A Probabilistic Approach to Geometric Hashing using Line Features

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Acknowledgements My most sincere gratitude goes to my research advisor Professor Jacob T. Schwartz for his generous guidance, without which this dissertation can not be possible. To whom, I also owe the understanding of identifying research directions of scientiæc interest. Iwould also like to express my gratitude to Professor Wen-Hsiang Tsai of National Chiao-Tung University, Hsin-Chu, Taiwan, Republic of China. I took his course ëImage Processing" when I was an undergraduate senior. This is my ærst taste of applying computer technology to the processing of images. After two-year R.O.T.C. military service upon graduation, I came here to the Courant Institute in 1987 to further my study. Professor Stçephane Mallat's ëComputer Vision" course again intrigued my interest in the æeld of image analysis. Thanks are also due to Professor Jaiwei Hong, Professor Robert Hummel, Professor Richard Wallace, Professor Haim Wolfson, Dr. Isidore Rigoutsos, Mr. Ronie Hecker and Mr. Jyh-Jong Liu for various kinds of helps and discussions. I also thank the staæs in the Courant Robotics Laboratory, for the days we worked together, especially Dr. Xiaonan Tan for her encouragement. Finally, I thank my parents, truly and sincerely, for their patience, support and constant encouragement throughout the work and my whole life. iv
Abstract One of the most important goals of computer vision research is object recognition. Most current object recognition algorithms assume reliable image segmentation, which in practice is often not available. This research exploits the combination of the Hough method with the geometric hashing technique for model-based object recognition in seriously degraded intensity images. We describe the analysis, design and implementation of a recognition system that can recognize, in a seriously degraded intensity image, multiple objects modeled by a collection of lines. We ærst examine the factors aæecting line extraction by the Hough transform and proposed various techniques to cope with them. Line features are then used as primitive features from which we compute the geometric invariants used by the geometric hashing technique. Various geometric transformations, including rigid, similarity, aæne and projective transformations, are examined. We then derive the ëspread" of computed invariant over the hash space caused by ëperturbation" of the lines giving rise to this invariant. This is the ærst of its kind for noise analysis on line features for geometric hashing. The result of the noise analysis is then used in a weighted voting scheme for the geometric hashing technique. We have implemented the system described and carried out a series of experiments on polygonal objects modeled by lines, assuming aæne approximations to perspective viewing transformations. Our experimental results show that the technique described is noise resistant and suitable in an environment containing many occlusions. v
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CHAPTER 4. INVARIANT MATCHING USING
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Chapter 5 The Eæect of Noise on th
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CHAPTER 5. THE EFFECT OF NOISE ON T
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Chapter 6 Bayesian Line Invariant M
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CHAPTER 6. BAYESIAN LINE INVARIANT
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CHAPTER 6. BAYESIAN LINE INVARIANT
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Chapter 7 The Experiments In this c
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CHAPTER 7. THE EXPERIMENTS 82 j det
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CHAPTER 7. THE EXPERIMENTS 84 Speci
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CHAPTER 7. THE EXPERIMENTS 86 Figur
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CHAPTER 7. THE EXPERIMENTS 88 èaè
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CHAPTER 7. THE EXPERIMENTS 90 èaè
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CHAPTER 7. THE EXPERIMENTS 92 èeè
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CHAPTER 7. THE EXPERIMENTS 94 of li
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CHAPTER 8. CONCLUSIONS 96 We have a
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Appendix A Given a correspondence b
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Appendix B The components of the ma
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Bibliography ë1ë A. Aho, J. Hopcr
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BIBLIOGRAPHY 104 ë23ë W. E. L. Gr
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BIBLIOGRAPHY 106 ë47ë I. Rigoutso
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A Probabilistic Approach to Geometric Hashing using Line Features

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