Statistical Optimization for Geometric Computation: Theory and Practice

by Kenichi Kanatani

Overview

This text discusses the mathematical foundations of statistical inference for building 3-dimensional models from image and sensor data that contain noise - a task involving autonomous robots guided by video cameras and sensors. The text employs a theoretical accuracy for the optimization procedure, which maximizes the reliability of estimations based on noise data. 1996 edition.

Product Details

ISBN-13:	9780486443089
Publisher:	Dover Publications
Publication date:	07/26/2005
Series:	Dover Books on Mathematics Series
Pages:	526
Product dimensions:	5.37(w) x 8.50(h) x (d)

Table of Contents

1. Introduction
2. Fundamentals of Linear Algebra
3. Probabilities and Statistical Estimation
4. Representation of Geometric Objects
5. Geometric Correction
6. 3-D Computation by Stereo Vision
7. Parametric Fitting
8. Optimal Filter
9. Renormalization
10. Applications of Geometric Estimation
11. 3-D Motion Analysis
12. 3-D Interpretation of Optical Flow
13. Information Criterion for Model Selection
14. General Theory of Geometric Estimation
References
Index

Editorial Reviews

Discusses the mathematical foundations of statistical inference for building a three-dimensional model of the environment from image and sensor data that contain noise, a task required of autonomous robots guided by video cameras and sensors. Derives a theoretical accuracy bound for the optimization procedure to maximize the reliability of the estimation based on noise data, and also the practical computation schemes to attain that bound. Includes examples of both synthetic and real data to demonstrate that conventional methods are not optimal and how accuracy improves if truly optimal methods are used. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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