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Advances in shape analysis impact a wide range of disciplines, from mathematics and engineering to medicine, archeology, and art. Anyone just entering the field, however, may find the few existing books on shape analysis too specific or advanced, and for students interested in the specific problem of shape recognition and characterization, traditional books on computer vision are too general.
Shape Analysis and Classification: Theory and Practice offers an integrated and conceptual introduction to this dynamic field and its myriad applications. Beginning with the basic mathematical concepts, it deals with shape analysis, from image capture to pattern classification, and presents many of the most advanced and powerful techniques used in practice. The authors explore the relevant aspects of both shape characterization and recognition, and give special attention to practical issues, such as guidelines for implementation, validation, and assessment.
Shape Analysis and Classification provides a rich resource for the computational characterization and classification of general shapes, from characters to biological entities. Both students and researchers can directly use its state-of-the-art concepts and techniques to solve their own problems involving the characterization and classification of visual shapes.
INTRODUCTION Introduction to Shape Analysis Case Studies Computational Shape Analysis Organization of The Book BASIC MATHEMATICAL CONCEPTS Basic Concepts Linear Algebra Differential Geometry Multivariate Calculus Convolution and Correlation Probability and Statistics Fourier Analysis SHAPE ACQUISITION AND PRE-PROCESSING Image Representation Image Processing and Filtering Image Segmentation: Edge Detection Image Segmentation: Additional Algorithms Binary Mathematical Morphology Further Image Processing References SHAPE CONCEPTS Introduction to Two-Dimensional Shapes Continuous Two-Dimensional Shapes Planar Shape Transformations Characterizing 2D Shapes in Terms of Features Classifying 2D Shapes Representing 2D Shapes Shape Operations Shape Metrics Morphic Transformations TWO-DIMENSIONAL SHAPE REPRESENTATION Introduction Parametric Contour Sets of Contour Points Curve Approximations Digital Straight Lines Hough Transforms Exact Dilations Distance Transforms Exact Distance Transform through Exact Dilations Voronoi Diagrams Scale Space Skeletonization Bounding Regions SHAPE CHARACTERIZATION Statistics for Shape Descriptors Some General Descriptors Fractal Geometry and Complexity Descriptors Curvature Fourier Descriptors MULTISCALE SHAPE CHARACTERIZATION Multiscale Transforms Fourier-Based Multiscale Curvature Wavelet-Based Multiscale Contour Analysis Multiscale Energies SHAPE RECOGNITION AND CLASSIFICATION Introduction to Shape Classification Supervised Pattern Classification Unsupervised Classification and Clustering A Case Study: Leaves Classification Evaluating Classification Methods EPILOGUE-FUTURE TRENDS IN SHAPE ANALYSIS