A Probabilistic Approach to Geometric Hashing using Line Features

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CHAPTER 2. PRIOR AND RELATED WORK 11 correspondence èhypothesisè between object models and the scene. Using this correspondence, a transformation can be computed and nearby features are sought èpredictionè. The privileged segments, together with their nearby features, are combined to compute a new transformation. Then the veriæcation step follows. Veriæcation is often accomplished using an alignment method. Usually there is a tradeoæ between the hypothesis generation stage and the veriæcation stage. If hypotheses are generated in a quick-and-dirty manner, then the veriæcation stage requires more eæort. If we want the veriæcation stage to be less pains-taking, then more reliable features have to be detected and more accurate hypotheses produced. In alignment by Huttenlocher and Ullman ë30,31ë, they consider aæne approximations to more general perspective transformations, using alignments of triplets of points. Models are processed sequentially during recognition. For each model, an exhaustive enumeration of all the possible pairings of three non-collinear points of the model and the scene is exercised. Thus the alignment method heavily relies on veriæcation. As a transformation is determined by the correspondence of model and scene features, the model is transformed and aligned to superimpose the image. Veriæcation of the entire edge contour, rather than just a few local feature points, is then performed to reduce the false alarm rate. To cope with the high computational cost of the veriæcation stage, a hierarchical scheme is used: Starting with a relatively simple and rapid check, they eliminate many false matches, and then conclude with a more accurate and slower check. To sum up, the hypothesis-prediction-veriæcation cycle relates scene images to object models and object models to scene images step by step with reænement in each step. Note also that any scheme using the ëhypothesis-prediction-veriæcation" paradigm can be tailored to a parallel implementation by using the overwhelming computing power to generate a great number of hypotheses concurrently and do veriæcations concurrently. 2.1.3 Transformation Accumulation Transformation accumulation is also called pose clustering ë50ë or the generalized Hough transform ë5ë, which ischaracterized by a ëparallel" accumulation of low level pose evidences, followed by a clustering step which selects pose hypotheses with strong support from the set of evidences. This method can be viewed as the inverse of template matching, which moves the model
CHAPTER 2. PRIOR AND RELATED WORK 12 template around all the positions of the scene and directly computes a value èusually crosscorrelationè as a measure of matching. Transformation accumulation, instead of trying all possible positions of the model in the scene, computes which positions are consistent with model features and scene features. Moreover, its use of all of the evidences without regard to their order of arrival can be advantageous when there are occlusions. The features used to generate pose hypotheses can be of high level or low level. If the level of features used are high enough, much less computational eæort is required for the accumulation stage. However, the trade-oæ is that higher level features are usually more diæcult to extract. The major problem of this technique usually lies in ensuring that all visible hypotheses are considered within acceptable limits of storage and computational resources. However, as computer power continues to grow while its cost continues to drop, this problem has been growing steadily less signiæcant. In the generalized Hough transform ë5ë, the transformation between a model and the scene is usually described by a set of transformation parameters. For example, four parameters are needed for the case of two-dimensional similarity transformations: two parameters for translation; one parameter for rotation; one parameter for scaling. Each transformation parameter is quantized in the so-called Hough space. The scene features vote for these parameters which are consistent with the pairings of these scene features and hypothesized model features. One problem of the generalized Hough transform is the size of the Hough space. In terms of two-dimensional cases, we face three-dimensional Hough space for rigid transformations; four-dimensional Hough space for similarity transformations; six-dimensional Hough space for aæne transformations. Tucker et al. ë53ë use local boundary features to constrain an object's position and orientation, which is then used as the basis for hypothesis generation. Their system takes advantage of the highly parallel processing power of the Connection Machine ë26ë to generate numerous transformation hypotheses concurrently and verify them concurrently. The number of processors required for each model is equal to the number of features of the model. Each scene feature participates, in parallel, independently in each processor to match model features for generating transformation hypotheses, which, after veriæed, are used for evidence accumulation for voting for the pose transformation of the object.
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
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Page 33 and 34: CHAPTER 3. NOISE IN THE HOUGH TRANS
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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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