Shape Classification and Analysis: Theory and

Shape analysis offers great potential for applications in diverse areas, from materials science to biology and neuroscience. Including numerical tools for characterization, this new edition presents the most advanced imaging techniques for the analysis of general biological shapes, such as cells, tissues, organs, and organisms. Various chapters review the main approaches for shape classification. Although focused on two-dimensional shapes, which are more effectively handled by current technology, the text also covers basic concepts and techniques for three-dimensional shapes. These methods offer a rich resource for the computational characterization and classification of biological shapes.

Preface - Second Edition	p. ix
Preface - First Edition	p. xi
List of Figures	p. xxiv
List of Tables	p. xxix
Introduction	p. 1
Introduction to Shape Analysis	p. 1
Case Studies	p. 6
Computational Shape Analysis	p. 9
Additional Material	p. 25
Organization of the Book	p. 26
Basic Mathematical Concepts	p. 27
Basic Concepts	p. 27
Linear Algebra	p. 51
Differential Geometry	p. 86
Multivariate Calculus	p. 96
Convolution and Correlation	p. 104
Probability and Statistics	p. 114
Fourier Analysis	p. 139
Graphs and Complex Networks	p. 180
Shape Acquisition and Processing	p. 191
Image Representation	p. 192
Image Processing and Filtering	p. 210
Image Segmentation: Edge Detection	p. 229
Image Segmentation: Additional Algorithms	p. 241
Binary Mathematical Morphology	p. 248
Further Image Processing References	p. 256
Shape Concepts	p. 259
Introduction to Two-Dimensional Shapes	p. 259
Continuous Two-Dimensional Shapes	p. 261
Planar Shape Transformations	p. 266
Characterizing 2D Shapes in Terms of Features	p. 270
Classifying 2D Shapes	p. 273
Representing 2D Shapes	p. 274
Shape Operations	p. 280
Shape Metrics	p. 283
Morphic Transformations	p. 291
Shape Representation	p. 319
Introduction	p. 319
Parametric Contours	p. 323
Sets of Contour Points	p. 339
Curve Approximations	p. 339
Digital Straight Lines	p. 352
Hough Transforms	p. 361
Exact Dilations	p. 383
Distance Transforms	p. 387
Exact Distance Transform Through Exact Dilations	p. 390
Voronoi Tessellations	p. 390
Scale-Space Skeletonization	p. 394
Bounding Regions	p. 400
Shape Characterization	p. 403
Statistics for Shape Descriptors	p. 403
Some General Descriptors	p. 404
Fractal Geometry and Complexity Descriptors	p. 424
Curvature	p. 431
Fourier Descriptors	p. 441
Multiscale Shape Characterization	p. 449
Multiscale Transforms	p. 449
Fourier-Based Multiscale Curvature	p. 464
Wavelet-Based Multiscale Contour Analysis	p. 481
Multiscale Energies	p. 500
Shape Recognition	p. 505
Introduction to Shape Classification	p. 505
Supervised Pattern Classification	p. 536
Unsupervised Classification and Clustering	p. 547
A Case Study: Leaves Classification	p. 569
Evaluating Classification Methods	p. 575
Structural Shape Recognition	p. 585
Introduction	p. 585
Syntactic Pattern Recognition	p. 588
Region Decomposition	p. 589
Graph Models	p. 590
Spatial Relations	p. 592
Graph Matching	p. 596
Case Study: Interactive Image Segmentation	p. 599
Complex Networks for Image and Shape Analysis	p. 601
Epilogue	p. 609
Future Trends in Shape Analysis and Classification	p. 609
Bibliography	p. 613
Index	p. 653
Table of Contents provided by Ingram. All Rights Reserved.

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Shape Classification and Analysis: Theory and Practice, Second Edition

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