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Innovations for Shape Analysis : Models and Algorithms

Author: Michael Breuß; Alfred Bruckstein; Petros Maragos
Publisher: Dordrecht : Springer, 2012.
Series: Mathematics and visualization.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
The concept of 'shape' is at the heart of image processing and computer vision, yet researchers still have some way to go to replicate the human brain's ability to extrapolate meaning from the most basic of outlines. This volume reflects the advances of the last decade, which have also opened up tough new challenges in image processing. Today's applications require flexible models as well as efficient,  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michael Breuß; Alfred Bruckstein; Petros Maragos
ISBN: 9783642341410 3642341411
OCLC Number: 843639498
Notes: Description based upon print version of record.
Description: 1 online resource (509 p.)
Contents: Innovations for Shape Analysis; Models and Algorithms; Preface; Acknowledgments; Contents; List of Contributors; Part I Discrete Shape Analysis; Chapter1 Modeling Three-Dimensional Morse and Morse-SmaleComplexes; 1.1 Introduction; 1.2 Background Notions; 1.3 Related Work; 1.4 Representing Three-Dimensional Morse and Morse-Smale Complexes; 1.4.1 A Dimension-Independent Compact Representation for Morse Complexes; 1.4.2 A Dimension-Specific Representation for 3D Morse-Smale Complexes; 1.4.3 Comparison; 1.5 Algorithms for Building 3D Morse and Morse-SmaleComplexes 1.5.1 A Watershed-Based Approach for Building the Morse Incidence Graph1.5.2 A Boundary-Based Algorithm; 1.5.3 A Watershed-Based Labeling Algorithm; 1.5.4 A Region-Growing Algorithm; 1.5.5 An Algorithm Based on Forman Theory; 1.5.6 A Forman-Based Approach for Cubical Complexes; 1.5.7 A Forman-Based Approach for Simplicial Complexes; 1.5.8 Analysis and Comparison; 1.6 Simplification of 3D Morse and Morse-Smale Complexes; 1.6.1 Cancellation in 3D; 1.6.2 Removal and Contraction Operators; 1.7 Concluding Remarks; References; Chapter2 Geodesic Regression and Its Application to Shape Analysis 2.1 Introduction2.2 Multiple Linear Regression; 2.3 Geodesic Regression; 2.3.1 Least Squares Estimation; 2.3.2 R2 Statistics and Hypothesis Testing; 2.4 Testing the Geodesic Fit; 2.4.1 Review of Univariate Kernel Regression; 2.4.2 Nonparametric Kernel Regression on Manifolds; 2.4.3 Bandwidth Selection; 2.5 Results: Regression of 3D Rotations; 2.5.1 Overview of Unit Quaternions; 2.5.2 Geodesic Regression of Simulated Rotation Data; 2.6 Results: Regression in Shape Spaces; 2.6.1 Overview of Kendall's Shape Space; 2.6.2 Application to Corpus Callosum Aging; 2.7 Conclusion; References Chapter3 Segmentation and Skeletonization on Arbitrary Graphs Using Multiscale Morphology and Active Contours3.1 Introduction; 3.2 Multiscale Morphology on Graphs; 3.2.1 Background on Lattice and Multiscale Morphology; 3.2.2 Background on Graph Morphology; 3.2.3 Multiscale Morphology on Graphs; 3.3 Geodesic Active Contours on Graphs; 3.3.1 Constant-Velocity Active Contours on Graphs; 3.3.2 Direction of the Gradient on Graphs; 3.3.3 Curvature Calculation on Graphs; 3.3.4 Convolution on Graphs; 3.3.5 Active Contours on Graphs: The Algorithm; 3.4 Multiscale Skeletonization on Graphs 3.5 ConclusionsReferences; Chapter4 Refined Homotopic Thinning Algorithms and Quality Measures for Skeletonisation Methods; 4.1 Introduction; 4.2 Algorithms; 4.2.1 New Algorithm: Flux-Ordered Adaptive Thinning (FOAT); 4.2.2 New Algorithm: Maximal Disc Thinning (MDT); 4.3 Analysis of MAT Algorithms; 4.3.1 Quality Criteria; 4.3.2 Graph Matching for Invariance Validation; 4.4 Experiments; 4.5 Conclusions; References; Chapter5 Nested Sphere Statistics of Skeletal Models; 5.1 Object Models Suitable for Statistics; 5.2 Skeletal Models of Non-branching Objects
Series Title: Mathematics and visualization.

Abstract:

The concept of 'shape' is at the heart of image processing and computer vision, yet researchers still have some way to go to replicate the human brain's ability to extrapolate meaning from the most basic of outlines. This volume reflects the advances of the last decade, which have also opened up tough new challenges in image processing. Today's applications require flexible models as well as efficient, mathematically justified algorithms that allow data processing within an acceptable timeframe.Examining important topics in continuous-scale and discrete modeling, as well as in modern algorithm

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