Louisiana State University
Department of Electrical and Computer Engineering
EE7730 - Image Analysis I
Fall 2006

Problem Set 3

Assigned: October 30, 2006 (Monday)
Due: November 6, 2006 (Monday)
What to Return: Email your m-files to me by midnight.

Problem (100points): 

(a) Find the mean and the covariance of a set of sample point in 2D space.

function [mu,cov] = meancov(x);

%
% Each sample is x_i. x_i is a 2-by-1 column vector.
% x = [x_1, x_2, ..., x_N];
%


(b) Find the Mahalanobis distance between a data point x and the mean of a class:

function [d] = mahalanobis(x,mu,cov);


%  
% d = (x-mu)'*inv(cov)*(x-mu)
%  


(c) Draw three-dimensional plot of Mahalanobis distances for all points in 2D space.

function [d] = drawmahalanobis(mu,cov)

%  
% d = (x-mu)'*inv(cov)*(x-mu) for all the points x in 2D space.
% 


(d)(Bonus 10points) Draw Mahalanobis ellipse for a given distance d, that is, 
the points x that satisfy the Mahalanobis distance equation (again in 2D space).

function [] = drawellipse(mu,cov,d)

%  
% x is such that (x-mu)'*inv(cov)*(x-mu)=d
%