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.
Spis treści
Preface.- List of Contributors.- Part I General.- 1 Digital Geometry in Image-Based Metrology; Alfred M. Bruckstein.- 2 Provably Robust Simplification of Component Trees of Multidimensional Images; Gabor T. Herman, T. Yung Kong, and Lucas M. Oliveira.- Part II Topology, Transformations.- 3 Discrete Topological Transformations for Image Processing; Michel Couprie and Gilles Bertrand.- 4 Modeling and Manipulating Cell Complexes in Two, Three and Higher Dimensions; Lidija Čomić and Leila De Floriani.- 5 Binarization of Gray-Level Images Based on Skeleton Region Growing; Xiang Bai, Quannan Li, Tianyang Ma, Wenyu Liu, and Longin Jan Latecki.- 6 Topology Preserving Parallel 3D Thinning Algorithms; Kálmán Palágyi, Gábor Németh, and Péter Kardos.- 7 Separable Distance Transformation and its Applications; David Coeurjolly and Antoine Vacavant.- 8 Separability and Tight Enclosure of Point Sets; Peter Veelaert.- Part III Image and Shape Analysis.- Digital Straightness, Circularity, and their Applications to Image Analysis; Partha Bhowmick and Bhargab B. Bhattacharya.- 10 Shape Analysis with Geometric Primitives; Fabien Feschet.- 11 Shape from Silhouettes in Discrete Space; Atsushi Imiya and Kosuke Sato.- 12 Combinatorial Maps for 2D and 3D Image Segmentation; Guillaume Damiand and Alexandre Dupas.- 13 Multigrid Convergence of Discrete Geometric Estimators; David Coeurjolly, Jacques-Olivier Lachaud, and Tristan Roussillon.- Index.
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