Digital Geometry Algorithms: Theoretical Foundations and Applications to Computational Imaging

✍ Scribed by Alfred M. Bruckstein (auth.), Valentin E. Brimkov, Reneta P. Barneva (eds.)

• Publisher: Springer Netherlands
• Year: 2012
• Tongue: English
• Leaves: 427
• Series: Lecture Notes in Computational Vision and Biomechanics 2
• Edition: 1
• Category: Library

✦ Synopsis

Digital geometry emerged as an independent discipline in the second half of the last century. It deals with geometric properties of digital objects and is developed with the unambiguous goal to provide rigorous theoretical foundations for devising new advanced approaches and algorithms for various problems of visual computing. Different aspects of digital geometry have been addressed in the literature. This book is the first one that explicitly focuses on the presentation of the most important digital geometry algorithms. Each chapter provides a brief survey on a major research area related to the general volume theme, description and analysis of related fundamental algorithms, as well as new original contributions by the authors. Every chapter contains a section in which interesting open problems are addressed.

✦ Table of Contents

Front Matter....Pages I-X
Front Matter....Pages 1-1
Digital Geometry in Image-Based Metrology....Pages 3-26
Provably Robust Simplification of Component Trees of Multidimensional Images....Pages 27-69
Front Matter....Pages 71-71
Discrete Topological Transformations for Image Processing....Pages 73-107
Modeling and Manipulating Cell Complexes in Two, Three and Higher Dimensions....Pages 109-144
Binarization of Gray-Level Images Based on Skeleton Region Growing....Pages 145-164
Topology Preserving Parallel 3D Thinning Algorithms....Pages 165-188
Separable Distance Transformation and Its Applications....Pages 189-214
Separability and Tight Enclosure of Point Sets....Pages 215-243
Front Matter....Pages 245-245
Digital Straightness, Circularity, and Their Applications to Image Analysis....Pages 247-299
Shape Analysis with Geometric Primitives....Pages 301-321
Shape from Silhouettes in Discrete Space....Pages 323-358
Combinatorial Maps for 2D and 3D Image Segmentation....Pages 359-393
Multigrid Convergence of Discrete Geometric Estimators....Pages 395-424
Back Matter....Pages 425-428

✦ Subjects

Signal, Image and Speech Processing; Computer Imaging, Vision, Pattern Recognition and Graphics; Algorithms; Appl.Mathematics/Computational Methods of Engineering; Convex and Discrete Geometry