A Probabilistic Approach to Geometric Hashing using Line Features

More documents

Recommendations

Info

CHAPTER 2. PRIOR AND RELATED WORK 19 èvè establish a hypothesis of the existence of an instance of model M i in the scene if èM i ;b j è, for some j, peaks in the histogram with suæciently many hits; and repeat from step èiè, if all hypotheses established in step èvè fail veriæcation. The complexity of this stage is Oènè+Oètè per probe, where n is the number of points extracted from the scene and t is the complexity ofverifying an object instance. 2.2.2 Strengths and Weaknesses At a glance, geometric hashing seems similar to the transformation accumulation techniques discussed in section 2.1.3. However, the similarity lies only in the use of ëaccumulating evidence" by voting. The techniques discussed in section 2.1.3 accumulate ëpose" evidence while geometric hashing accumulates ëfeature correspondence" evidence. The former analysis always votes for parameters of transformations while the latter votes for èmodel identiæer, basis setè pair, where transformation parameters can be computed when the correspondence of scene feature set and model basis set is hypothesized. Strengths Most of the methods discussed in section 2.1 are search-based: Model features are searched to match scene features and this search process goes through each model in the model base sequentially. For example, the interpretation tree technique by Grimson ë23ë has inherent exponential complexity by pairing each scene feature to each model feature combinatorially. Geometric hashing greatly accelerates search of the model base by using a hashing technique to select candidate model features to match scene features. This process is at worst sublinear in the size of the model base. Like the transformation accumulation techniques, geometric hashing's voting scheme copes well with occlusion and with the fragility of existing image segmentation techniques. The accumulation of evidence without regard to order makes parallel implementation easy. Weaknesses Errors in feature extraction will commonly lead to perturbation of invariants and degradation of recognition performance, since perturbed invariant values are used to index the
CHAPTER 2. PRIOR AND RELATED WORK 20 hash table to retrieve candidate model features. Performance is similarly degraded by quantization noise introduced in constructing the hash table. Thus use of point features does not seem viable in a seriously degraded image, see ë21ë. The inherently non-uniform distribution of computed invariants in the hash table results in non-uniform hash bin occupancy for uniformly quantized hash table ë47ë. This degrades the index selectivity power of the hashing scheme used. 2.2.3 Geometric Hashing Systems Since the introduction of the geometric hashing method by Wolfson and Lamdan, a number of subsequent applications and improvements have been developed at the Robotics Research Laboratory of New York University and other research laboratories. Gavrila and Groen ë18ë apply the hashing technique for recognition of 3-D objects from single 2-D images. They determine limits of discriminability by experiments to generate viewpoint-centered models. Gueziec and Ayache ë24ë address the problem of fast rigid matching of 3-D curves in medical images. They incorporate six diæerential invariants associated with the surface and introduce an original table, where they hash values for the six transformation parameters. Hummel and Wolfson ë29ë discuss both the object matching and the curve matching by geometric hashing. Flynn and Jain ë17ë use invariant feature and the hashing technique to generate hypotheses without resorting to a voting procedure. They conclude that this method is more eæcient than a constrained search technique, for example, interpretation tree technique ë23ë. Recently, the work of Rigoutsos develops geometric hashing by incorporating a Bayesian model for weighted voting, which we describe in the next section. 2.3 The Bayesian Model of Rigoutsos The thesis work of Rigoutsos ë43ë from 1992 considerably extends the capability of the geometric hashing scheme. To cope with the problem caused by the positional uncertainty of point features, a Gaussian distribution is used to model the perturbation of the coordinate of the point. That
Page 1 and 2: A Probabilistic Approach to Geometr
Page 3 and 4: Dedication This dissertation is ded
Page 5 and 6: Abstract One of the most important
Page 7 and 8: 2.2.1 A Brief Description : : : : :
Page 9 and 10: List of Figures 3.1 A comparison of
Page 11 and 12: CHAPTER 1. INTRODUCTION 2 1.1 Model
Page 13 and 14: CHAPTER 1. INTRODUCTION 4 texture a
Page 15 and 16: CHAPTER 1. INTRODUCTION 6 reconstru
Page 17 and 18: CHAPTER 1. INTRODUCTION 8 Both synt
Page 19 and 20: CHAPTER 2. PRIOR AND RELATED WORK 1
Page 27: CHAPTER 2. PRIOR AND RELATED WORK 1
Page 33 and 34: CHAPTER 3. NOISE IN THE HOUGH TRANS
Page 49 and 50: CHAPTER 4. INVARIANT MATCHING USING
Page 69 and 70: Chapter 5 The Eæect of Noise on th
Page 71 and 72: CHAPTER 5. THE EFFECT OF NOISE ON T
Page 79 and 80:
CHAPTER 5. THE EFFECT OF NOISE ON T
Page 81 and 82:
CHAPTER 5. THE EFFECT OF NOISE ON T
Page 83 and 84:
Chapter 6 Bayesian Line Invariant M
Page 85 and 86:
CHAPTER 6. BAYESIAN LINE INVARIANT
Page 87 and 88:
CHAPTER 6. BAYESIAN LINE INVARIANT
Page 89 and 90:
Chapter 7 The Experiments In this c
Page 91 and 92:
CHAPTER 7. THE EXPERIMENTS 82 j det
Page 93 and 94:
CHAPTER 7. THE EXPERIMENTS 84 Speci
Page 95 and 96:
CHAPTER 7. THE EXPERIMENTS 86 Figur
Page 97 and 98:
CHAPTER 7. THE EXPERIMENTS 88 èaè
Page 99 and 100:
CHAPTER 7. THE EXPERIMENTS 90 èaè
Page 101 and 102:
CHAPTER 7. THE EXPERIMENTS 92 èeè
Page 103 and 104:
CHAPTER 7. THE EXPERIMENTS 94 of li
Page 105 and 106:
CHAPTER 8. CONCLUSIONS 96 We have a
Page 107 and 108:
Appendix A Given a correspondence b
Page 109 and 110:
Appendix B The components of the ma
Page 111 and 112:
Bibliography ë1ë A. Aho, J. Hopcr
Page 113 and 114:
BIBLIOGRAPHY 104 ë23ë W. E. L. Gr
Page 115:
BIBLIOGRAPHY 106 ë47ë I. Rigoutso
show all

A Probabilistic Approach to Geometric Hashing using Line Features

Create successful ePaper yourself

Delete template?

Save as template?