University of Central Florida
CAP5415 - Computer Vision
Problem Set 2
Fall 2009
Assigned: Friday, September 18, 2009
Due: Thursday, October 1, 2009
Note that because class will not be held on October 1, 2009, this problem set should be turned in on
October 6, 2009. However, the next assignment will be released on October 1, 2009, so please plan
accordingly.
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. For the questions that require you to code, please turn in the code.
Both Python and MATLAB versions of all files are available on the course webpage.
Problem 1
Given a set of Ntraining examples x1,...,xN, and labels l1, . . . , lNthe log-likelihood of the data is
L=
N
X
i=1
log 1 + exp ( −li(xi·θ) )
Where θis a vector of line parameters. Note that xi·θis the vector inner product (or dot-product) between
two vectors.
In the files associated with this problem set, we have included data and labels. Complete the function
calculate_log_loss(pts, labels), using the function header that we have provided as a starting
point.
To check your solution, we have gotten the following values in our implementation:
θ L
[0; 0; 1] 81.32
[1; 0; 1] 48.15
[1; 1; 1] 28.60
[1; 2; 2] 36.46
Problem 2
If f(x, y)=(x−2y)2+ (y−60)2, compute the gradient vector of f.
Problem 3
Complete the framework code provided in grad_desc_mod.m to implement steepest descent optimiza-
tion of the function from Problem 2. You should be able to achieve a value very close to zero. We have also
included visualization code.
1
