCI 510/EENG 510
Image and Multidimensional Signal Processing
Fall 2015
class center. Apply this classifier to the unknown shape, and find which class it belongs to.
Use the Mahalanobis distance as described in the lecture notes, and give the value of the
distance to the closest class. Use the same features that we used in class (i.e., “area” and
“solidity”). Although Matlab has a function to compute Mahalanobis distance, don’t use
that; compute it yourself instead.
4. (20 pts) Below is a small region of an image consisting of a noisy step edge. (The original
image had value=30 on the left of the step, and value=10 to the right of the step.) It was
corrupted by additive Gaussian noise with zero mean and variance = 6.5.
32
28
32
27
32
25
31
28
28
30
29
32
30
33
29
30
31
33
32
29
27
28
31
27
31
13
11
10
11
13
14
7
11
12
9
16
12
8
12
12
12
6
14
6
13
7
11
12
12
10
At the three points indicated by the boxes, compute the value of the adaptive filter shown in
Equation 5.3-12 in the textbook. (The size of the filter is 5x5.)
5. (20 pts) Give a summary of your progress so far on your final project. Describe your
approach, any findings or results obtained so far, and any problems that you are
encountering. Points will be given based on how much progress has been made, and how
specific the description is.
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