Optimal Edge Detection &
Digital Picture Processing

1st edition, by James A. Green, Greenwood Research.
[ ] Large Hardback, ISBN-13: 978-1-890121-17-4 (ISBN 1-890121-17-7), 56.00 dollars.
[ ] Large Paperback, ISBN-13: 978-1-890121-50-1 (ISBN 1-890121-50-9), 43.20 dollars.

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This volume presents advanced Fourier optics with optimal edge detection based on spacial filtering using prolate spheroidal wavefunctions and their discrete digital equivalents. The effect of noise and blurred edge performance is treated along with the presentation of the filter functions, examples, competitive filters, and computed comparisons with other popular edge-detection algorithms.

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I. INTRODUCTION
II. OPTIMAL EDGE DETECTION - CONTINOUS CASE
__II.1 The Problem Definition.
__II.2 Prolate Spheroidal Wavefunctions
__II.3 Solution by Decomposition into Prolate Spheroidal Wave Functions
__II.4 The Asymptotic Form
__II.5 Blurred Edge Performance
__II.6 Noise
III. OPTIMAL EDGE DETECTION - DIGITAL CASE
__III.1 Three Formulations.
__III.2 Asymptotic Zero-Order Simulation.
__III.3 Aliasing Errors.
IV. COMPARATIVE STUDY.
V. SUMMARY.

APPENDIX A. Discrete Prolate Functions
APPENDIX B. Discrete-Orthogonality Prolate Functions
BIBLIOGRAPHY
INDEX
ABOUT THE AUTHOR
PROFILE
BOOKS BY JAMES A. GREEN

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LIST OF ILLUSTRATIONS
Portrait of the Author in 1990.
Figure 1. Plot of Prolate spheroidal wavefunctions for various values of C.
Figure 2. Blur Width.
Figure 3. Blurred Steps and Spectral Amplitudes.
Figure 6A. Edge Detection Filter Performance on a solid box.
Figure 6B. Edge Detection Filter Performance on a solid box.
Figure 7A. Edge Detection Filter Performance on a solid box with noise.
Figure 7B. Edge Detection Filter Performance on a solid box with noise.
Figure 8A. Relative Performance of Edge Detection Filters on Type.
Figure 8B. Relative performance of Edge Detection Filters.
Figure 9. Performance for Optimal, Laplacian, V-filter, Prolate Filter S/N=20 db.
Figure 9B. Performance of Optimal, Laplacian, High-Pass Filter with S/N=20 db.
Figure 10A. Performance of Edge Detection Filters on Photo of a Model.
Figure 10B. Performance of Edge Detection Filters on Photo of a Model.
Figure 11. Output of Optimal, Laplacian, & High-Pass filters for Noise Free Case.
Figure 12. Output of Optimal, Laplacian, & High-Pass filters for Low Noise.
Figure 13. Output of Edge Detection Filters, High-Noise Case.
Table 2. Edge Visibility Constants.
The M51 galactic system.
Les Mysteres des Infinis, by Grandville, 1844.
Electromagnetic Shower in the BEBC at CERN.
Orion and the Mythos of Light Speed.
Portrait of the Author in 1994.
Ablah Library Next to the Engineering Building Wallace Hall at WSU.

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No software is presently provided for this volume.

Supplemental Notes
[Links/Optimal Edge Detection, Papers, Books, Amazon; Links/Edge Detection in Digitized Images, Papers, Books, Amazon; Links/Digital Picture Processing, Papers, Books, Amazon; Wikipedia/Image Processing, Links/Image Processing, Papers, Books, Amazon].
This MSEE thesis was written in 1977. Since then, there has been progress in edge detection technology. The technique presented using prolate spheroidal wavefunctions in filtering to maximize energy in a chosen resolution width interval is optimal in some sense of the term, but produces doubled lines within the resolution width. The actual edge is located just between the two doubled lines. If an continuous-wave domain version of the filter is used with a laser, the lines may be focused so close together that the result seems to be a single solid line due to the finite resoluion of film, but in digital pictures one usually sees line doubling. Due to this circumstance, other edge detection techniques may seem better suited to the problem at hand. For instance, see John F. Canny's 1986 proposal:
Wikipedia/The Canny Edge Detector [Links/Canny Edge Detector, Papers, Books, Amazon].
Wikipedia/Edge Detection [Links/Edge Detection, Papers, Books, Amazon].
The edge detection problem was a subset of the feature extraction problem applied to computer vision analysis of scenes. For instance, an edge detection algorithm might be used to implement computer vision in flying robots, or to analyze scenes involving blood cells, to count blood cells in a sample. See
Wikipedia/Feature_detection_(computer_vision)
[Links/Feature Detection in Computer Vision, Papers, Books, Amazon].
Wikipedia/Computer Vision [Links/Computer Vision, Papers, Books, Amazon].
Because of these developments, my 1977 MSEE thesis now includes a short set of supplemental notes with links to websites and books dealing with optimal edge detection and related problems.
- April 12, 2010.

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