Fourier Vision

Segmentation and Velocity Measurement using the Fourier Transform

By: David Vernon

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Hardcover | 30 June 2001

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210 Pages

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23.5 x 15.88 x 1.27

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Fourier Vision provides a new treatment of figure-ground segmentation in scenes comprising transparent, translucent, or opaque objects. Exploiting the relative motion between figure and ground, this technique deals explicitly with the separation of additive signals and makes no assumptions about the spatial or spectral content of the images, with segmentation being carried out phasor by phasor in the Fourier domain. It works with several camera configurations, such as camera motion and short-baseline binocular stereo, and performs best on images with small velocities/displacements, typically one to ten pixels per frame. The book also addresses the use of Fourier techniques to estimate stereo disparity and optical flow. Numerous examples are provided throughout.
Fourier Vision will be of value to researchers in image processing & computer vision and, especially, to those who have to deal with superimposed transparent or translucent objects. Researchers in application areas such as medical imaging and acoustic signal processing will also find this of interest.

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Preface	p. ix
Introduction	p. 1
Computer Vision	p. 1
Overview of the Fourier Vision Approach	p. 4
Camera Configurations	p. 7
Scope of the Book	p. 8
Mathematical Preliminaries	p. 11
The 2-D Fourier Transform	p. 11
The Continuous Fourier Transform	p. 11
The Discrete Fourier Transform	p. 13
Phasor Notation	p. 16
Properties of the Fourier Transform	p. 17
The Hough Transform	p. 21
Monocular Vision--Segmentation in Additive Images	p. 27
Overview	p. 27
The Segmentation Problem	p. 27
The Fourier Model of Segmentation	p. 29
The Additive Model for Temporal Sequences	p. 30
Solving for the Component Phasors	p. 31
Combining Phasors	p. 34
Application of the Technique	p. 36
Synthetic Images	p. 36
Real Images	p. 42
Conclusion	p. 46
Monocular Vision--Segmentation in Occluding Images	p. 49
Overview	p. 49
Figure-Ground Segmentation of Occluding Translating Objects	p. 50
Solution for the Phase Changes	p. 53
Solution for the Fourier Components	p. 56
Application of the Technique	p. 57
Synthetic Images	p. 57
Real Images	p. 57
Image Complexity	p. 64
Outstanding Issues	p. 69
The Three-Object Model	p. 70
Complex Motion	p. 71
A Sample of Motion/Stereo Segmentation Techniques	p. 71
Articulated Binocular Vision	p. 75
Motivation	p. 75
Overview	p. 76
Theoretical Framework	p. 76
Effecting Vergence and Fixation	p. 79
Fronto-Parallel Binocular Vision	p. 81
Formulation of the Problem	p. 81
The Computational Model	p. 83
Application of the Technique	p. 88
Caveat	p. 88
Instantaneous Optical Flow	p. 109
Motivation	p. 109
Velocity from Phase Change	p. 109
Overview--Two Images or Four?	p. 110
Measurement of Phase Change and Image Velocity	p. 110
Local Application using Apodized Windows	p. 111
Algorithm	p. 112
Examples	p. 114
Simple Gull Sequence	p. 114
Otte and Nagel Test Sequence	p. 116
Sunflower Garden Test Sequence	p. 121
Post-Processing	p. 123
Discussion	p. 123
Discontinuities in the Velocity Profile	p. 123
The Aperture Problem	p. 130
Accuracy	p. 131
Conclusions	p. 133
Postscript: Other Approaches	p. 133
Decoupled Optical Flow	p. 135
The Problem of Non-Unique Multiple Local Velocities	p. 135
Algorithm	p. 136
Examples	p. 136
Simple Gull Sequence	p. 136
Otte and Nagel Test Sequence	p. 138
Sunflower Garden Test Sequence	p. 144
Conclusion	p. 145
Epilogue	p. 155
References	p. 157
Index	p. 193
Table of Contents provided by Syndetics. All Rights Reserved.

Fourier Vision

Segmentation and Velocity Measurement using the Fourier Transform

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Hardcover

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