CSE586 Assignment 3, due March 17 Thurs
1) Prove that the set of all 2x2 matrices of the form [cos(theta) -sin
(theta); sin(theta) cos(theta)] form a group under matrix
multiplication.
2) Prove that the set of all complex numbers of the form e^cfw_i theta
CSE586/EE554 Computer Vision II
EM incremental assignments
Spring 2011
1. Given a d-dimensional mean vector v and dxd covariance matrix C (symmetric, pos def), generate
N random sample points distributed according to a Gaussian with mean v and covariance
Robert Collins
CSE586
CSE 586/EE554
Topics in Computer Vision
Course Introduction
Spring 2012
Robert Collins
CSE586
Course Goals
Gain practical knowledge in Computer Vision
focusing on solution methods
understanding the underlying math
knowing when/how
Homework 1 (due Monday Jan 24 by end of the day)
1. Consider the
x=1
y=0:
10
y=1:
10
y=2:
0
(unnormalized) 2D bivariate distribution f(x,y)
x=2
x=3
x=4
10
10
10
20
20
0
10
0
0
For each of the following, give your answer
to 1)
a) What is the marginal distr
Note: this derivation for the covariance matrix may not be correct
(although it gets the right answer). The reason why is that we havent
done anything to constrain the sigma matrix to be symmetric. For a
symmetric matrix, all the elements are not independ
Robert Collins
CSE586
Introduction to Graphical Models
Readings in Prince textbook: Chapters 10 and 11
but mainly only on directed graphs at this time
Credits: Several slides are from:
Review: Probability Theory
Sum rule (marginal distributions)
Product
Robert Collins
CSE586
CSE 586, Spring 2011
Advanced Computer Vision
Procrustes Shape Analysis
Robert Collins
CSE586
Credits
lots of slides are due to
Lecture material from Tim Cootes University of Manchester.
For more info, see http:/www.isbe.man.ac.uk/~b
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Robert Collins
CSE586, PSU
Intro to Sampling Methods
CSE586 Computer Vision II
Penn State Univ
Robert Collins
CSE586, PSU
A Brief Overview of Sampling
Monte Carlo Integration
Sampling and Expected Values
Inverse Transform Sampling (CDF)
Rejection Sampling
CSE586/EE554: Computer Vision II
Spring 2012 Course Overview
Instructor: Dr. Robert Collins, email: [email protected]
Office: IST 354H Office Hours: TBA
Course Description: Introduction of mathematical methods commonly used in computer vision
along wit
EM Motivation
want to do MLE of mixture of Gaussian parameters
But this is hard, because of the summation in the mixture
of Gaussian equation (cant take the log of a sum).
If we knew which point contribute to which Gaussian
component, the problem would