Name: _________________________________
Score: /12
CSE 5524 Computer Vision for HCI
Homework Assignment #4
Due: See Carmen for due date
1) Write a function to compute the 7 similitude moment shape descriptors. Test and
compare results on the rectangle box images ‘boxIm[1-4].bmp’ on the website
(provide the computed moment values). Normalize each image before computing the
moments so that the range of grayscale values is between 0-1. How do the moments
change across the box images? Why are some moments zero? Please make sure your
function will work with non-binary (grayscale) imagery, as you will need this for later
assignments (do not use Matlab’s regionprops function). [4 pts]
Nvals = similitudeMoments(boxIm1);
2) Using the datafile (eigdata.txt) provided on the WWW site, perform the following
MATLAB commands [1 pt]:
%% Load the data
clear; close all;
load eigdata.txt;
X = eigdata;
subplot(2,1,1);
plot(X(:,1),X(:,2),'b.');
axis(‘equal’);
%% mean-subtract data
m = mean(X);
Y = X – ones(size(X,1),1)*m;
subplot(2,1,2);
plot(Y(:,1),Y(:,2),'r.');
axis(‘equal’);
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3) Compute the eigenvalues (V) and eigenvectors (U) of the data (stored in Y) using the
function eig() in Matlab (recall that you use either the covariance matrix or the
inverse-covariance matrix of the data – see class notes). Plot the mean-subtracted
data Y and the 2-D Gaussian ellipse axes for given the eigenvectors in U (you can use
the plot command in Matlab for this. Make sure the axes have equal scale in the
plot!). Use the eigenvalues in V to give the appropriate 3σ (standard deviation - not
variance!) length to each axis (did you compute the eigenvalues from the covariance
or inverse covariance of Y? The eigenvalues will be related but different! See class
notes). [4 pts]
[Note: it would also be nice to draw the 3σ ellipse around Y if you can – Google
‘matlab ellipse.m’ for some Matlab code if you are interested.]
4) Rotate Y using the eigenvectors to make the data uncorrelated (i.e., project data Y
onto the eigenvectors – see class slides). Plot the results (using equal scale axes as
before). [2 pts]
5) Perform a simple data reduction technique by keeping only the values resulting from
projection of Y onto the eigenvector corresponding the largest eigenvalue of the
covariance (not inverse-covariance) matrix. Plot a 1-D histogram of the values. Does
it look like a 1-D Gaussian? [1 pt]
6) Submit a report containing all code, printouts of images, and discussion of results.
Make a script to do the above tasks and call needed functions. Upload your report,
code, and images to Carmen as usual. [No free points for this last step anymore!]
From now on you MUST submit (on time) your report, all code, and imagery on Carmen to
receive points on the homework. Any portion missing will result in a 0 for the assignment!