CSCI 510/EENG 510
Image and Multidimensional Signal Processing
Fall 2015
Homework Assignment 1
Due Monday, September 7, 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!).
I would like to get to know you and your interests so that I can provide the best possible
educational experience for you in this course. Please describe yourself – your general
background, education, interests, and goals. What specifically would you be interested in
learning about image processing? Are there any application areas that you are particularly
interested in? Are you currently doing thesis research that might benefit from image processing?
1.
(20 pts) It is often useful to generate a synthetic image with known properties that can be
used to test algorithms. Generate an image composed of two concentric circles as shown
below. The inner circle should have a radius of 50 pixels and a mean value of 192. The
outer circle should have a radius of 100 pixels and a mean value of 128. The background
should have a mean value of 64. Add uniform random noise to each pixel in the range -16 ..
+16 (see Matlab’s rand function). Save the image in “tif” format, and make sure the saved
image looks correct. Turn in the Matlab program and the image that you generated. (Hint:
recall the equation of a circle: x^2 + y^2 = r^2. These are the points on the circle border; to
represent points inside the circle, you would you use an inequality.)
2.
(20 pts) The “coins.png” image (available in the Matlab example images directory) has
light-colored coins against a dark background. As done in class, you can segment the coins
from the background using a simple global thresholding technique, such as
B = I > t;
where t is a value between 0 and 255 1. Write a Matlab program to calculate the maximum,
mean and standard deviation of the pixels in the regions corresponding to the coins (you
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There may be a couple of pixels that are not segmented correctly; don’t worry about that.
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CSCI 510/EENG 510
Image and Multidimensional Signal Processing
Fall 2015
don’t need to do this for each coin; just the union of the coin regions). Turn in the Matlab
program, the calculated values, and the image of the segmented coins.
3. (20 pts) As described in Section 2.1.1 of the textbook, we can treat the human fovea as a
square sensor array of size 1.5 mm x 1.5 mm, containing about 337,000 cones. Also, the
space between the cones is equal to width of the cones.
a) What is the field of view (in degrees) of the human fovea?
b) Estimate the distance from Brown Hall to the top of South Table Mountain (you can find
this using a map, or a webtool such as Microsoft Bing Maps, or Google Earth). What is
the minimum size object that you can see with the naked eye on top of the mountain?
Can you see a person on top of the mountain? Assume for simplicity that size of the
image of the object must cover at least two receptors (cones).
4. (20 pts) A pool-playing robot uses an overhead camera to determine the positions of the balls
on the pool table. Assume that:
a) We are using a standard billiard table of size 44" x 88".
b) We need at least 100 square pixels per ball to reliably determine the identity of each
ball.
c) The center of the ball can be located to a precision of +- one pixel in the image.
d) We need to locate the ball on the table to an accuracy of +- one cm.
e) We are going to mount the camera on the ceiling, looking straight down. The
distance from the camera to the table is 2 m.
Determine a configuration of the camera resolution and lens field of view (FOV) that will
meet these requirements. Assume that you can choose from the following parts:
Lenses with field of view 30, 60, 90 degrees
Cameras with resolutions of 256x256, 512x512, or 1024x1024 pixels
Choose the lowest camera resolution that will meet the requirements.
5. (20 pts) Develop a program to resize the example image “cameraman.tif” from its original
size of 256x256 to an enlarged size of 400x400, using bilinear interpolation. For this
problem, don’t use the Matlab functions “imresize” , “interp2” or the equivalent
OpenCV function. Turn in your program and the resulting image.
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