HETEROSCEDASTICITY,

A FUNDAMENTAL PROPERTY IN 3D VISION

12/14/1999

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Table of Contents

HETEROSCEDASTICITY, A FUNDAMENTAL PROPERTY IN 3D VISION

Outline of the Talk

Errors-in-Variables (EIV) Model

Heteroscedasticity

Heteroscedasticity

An Example

Heteroscedasticity in Computer Vision

Heteroscedasticity in Computer Vision

Heteroscedasticity in Computer Vision

Heteroscedasticity in Computer Vision

Heteroscedasticity in Computer Vision

The Traditional "Smallest" Eigenvector Method

The Traditional "Smallest" Eigenvector Method

Estimation Methods under Heteroscedasticity

Multivariate HEIV Algorithm

Multivariate HEIV Algorithm

HEIV

Properties of the HEIV algorithm

Properties of the HEIV algorithm

Relationship of HEIV to Other Methods

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HEIV Convergence

Levenberg-Marquardt Convergence

Ancillary Constraints

Fundamental Matrix Estimation

Fundamental Matrix Estimation

Fundamental Matrix Estimation

Fundamental Matrix Estimation

Fundamental Matrix Estimation

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Ellipse Fitting

Ellipse Fitting

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Ellipse Fitting - Estimation Errors

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3D Motion of a Stereo Head

Bootstrap Principle [Efron, 1979]

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Bootstrap Confidence Regions 

A 3D Vision System Example

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Author: Bogdan Matei  and Peter Meer

Email: matei@caip.rutgers.edu

Home Page: http://www.caip.rutgers.edu/~matei