Engineering Applications of Noncommutative Harmonic Analysis

With Emphasis on Rotation and Motion Groups

Gregory S. Chirikjian, Alexander B. Kyatkin

• Publisher: CRC Press
• Year: 2021
• Print ISBN:
  9780367257187
• eBook ISBN:
  9781000697339
• Topic: Mathematics
• Subtopic: Computer Engineering
• Index: Mathematics

First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.

Table of contents

• Cover
• Halftitle page
• Title Page
• Copyright Page
• Dedication
• Authors
• Preface
• Table of Contents
• 1 Introduction and Overview of Applications
• 2 Classical Fourier Analysis
• 3 Sturm-Liouville Expansions, Discrete Polynomial Transforms and Wavelets
• 4 Orthogonal Expansions in Curvilinear Coordinates
• 5 Rotations in Three Dimensions
• 6 Rigid-Body Motion
• 7 Group Theory
• 8 Harmonic Analysis on Groups
• 9 Representation Theory and Operational Calculus for SU(2) and SO(3)
• 10 Harmonic Analysis on the Euclidean Motion Groups
• 11 Fast Fourier Transforms for Motion Groups
• 12 Robotics
• 13 Image Analysis and Tomography
• 14 Statistical Pose Determination and Camera Calibration
• 15 Stochastic Processes, Estimation, and Control
• 16 Rotational Brownian Motion and Diffusion
• 17 Statistical Mechanics of Macromolecules
• 18 Mechanics and Texture Analysis
• A Computational Complexity, Matrices, and Polynomials
• B Set Theory
• C Vector Spaces and Algebras
• D Matrices
• E Techniques from Mathematical Physics
• F Variational Calculus
• G Manifolds and Riemannian Metrics
• References
• Index