Mathematical Methods in Computer Vision / Edition 1

by Peter J. Olver, Allen Tannenbaum

Overview

This volume comprises some of the key work presented at two IMA Workshops on Computer Vision during fall of 2000. Recent years have seen significant advances in the application of sophisticated mathematical theories to the problems arising in image processing. Basic issues include image smoothing and denoising, image enhancement, morphology, image compression, and segmentation (determining boundaries of objects-including problems of camera distortion and partial occlusion). Several mathematical approaches have emerged, including methods based on nonlinear partial differential equations, shastic and statistical methods, and signal processing techniques, including wavelets and other transform theories. Shape theory is of fundamental importance since it is the bottleneck between high and low level vision, and formed the bridge between the two workshops on vision. The recent geometric partial differential equation methods have been essential in throwing new light on this very difficult problem area. Further, shastic processes, including Markov random fields, have been used in a Bayesian framework to incorporate prior constraints on smoothness and the regularities of discontinuities into algorithms for image restoration and reconstruction. A number of applications are considered including optical character and handwriting recognizers, printed-circuit board inspection systems and quality control devices, motion detection, robotic control by visual feedback, reconstruction of objects from stereoscopic view and/or motion, autonomous road vehicles, and many others.

Product Details

ISBN-13:	9781441918260
Publisher:	Springer New York
Publication date:	11/29/2010
Series:	The IMA Volumes in Mathematics and its Applications , #133
Edition description:	Softcover reprint of hardcover 1st ed. 2003
Pages:	156
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

A large deviation theory analysis of Bayesian tree search * Expectation-based, multi-focal, saccadic vision * Statistical shape analysis in high-level vision * Maximal entropy for reconstruction of back projection images * On the Monge-Kantorovich problem and image warping * Analysis and synthesis of visual images in the brain: evidence for pattern theory * Nonlinear diffusions and optimal estimation * The Mumford-Shah functional: from segmentation to stereo