A Computational Framework for Segmentation and Grouping

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 thefundamental 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.