Digital and image geometry : advanced lectures ; [the volume presents extended and updated versions of 27 talks given at the Winterschool Digital and Image Geometry (December 18 - December 22, 2000, Schloss Dagstuhl, Germany)

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. Topology -- An Axiomatic Approach To Digital Topology -- Generic Programming Techniques That Make Planar Cell Complexes Easy To Use -- Algorithms And Data Structures For Computer Topology -- Computer Presentation Of 3-manifolds -- “continuous” Multifunctions In Discrete Spaces With Applications To Fixed Point Theory -- Representation -- Spamod: Design Of A Spatial Modeling Tool -- To Combinatorial Pyramids -- Representing Vertex-based Simplicial Multi-complexes -- Discrete Polyhedrization Of A Lattice Point Set -- Digital Partitions Encoding -- Geometry -- Stability And Instability In Discrete Tomography -- Point-to-line Mappings And Hough Transforms -- Digital Lines And Digital Convexity -- Curvature Flow In Discrete Space -- Hausdorff Sampling Of Closed Sets Into A Boundedly Compact Space -- Cell Complexes And Digital Convexity -- Multigrid Convergence -- Approximation Of 3d Shortest Polygons In Simple Cube Curves -- Segmentation And Length Estimation Of 3d Discrete Curves -- Multigrid Convergence Of Geometric Features -- Length Estimation For Curves With Different Samplings -- The 2-d Leap-frog: Integrability, Noise, And Digitization -- On Approximation Of Jordan Surfaces In 3d -- Shape Similarity And Simplification -- Similarity Measure Computation Of Convex Polyhedra Revisited -- Reversible Surface Skeletons Of 3d Objects By Iterative Thinning Of Distance Transforms -- Distance Transformation And Skeletonization Of 3d Pictures And Their Applications To Medical Images -- About The Limiting Behaviour Of Iterated Robust Morphological Operators -- Collinearity And Weak Collinearity In The Digital Plane. Gilles Bertrand, Atsushi Imiya, Reinhard Klette (eds.). Includes Bibliographical References And Index. An Axiomatic Approach to Digital Topology....Pages 3-16 Generic Programming Techniques that Make Planar Cell Complexes Easy to Use....Pages 17-37 Algorithms and Data Structures for Computer Topology....Pages 38-58 Computer Presentation of 3-Manifolds....Pages 59-74 “Continuous” Multifunctions in Discrete Spaces with Applications to Fixed Point Theory....Pages 75-88 SpaMod: Design of a Spatial Modeling Tool....Pages 91-108 Introduction to Combinatorial Pyramids....Pages 108-128 Representing Vertex-Based Simplicial Multi-complexes....Pages 129-149 Discrete Polyhedrization of a Lattice Point Set....Pages 150-162 Digital Partitions Encoding....Pages 163-172 Stability and Instability in Discrete Tomography....Pages 175-186 Point-to-Line Mappings and Hough Transforms....Pages 187-208 Digital Lines and Digital Convexity....Pages 209-228 Curvature Flow in Discrete Space....Pages 229-249 Hausdorff Sampling of Closed Sets into a Boundedly Compact Space....Pages 250-271 Cell Complexes and Digital Convexity....Pages 272-282 Approximation of 3D Shortest Polygons in Simple Cube Curves....Pages 285-298 Segmentation and Length Estimation of 3D Discrete Curves....Pages 299-317 Multigrid Convergence of Geometric Features....Pages 318-338 Length Estimation for Curves with Different Samplings....Pages 339-351 The 2-D Leap-Frog: Integrability, Noise, and Digitization....Pages 352-364 On Approximation of Jordan Surfaces in 3D....Pages 365-386 Similarity Measure Computation of Convex Polyhedra Revisited....Pages 389-399 Reversible Surface Skeletons of 3D Objects by Iterative Thinning of Distance Transforms....Pages 400-411 Distance Transformation and Skeletonization of 3D Pictures and Their Applications to Medical Images....Pages 412-429 About the Limiting Behaviour of Iterated Robust Morphological Operators....Pages 429-438 Collinearity and Weak Collinearity in the Digital Plane....Pages 439-453