Digital and Image Geometry

by Bertrand, Gilles; Imiya, Atsushi; Klette, Reinhard

• ISBN13: 9783540430797
• ISBN10: 3540430792
• Format: Paperback
• Copyright: 2002-04-01
• Publisher: Springer Verlag

Summary

Images or discrete objects, to be analyzed based on digital image data, need to be represented, analyzed, transformed, recovered etc. These problems have stimulated many interesting developments in theoretical foundations of image processing. This coherent anthology presents 27 state-of-the-art surveys and research papers on digital image geometry and topology. It is based on a winter school held at Dagstuhl Castle, Germany in December 2000 and offers topical sections on topology, representation, geometry, multigrid convergence, and shape similarity and simplification.

Table of Contents

Part I Topology
An Axiomatic Approach to Digital Topology	3	(14)
Eladio Dominguez
Angel R. Frances
Generic Programming Techniques that Make Planar Cell Complexes Easy to Use	17	(21)
Ullrich Kothe
Algorithms and Data Structures for Computer Topology	38	(21)
Vladimir Kovalevsky
Computer Presentation of 3-Manifolds	59	(16)
Sergei Matveev
``Continuous'' Multifunctions in Discrete Spaces with Applications to Fixed Point Theory	75	(16)
Rueiher Tsaur
Michael B. Smyth
Part II Representation
SpaMod: Design of a Spatial Modeling Tool	91	(17)
Eric Andres
Rodolphe Breton
Pascal Lienhardt
Introduction to Combinatorial Pyramids	108	(21)
Luc Brun
Walter Kropatsch
Representing Vertex-Based Simplicial Multi-complexes	129	(21)
Emanuele Danovaro
Leila De Floriani
Paola Magillo
Enrico Puppo
Discrete Polyhedrization of a Lattice Point Set	150	(13)
Yukiko Kenmochi
Atsushi Imiya
Digital Partitions Encoding	163	(12)
Jovisa Zunic
Part III Geometry
Stability and Instability in Discrete Tomography	175	(12)
Andreas Alpers
Peter Gritzmann
Lionel Thorens
Point-to-Line Mappings and Hough Transforms	187	(22)
Prabir Bhattacharya
Azriel Rosenfeld
Isaac Weiss
Digital Lines and Digital Convexity	209	(20)
Ulrich Eckhardt
Curvature Flow in Discrete Space	229	(21)
Atsushi Imiya
Hausdorff Sampling of Closed Sets into a Boundedly Compact Space	250	(22)
Christian Ronse
Mohamed Tajine
Cell Complexes and Digital Convexity	272	(13)
Julian Webster
Part IV Multigrid Convergence
Approximation of 3D Shortest Polygons in Simple Cube Curves	285	(14)
Thomas Bulow
Reinhard Klette
Segmentation and Length Estimation of 3D Discrete Curves	299	(19)
David Coeurjolly
Isabelle Debled-Rennesson
Olivier Teytaud
Multigrid Convergence of Geometric Features	318	(21)
Reinhard Klette
Length Estimation for Curves with Different Samplings	339	(13)
Lyle Noakes
Ryszard Kozera
Reinhard Klette
The 2-D Leap-Frog: Integrability, Noise, and Digitization	352	(13)
Lyle Noakes
Ryszard Kozera
On Approximation of Jordan Surfaces in 3D	365	(24)
Fridrich Sloboda
Bedrich Zatko
Part V Shape Similarity and Simplification
Similarity Measure Computation of Convex Polyhedra Revisited	389	(11)
Jos B.T.M. Roerdink
Henk Bekker
Reversible Surface Skeletons of 3D Objects by Iterative Thinning of Distance Transforms	400	(12)
Stina Svensson
Distance Transformation and Skeletonization of 3D Pictures and Their Applications to Medical Images	412	(17)
Jun-ichiro Toriwaki
Kensaku Mori
About the Limiting Behaviour of Iterated Robust Morphological Operators	429	(10)
Johan Van Horebeek
Ernesto Tapia-Rodriguez
Collinearity and Weak Collinearity in the Digital Plane	439	(16)
Peter Veelaert
Author Index	455