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A Computational Framework for Segmentation and Grouping
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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 t...
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.
Table of contents:
Chapter 1. Introduction. Motivation and goals. The problem. General approaches in computer vision. Common limitations of current methods. Desirable solutions. Our approach. Data representation. Computational methodology. Overview of the proposed method. Contribution of this book. Notations. Chapter 2. Previous Work. Regularization. Ill-posed problems. Regularization methods. Stochastic regularization. Regularization in computer vision. Level-set approach. Characteristics of methods using regularization. Consistent labeling. Discrete relaxation labeling.
Continuous relaxation labeling.
Stochastic relaxation labeling.
Characteristics of consistent labeling.
Clustering and robust methods.
Clustering.
Robust techniques.
Artificial neural network approach.
Novelty of our pproach.
Chapter 3. The Salient Feature Inference Engine.
Overview of the salient inference engine.
Representation.
Vector-based representation.
Tensor representation.
Tensor decomposition.
Communication through tensor voting.
Overview.
Mathematical formulation.
Representing the voting function by discrete tensor fields.
Deriving the stick, plate and ball tensor fields from the
fundamental field.
The voting process.
Vote interpretation.
Derivation and properties of the fundamental voting field.
Deriving the field from perceptual organization principles.
Analogy with particle physics.
Implementation of tensor voting.
Feature extraction.
Surface extremality.
Curve extremality.
Complexity.
Summary.
Chapter 4. Feature Extraction.
Extremal curves in 2-D.
Extremal surfaces in 3-D.
Definitions.
Discrete version.
Extremal curves in 3-D
Definitions.
Discrete version.
Complexity.
Summary.
Chapter 5. Feature Inference in 2-D.
Related work.
Inference of junctions and curves from oriented data.
Information broadcasting.
Vote accumulation.
Vote interpretation.
Inference of junctions and curves from non-oriented data.
Interesting properties.
Correction of erroneous orientation.
Multiple scales.
Noise robustness.
End-point grouping.
Experimenting with the End-Point field.
End-point and fundamental field interaction.
Detection of curve end-points and region boundaries.
End-point inference.
Region boundary inference.
Integrated feature extraction in 2-D.
Applications.
Inferring features for Chinese character processing.
Non-uniform skew estimation.
Summary.
Chapter 6. Feature Inference in 3-D.
Related Work.
Surface fitting.
Curve fitting in 3-D.
Feature inference from oriented and non-oriented data.
Feature inference from oriented data.
Information broadcasting.
Vote accumulation.
Vote interpretation.
Illustrations of feature inference from oriented data.
Feature inference from non-oriented data.
Illustrations of feature inference from non-oriented data.
Examples.
Noisy peanut.
Two bowls.
Two tori.
Plane and sphere.
Plane and peanut.
Three planes.
Triangular wedge.
Two cones.
Pipe.
Integrated feature inference in 3-D.
Experiments.
Noise robustness.
Applicability over a wide range of scales.
Applications.
Flow visualization.
Vortex extraction.
Terrain reconstruction.
Fault detection.
Medical imagery.
3-D object modeling from photographs.
Summary.
Chapter 7. Application to Early Vision Problems.
Shape from shading.
Shape from surface orientations.
Shape from shading.
Shape from stereo.
Overview of our stereo algorithm.
Initial correspondence and correspondence saliency.
Unique disparity assignment.
Salient surface extraction.
Region trimming.
Experimental results
Accurate motion flow estimation with discontinuities.
Introduction.
Overview of the approach.
Tensor representation and voting for flow representation.
Initial Vote.
Velocity field from three frames.
Segmentation of the motion field.
Region refinement.
Handling occlusion.
Additional results.
Conclusions and future work.
Chapter 8. Conclusion.
Summary.
Future research.
Breaking point.
The scale issue.
Dealing with images.
Extensions to N-dimensions.
Tensor.
References.
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.
Table of contents:
Chapter 1. Introduction. Motivation and goals. The problem. General approaches in computer vision. Common limitations of current methods. Desirable solutions. Our approach. Data representation. Computational methodology. Overview of the proposed method. Contribution of this book. Notations. Chapter 2. Previous Work. Regularization. Ill-posed problems. Regularization methods. Stochastic regularization. Regularization in computer vision. Level-set approach. Characteristics of methods using regularization. Consistent labeling. Discrete relaxation labeling.
Continuous relaxation labeling.
Stochastic relaxation labeling.
Characteristics of consistent labeling.
Clustering and robust methods.
Clustering.
Robust techniques.
Artificial neural network approach.
Novelty of our pproach.
Chapter 3. The Salient Feature Inference Engine.
Overview of the salient inference engine.
Representation.
Vector-based representation.
Tensor representation.
Tensor decomposition.
Communication through tensor voting.
Overview.
Mathematical formulation.
Representing the voting function by discrete tensor fields.
Deriving the stick, plate and ball tensor fields from the
fundamental field.
The voting process.
Vote interpretation.
Derivation and properties of the fundamental voting field.
Deriving the field from perceptual organization principles.
Analogy with particle physics.
Implementation of tensor voting.
Feature extraction.
Surface extremality.
Curve extremality.
Complexity.
Summary.
Chapter 4. Feature Extraction.
Extremal curves in 2-D.
Extremal surfaces in 3-D.
Definitions.
Discrete version.
Extremal curves in 3-D
Definitions.
Discrete version.
Complexity.
Summary.
Chapter 5. Feature Inference in 2-D.
Related work.
Inference of junctions and curves from oriented data.
Information broadcasting.
Vote accumulation.
Vote interpretation.
Inference of junctions and curves from non-oriented data.
Interesting properties.
Correction of erroneous orientation.
Multiple scales.
Noise robustness.
End-point grouping.
Experimenting with the End-Point field.
End-point and fundamental field interaction.
Detection of curve end-points and region boundaries.
End-point inference.
Region boundary inference.
Integrated feature extraction in 2-D.
Applications.
Inferring features for Chinese character processing.
Non-uniform skew estimation.
Summary.
Chapter 6. Feature Inference in 3-D.
Related Work.
Surface fitting.
Curve fitting in 3-D.
Feature inference from oriented and non-oriented data.
Feature inference from oriented data.
Information broadcasting.
Vote accumulation.
Vote interpretation.
Illustrations of feature inference from oriented data.
Feature inference from non-oriented data.
Illustrations of feature inference from non-oriented data.
Examples.
Noisy peanut.
Two bowls.
Two tori.
Plane and sphere.
Plane and peanut.
Three planes.
Triangular wedge.
Two cones.
Pipe.
Integrated feature inference in 3-D.
Experiments.
Noise robustness.
Applicability over a wide range of scales.
Applications.
Flow visualization.
Vortex extraction.
Terrain reconstruction.
Fault detection.
Medical imagery.
3-D object modeling from photographs.
Summary.
Chapter 7. Application to Early Vision Problems.
Shape from shading.
Shape from surface orientations.
Shape from shading.
Shape from stereo.
Overview of our stereo algorithm.
Initial correspondence and correspondence saliency.
Unique disparity assignment.
Salient surface extraction.
Region trimming.
Experimental results
Accurate motion flow estimation with discontinuities.
Introduction.
Overview of the approach.
Tensor representation and voting for flow representation.
Initial Vote.
Velocity field from three frames.
Segmentation of the motion field.
Region refinement.
Handling occlusion.
Additional results.
Conclusions and future work.
Chapter 8. Conclusion.
Summary.
Future research.
Breaking point.
The scale issue.
Dealing with images.
Extensions to N-dimensions.
Tensor.
References.