ABSTRACT

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 sti

chapter 1|14 pages

Introduction and Overview of Applications

chapter 2|24 pages

Classical Fourier Analysis

chapter 5|38 pages

Rotations in Three Dimensions

chapter 6|38 pages

Rigid-Body Motion

chapter 7|52 pages

Group Theory

chapter 8|42 pages

Harmonic Analysis on Groups

chapter 11|26 pages

Fast Fourier Transforms for Motion Groups

chapter 12|40 pages

Robotics

chapter 13|36 pages

Image Analysis and Tomography

chapter 16|30 pages

Rotational Brownian Motion and Diffusion

chapter 17|34 pages

Statistical Mechanics of Macromolecules

chapter 18|28 pages

Mechanics and Texture Analysis