ECE4580 Homework #2

ECE4580 Homework #2

On t-square you should be able to find the necessary Matlab files containing all that you will need to implement
the homework.
Note: There is no need to turn in any code. It is sufficient to include your lines of code in the homework document,
or the values requested.
Problem 1. (15 pts) Many times in computer vision, a decision must be made given some kind of numerical criteria.
For scalar values, one simple decision is to threshold the quantity. Anything bigger than a given value belongs to class
A, while anything smaller belongs to class B (the equality case is application dependent). Humans rarely apply such a
technique due to its rather arbitrary and global nature. Let’s explore how such a simple decision can vary when we let
a computer numerically decide. You will partially play the role of the computer in this case.
As part of this homework problem, you will find a file called edgethresh.mat which has two Matlab variables
in it, edges1 and edges2 plus an image tsrb1. Both edges1 and edges2 are images that represent the output of
edge scoring algorithms. The algorithms ouput a numerical quantity that indicates how strong the evidence is towards
that particular region being an edge.
Look at the image and identify, in your head, where you think all of the edge looking parts of the image should be.
Then do the following in order (the a, b order is more important):
a) Modify the plotEdges.m m-file to include the threshold on the edge score. For this part, turn in the thresholds
used for each edge image, plus turn in the resulting edge plot images.
b) Now, most likely you will have noticed some unpleasant behavior in the thresholding process. Plus you wonder,
how in the world would a computer decide the threshold. Well, some people like to write a program that analyzes
the statistics of a property and use the statistics to decide the threshold.
Use the Matlab’s histogram function hist to generate a histogram of the edge scores. Edge’s are sparse objects
in the scene (meaning that the should represent a small percentage of the scene). Using the histogram plot, pick
a threshold for the edge score based on a value that rejects the majority of the edge scores. (In statistics, one
would say to avoid the peak and pick a value more in the tail of the distribution).
Using the histogram alone, pick a threshold for each edge score and repeat part a. Use the histEdges.m
m-file for this. Turn in the same information as part (a), but also include the histogram plot and mark where
your threshold was in relation to the histogram.
Hints: The hist function in Matlab implements a histogram, but it takes a 1D array, not a 2D array. So be
careful to send the proper argument. Also, the second argument to histogram are the histogram bins. I am not
a fan of the default bin selection. You may want to consider passing in your own bin array. You can pick the
bin centers, use linspace to generate them, or use the [xmin:dx:xmax] way of generating a regularly
spaced linear array of values.
c) Comment on the joy or frustration of selecting an edge set that roughly aligns with what you envisioned. What
were you trying to achieve, but somehow not being able to using the thresholds? If you did get what you wanted,
then explain why you feel satisfied by the final answer plots.
Problem 2. (15 pts) The filtering or image processing step discussed as part of the computer vision block diagram can be performed by utilizing many of Matlab’s built-in image processing functions. One such function is the
imfilter function. Let’s get used to this function by applying an averaging filter to some image. To apply the filter
requires invoking the Matlab command
aFilt = ones(n)/(nˆ2);
which generates an n × n matrix of ones, then divides by the size of the matrix. When this matrix is applied to an
image using Matlab’s imfilter command, it basically replaces each pixel with an average of its neighbors. The
neighborhood size is determined by the number n.
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a) Apply the imfilter command to the campus3 image in the filterme.mat Matlab file with a filter size of 5.
Now the averaging filter ends up smoothing things, which tends to have the effect of blurring the image. Tell me
one area that is no longer legibile due to the blurring, and one area that can still be read in spite of the blurring.
Why did the area pass through OK? What would be needed to make it unreadable?
b) The averaging filter matrix is an example of a convolution kernel. Read the course textbook, the online books, or
any other reliable source and describe another convolution kernel besides the averaging filter. What form does
it take and what does it do?
Hint: The images are in uint8 format which imfilter cannot really handle. A good first step would be to
convert them to double. An example conversion of the image I would be:
dI = double(I);
Also, when in doubt type help MatlabCommand, with the actual matlab command you are interested in knowing
more about, to get some help.
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