A Computational Framework for Segmentation and Grouping
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Table of contents
- Cover
- Table of Contentsv
- List of Figuresix
- Prefacexiii
- Acknowledgementsxv
- Chapter 1. Introduction1
- 1.1 Motivation and Goals3
- 1.2 Our Approach9
- 1.3 Overview of the Proposed Method15
- 1.4 Contribution of this book15
- 1.5 Notations20
- Chapter 2. Previous Work21
- 2.1 Regularization21
- 2.2 Consistent Labeling28
- 2.3 Clustering and Robust Methods30
- 2.4 Artificial Neural Network Approach32
- 2.5 Novelty of Our Approach32
- Chapter 3. The Salient Feature Inference Engine33
- 3.1 Overview of the Salient Inference Engine34
- 3.2 Representation37
- 3.3 Communication through Tensor Voting43
- 3.4 Derivation and Properties of the Fundamental Voting Field55
- 3.5 Implementation of Tensor Voting60
- 3.6 Feature Extraction62
- 3.7 Complexity63
- 3.8 Summary64
- Chapter 4. Feature Extraction65
- 4.1 Extremal Curves in 2-D66
- 4.2 Extremal Surfaces in 3-D67
- 4.3 Extremal Curves in 3-D69
- 4.4 Complexity71
- 4.5 Summary73
- Chapter 5. Feature Inference in 2-D75
- 5.1 Related work75
- 5.2 Inference of junctions and curves from oriented data76
- 5.3 Inference of junctions and curves from non-oriented data81
- 5.4 Interesting properties89
- 5.5 End-point grouping90
- 5.6 Detection of curve end-points and region boundaries96
- 5.7 Integrated feature extraction in 2-D106
- 5.8 Applications106
- 5.9 Summary109
- Chapter 6. Feature Inference in 3-D113
- 6.1 Related Work113
- 6.2 Feature inference from oriented and non-oriented data116
- 6.3 Feature inference from oriented data116
- 6.4 Feature inference from non-oriented data124
- 6.5 Examples131
- 6.6 Integrated feature inference in 3-D146
- 6.7 Experiments147
- 6.8 Applications149
- 6.9 Summary168
- Chapter 7. Application to Early Vision Problems171
- 7.1 Shape from Shading171
- 7.2 Shape from Stereo183
- 7.3 Accurate Motion Flow Estimation with Discontinuities198
- Chapter 8. Conclusion217
- 8.1 Summary217
- 8.2 Future Research217
- Appendix A: Tensor analysis219
- Appendix B: Details of the Marching Algorithms225
- Appendix C: Software Systems233
- References243
- Author Index255
- Index257
- Color Plate Section261
This book represents a summary of the research we have been conducting since the early 1990s, and describes a conceptual framework which addresses some current shortcomings, and proposes a unified approach for a broad class of problems. While the framework is defined, our research continues, and some of the elements presented here will no doubt evolve in the coming years.It is organized in eight chapters. In the Introduction chapter, we present the definition of the problems, and give an overview of the proposed approach and its implementation. In particular, we illustrate the limitations of the 2.5D sketch, and motivate the use of a representation in terms of layers instead.
In chapter 2, we review some of the relevant research in the literature. The discussion focuses on general computational approaches for early vision, and individual methods are only cited as references. Chapter 3 is the fundamental chapter, as it presents the elements of our salient feature inference engine, and their interaction. It introduced tensors as a way to represent information, tensor fields as a way to encode both constraints and results, and tensor voting as the communication scheme. Chapter 4 describes the feature extraction steps, given the computations performed by the engine described earlier. In chapter 5, we apply the generic framework to the inference of regions, curves, and junctions in 2-D. The input may take the form of 2-D points, with or without orientation. We illustrate the approach on a number of examples, both basic and advanced. In chapter 6, we apply the framework to the inference of surfaces, curves and junctions in 3-D. Here, the input consists of a set of 3-D points, with or without as associated normal or tangent direction. We show a number of illustrative examples, and also point to some applications of the approach. In chapter 7, we use our framework to tackle 3 early vision problems, shape from shading, stereo matching, and optical flow computation. In chapter 8, we conclude this book with a few remarks, and discuss future research directions.
We include 3 appendices, one on Tensor Calculus, one dealing with proofs and details of the Feature Extraction process, and one dealing with the companion software packages.
In chapter 2, we review some of the relevant research in the literature. The discussion focuses on general computational approaches for early vision, and individual methods are only cited as references. Chapter 3 is the fundamental chapter, as it presents the elements of our salient feature inference engine, and their interaction. It introduced tensors as a way to represent information, tensor fields as a way to encode both constraints and results, and tensor voting as the communication scheme. Chapter 4 describes the feature extraction steps, given the computations performed by the engine described earlier. In chapter 5, we apply the generic framework to the inference of regions, curves, and junctions in 2-D. The input may take the form of 2-D points, with or without orientation. We illustrate the approach on a number of examples, both basic and advanced. In chapter 6, we apply the framework to the inference of surfaces, curves and junctions in 3-D. Here, the input consists of a set of 3-D points, with or without as associated normal or tangent direction. We show a number of illustrative examples, and also point to some applications of the approach. In chapter 7, we use our framework to tackle 3 early vision problems, shape from shading, stereo matching, and optical flow computation. In chapter 8, we conclude this book with a few remarks, and discuss future research directions.
We include 3 appendices, one on Tensor Calculus, one dealing with proofs and details of the Feature Extraction process, and one dealing with the companion software packages.