Author | Herman, Gabor T. author |
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Title | Geometry of Digital Spaces [electronic resource] / by Gabor T. Herman |
Imprint | Boston, MA : Birkhรคuser Boston, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4136-2 |
Descript | X, 216 p. online resource |
1 Cloning Flies on Sugar Cubes -- 1.1 What Is Our Game? -- 1.2 A Methodology for Extracting Object Boundaries -- 1.3 Flies in Flatland -- 1.4 Components Determined by Binary Relations -- 1.5 So, What Does a Flat Fly Do? -- 1.6 Back to the Cuberille -- 1.7 Algorithms for Fat Flies -- 1.8 Digraphs -- 1.9 So, What Can a Fat Fly Do? -- 1.10 Algorithms for Cloning Flies -- 1.11 An Efficient Implementation -- 1.12 Exercises -- 2 Enhancing the Cube -- 2.1 Why Study Noncubic Grids? -- 2.2 Other Spaces -- 2.3 Exercises -- 3 Digital Spaces -- 3.1 The Basic Definitions -- 3.2 Interiors and Exteriors -- 3.3 Connectedness in Digital Spaces -- 3.4 Isomorphisms between Digital Spaces -- 3.5 Exercises -- 4 Topological Digital Spaces -- 4.1 What Is a Topology? -- 4.2 Some Topological Digital Spaces -- 4.3 Many Digital Spaces Are Not Topological -- 4.4 Connectedness of Topological Interiors -- 4.5 Exercises -- 5 Binary Pictures -- 5.1 Digital Pictures -- 5.2 Fuzzy Segmentation -- 5.3 Boundaries in Binary Pictures -- 5.4 Jordan Pairs of Spel-Adjacencies -- 5.5 New Jordan Pairs from Old Ones -- 5.6 Exercises -- 6 Simply Connected Digital Spaces -- 6.1 N-Simply Connected Digital Spaces -- 6.2 Locally-Jordan Surfaces -- 6.3 Applications to Finding Jordan Pairs -- 6.4 1-Simply Connected Digital Spaces -- 6.5 Exercises -- 7 Jordan Graphs -- 7.1 The Theory of (Strong) Jordan Graphs -- 7.2 Jordan Surfaces -- 7.3 Spel-Manifolds -- 7.4 Exercises -- 8 Boundary Tracking -- 8.1 Tracking in Finitary 1-Simply Connected Spaces -- 8.2 Efficient Tracking of Boundary Elements -- 8.3 Boundary Tracking on Hypercubes -- 8.4 Proofs of the Boundary-Tracking Claims -- 8.5 Boundary Tracking in the FCC Grid -- 8.6 Pointers to Further Reading -- 8.7 Exercises -- Appendix List of Symbols -- References