Statistical Optimization for Geometric Computation: Theory and Practice

Kenichi Kanatani (Eds.)0444824278, 9780444824271

This book discusses mathematical foundations of statistical inference for building a 3-D model of the environment from image and sensor data that contain noise – a central task for autonomous robots guided by video cameras and sensors. A theoretical accuracy bound is derived for the optimization procedure for maximizing the reliability of the estimation based on noisy data, and practical computational schemes that attain that bound are derived. Many synthetic and real data examples are given to demonstrate that conventional methods are not optimal and how accuracy improves if truly optimal methods are employed.

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Table of contents :
Content:
Preface
Pages v-vi
Kenichi Kanatani

Chapter 1 Introduction Original Research Article
Pages 1-26

Chapter 2 Fundamentals of linear algebra Original Research Article
Pages 27-60

Chapter 3 Probabilities and statistical estimation Original Research Article
Pages 61-93

Chapter 4 Representation of geometric objects Original Research Article
Pages 95-130

Chapter 5 Geometric correction Original Research Article
Pages 131-170

Chapter 6 3-D computation by stereo vision Original Research Article
Pages 171-207

Chapter 7 Parametric fitting Original Research Article
Pages 209-246

Chapter 8 Optimal filter Original Research Article
Pages 247-265

Chapter 9 Renormalization Original Research Article
Pages 267-294

Chapter 10 Applications of geometric estimation Original Research Article
Pages 295-323

Chapter 11 3-D motion analysis Original Research Article
Pages 325-368

Chapter 12 3-D interpretation of optical flow Original Research Article
Pages 369-414

Chapter 13 Information criterion for model selection Original Research Article
Pages 415-450

Chapter 14 General theory of geometric estimation Original Research Article
Pages 451-499

Index
Pages 501-509