ECE4580 Homework #3

ECE4580 Homework #3

On t-square you should be able to find the Matlab files needed for this assignment. Turn in code only if specified
in the homework. If submitting a homework document to t-square, please make sure that it is a single pdf file.
Problem 1. (25 pts) Implement the projection of a point in the world to a point on the image plane, then to a point
read in by a sensor. Use the viewer-centered projection equations given by,
r
1 = f
x
z
and r
2 = f
y
z
,
and the evenly-gridded sensor array equations,
R
1 = dr
1
/dr1
e +
W
2
and R
2 = dr
2
/dr2
e +
H
2
,
where d·e is the ceiling function. The sensor properties are those from a Panasonic WV-BP104 CCTV Camera, which
are as follows: the focal length parameter is 4 millimeters, the sensor dimensions are 4.8 × 3.6 millimeters, and the
sensor resolution is 800 × 600 (all given as width × height). These should be implemented in Matlab by a function
camera.m that takes in (x, y, z) world coordinate in meters (in 3x1 column vector form) and returns (R1
, R2
)
coordinate in pixels (in 2x1 column vector form).
(a) What is the field of view of the camera (horizontal and vertical) in degrees?
(b) The camera projection equations plot generalized lines to to generalized lines (where a point is a degenerate line,
e.g., a line that goes nowhere). After transformation under the camera projection equations, plot the following
lines and tell me what you see:
1. the line going from (−36.6, −25.7, 66.0) to (23.1, 0.1, 77.0), and
2. the line going from (−45.0, 49.7, 150.0) to (−81.0, 89.5, 270.0).
Either plot it with the axes set to [0, 800, 0, 600] using the axis command, or actually generate an image (this
is a bit more challenging) with zeros where there is nothing and ones where the line is.
(c) Likewise, plot the following:
1. a square whose bottom left corner is located at (−30.0, −15, 100.0) of width 7.5, and another one located
at (0.0, 27.6, 160.0) of width 12. The other corners of the squares should have the same z-distance as the
bottom left corner (so they are standing squares, so to speak).
Comment on their relative sizes? Make sure to set axes to be equal (e.g., ‘axis equal’) for all parts of the problem.
Make sure that your homework submission includes the plots in it. Also, please make sure to include the completed
stub as a separate submission attachment.
Problem 2. (15 pts) On t-square, there will be a Matlab file, called dpic, containing a depth image taken using
Microsoft’s Kinect camera. If you’ve played on the X-Box with the Kinect, you know that the game console can depict
a little image of you based on the camera information. In the Matlab file there is a depth image with a person in it. Try
to find two threshold values, upper and lower, such that when you threshold the images, what is left is a binary blob
that captures the person. Now, there might be other things that pass the threshold too. Use Matlab’s bwselect to
pick out only the blob the corresponds to the person.
Turn in, the depth range thresholds, the pixel coordinate used for bwselect, and the final extracted blob of the
person.
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Problem 3. (15 pts) In computer vision, binary decisions can sometimes be frustrating due to their, well, binary
nature. It is or it isn’t, yet sometimes you’d like it to be the other. Well, the clever people in image processing have
come up with this notion of performing a hysteresis type of computation.
Hysteresis is hard to explain, but a simplification is to say that the direction matters when considering the decision.
If a value is going upwards, then the threshold should be a bit higher. When it is going downwards, then the threshold
should be lower. By creating two thresholds, that are conditionally dependent, it is possible to capture regions that
might fail the first threshold test.
In a hysteresis approach to thresholding, there is an upper and a lower threshold. First, the algorithm binarizes
based on the upper threshold to arrive at candidate seed points. The second step seeks out neighbors of the candidate
seed points that pass the lower threshold test. In this way, some of the intially rejected regions can be subsequently
accepted.
The algorithm goes as:
1. First apply a high threshold to get candidate regions. (the easiest might be to use a threshold from your homework, or maybe a threshold from the solutions).
2. Apply a lower threshold to get a bigger set of regions, let’s call them the forgiving regions.
3. Using the points in the candidate regions and accept their (connected) neighbors if they are part of the forgiving
regiions.
4. The final answer is the set of candidate regions and the accepted neighbors.
A Matlab code stub, edgefind.m, already exists sort of outlining the above algorithm. The code stub gives hints
as to what Matlab functions to use in order to have simpler, more efficient code. Your job is to follow through on
the documented hints to finish the hysteresis algorithm as applied to edge detection. (Just as a note, the edgefind
function generates the same score as the edges1 score, so that’s the threshold that can be recycled.)
Using the grayscale image from the last edge assignment, finish up with the hysteresis-based edge finding function
and give it a run:
a) Flesh out the code associated to the code stub.
b) Pick a pair of hysteresis threshold values for the edge finding code stub. Turn in the threshold values plus the
edge image, and explain your selection.
c) Explain what you found easy or challenging about the upper and lower threshold selection. Do you like the
results better than when using a single threshold?
d) Turn in the code to t-square.
Problem 4. (10 pts) Read the paper by Lettvin et al that has been posted with the homework. This is the frog rewiring
experiment that discovered a frog’s sensitivity to small dark objects. A light reading, or skimming, is sufficient as you
won’t be tested on the paper. You should know kinda what they did and what they found. Tell me one thing that you
found interesting about the paper. Could be about their experiment, about their findings, or whatever else caught your
eye in the paper.
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