Invariants for pattern recognition and classification / editor, Marcos A. Rodrigues.

Format:

Book

Contributor:

Rodrigues, Marcos A. (Marcos Aurelio)

Series:

Series in machine perception and artificial intelligence ; vol. 42.

Series in machine perception and artificial intelligence ; vol. 42

Language:

English

Subjects (All):

Optical pattern recognition.

Invariants.

Physical Description:

1 online resource (249 p.)

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, 2000.

Language Note:

English

Summary:

"This book was conceived from the realization that there was a need to update recent work on invariants in a single volume providing a useful set of references and pointers to related work. Since the publication in 1992 of J L Mundy and A Zisserman's Geometric Invariance in Computer Vision, the subject has been evolving rapidly. New approaches to invariants have been proposed and novel ways of defining and applying invariants to practical problem solving are testimony to the fundamental importance of the study of invariants to machine vision. This book represents a snapshot of current research around the world.A version of this collection of papers has appeared in the International Journal of Pattern Recognition and Artificial Intelligence (December 1999). The papers in this book are extended versions of the original material published in the journal. They are organized into two categories: foundations and applications. Foundation papers present new ways of defining or analyzing invariants, and application papers present novel ways in which known invariant theory is extended and effectively applied to real-world problems in interesting and difficult contexts. Each category contains roughly half of the papers, but there is considerable overlap. All papers carry an element of novelty and generalization that will be useful to theoreticians and practitioners alike. It is hoped that this volume will be not only useful but also inspirational to researchers in image processing, pattern recognition and computer vision at large."

Contents:

Contents; Preface; Chapter 1 Analysis and Computation of Projective Invariants from Multiple Views in the Geometric Algebra Framework; 1.1 Introduction; 1.2 Geometric Algebra: an Outline; 1.2.1 The geometric product and multivectors; 1.3 Projective Geometry and the Projective Split; 1.3.1 Projective transformations; 1.4 1D and 2D Projective Invariants from a Single View; 1.4.1 The 2D generalization of the cross-ratio; 1.5 3D Projective Invariants from Multiple Views; 1.5.1 The 3D generalization of the cross-ratio; 1.5.2 3D point projective invariants from image coordinates in two views

1.5.3 3D point projective invariants from image coordinates in three views1.6 Experimental Results; 1.7 Conclusions; Acknowledgments; Bibliography; Chapter 2 Invariants to Convolution and Rotation; 2.1 Introduction; 2.2 Mathematical Background; 2.3 Invariants to Convolution Composed of the Complex Moments; 2.4 Combined Invariants; 2.5 Additional Invariance; 2.6 Testing the Numerical Properties; 2.7 Application to Satellite Image Registration; 2.8 Conclusion; Acknowledgments; Bibliography; Chapter 3 A New Representation for Quartic Curves and Complete Sets of Geometric Invariants

3.1 Introduction3.2 Elliptical-Circular (E2C) Representation of Quartic Curves; 3.3 A Complete Set of Geometric Invariants; 3.4 Alignment; 3.5 Affine Equivalent Quartics; 3.6 Experiments; 3.7 Concluding Remarks; Bibliography; Chapter 4 A Robust Affine Invariant Metric on Boundary Patterns; 4.1 Introduction; 4.2 Invariant Metrics on Patterns; 4.3 Robustness Axioms; 4.4 Constructing Invariant Pattern Metrics; 4.5 The Reflection Metric; 4.6 Experimental Results; 4.7 Conclusion; Bibliography

Chapter 5 Invariant Geometric Properties of Image Correspondence Vectors as Rigid Constraints to Motion Estimation5.1 Introduction; 5.2 The Method: a Geometric Constraints Framework for Motion Analysis; 5.2.1 The 2D case; 5.2.2 The 3D case; 5.3 Description of the Algorithms; 5.3.1 Modified Geometric Algorithm with Total Least Squares Method (MGAT); 5.3.2 Modified Geometric Algorithm with Median Filter (MGAMF); 5.4 Experimental Results; 5.4.1 Experimental results based on synthetic images; 5.4.2 Experimental results based on real images; 5.5 Conclusions; Acknowledgements; Bibliography

Chapter 6 Features of Derivative Continuity in Shape6.1 Introduction; 6.2 Means and Methods; 6.2.1 Derivative interpolation and smoothing; 6.2.2 Difference scaling exponent, Hσ; 6.3 Demonstrations; 6.3.1 Fine shapes of gamma ray burst BATSE Trigger 551; 6.3.2 Comparing measures of scaling; 6.3.3 Evolutionary rates of G. tumida; 6.3.4 Shape scale display; 6.4 Discussion; Acknowledgements; Bibliography; Chapter 7 Fourier-Mellin Based Invariants for the Recognition of Multi-Oriented and Multi-Scaled Shapes - Application to Engineering Drawing Analysis; 7.1 Introduction

7.2 General Interpretation Structure

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786611934026

9781281934024

128193402X

9789812791894

9812791892

OCLC:

824359905