Ebook: Digital and Image Geometry: Advanced Lectures

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.

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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.

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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.
Content:
Front Matter....Pages I-VIII
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
Back Matter....Pages 455-455

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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.
Content:
Front Matter....Pages I-VIII
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
Back Matter....Pages 455-455
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