University of Central Florida
CAP5415 - Computer Vision
Problem Set 1
Fall 2008
Assigned: Thursday, September 4, 2008
Due: Tuesday, September 16, 2008
Introduction
Each of the sections below constitute one problem. If the problem asks for images, you should turn in a
print-out with the requested images. Ideally, your assignment should be composed in a word-processor,
such as L
A
T
E
Xor Microsoft Word. You are welcome to write out derivations by hand.
In your writeup, described the steps you completed for each problem and show the results. Readability
will be part of your grade.
1 Warmup
For this problem, turn in the necessary code to complete the following steps. Also turn in the resulting
images.
1. Download the images for PS 1 from the course web-page.
2. Choose two images
3. For each of these images
(a) Load the image into your environment
(b) Blur the image
(c) Display the result.
(d) Compute the DFT of the image
(e) Display the magnitude of the DFT
2 Fast Convolution
One day, you’re complaining to your officemate that your current research project requires you to do convo-
lution with very large kernels and that is just too slow. Your officemate smiles at you and cryptically says,
“But, computing an FFT on an image is O(N2log N) for an N×Nimage.”
1. If you have an N×Nimage and an M×Mkernel, what is the complexity (in big-Oh notation) of
convolving the kernel with the image.
2. How could you use the FFT to perform the same convolution?
3. What is the complexity of convolving the image using the method you just described?
4. Assuming that the big-Oh complexities were the actual complexities, for what sized kernel would the
FFT-based method be faster? You may assume that the image is a 512 ×512 image.
1
