內容簡介
《數碼幾何》的作者是數碼幾何學的開創者。《數碼幾何》是第一部詳盡介紹數碼幾何概念、算法和實際應用的專著,書中全麵而係統提供瞭數碼幾何重要的數學思想和方法,其中某些思想源於古代數學。
全書共有17章。第1章簡單介紹瞭一些幾何學的基本概念。第2—8章詳細論述瞭數碼幾何學的基礎理論,包括格點、度規、圖、拓撲和幾何,以及如何在數碼幾何中應用這些理論。第9—12章詳細論述瞭直綫、麯綫、平麵和麯麵等重要幾何概念。13—16章重點論述瞭Hull算子、圖和三種重要變換。最後一章是圖像的其它特性及其相互關係。
《數碼幾何》適應於從事數碼圖像、圖像傳輸、醫療影像、模式識彆和機器人技術等相關領域的研究人員和研究生。
目錄
1 Introduction
1.1 Pictures
1.2 DigitalGeometryandRelatedDisciplines
1.3 Exercises
1.4 CommentedBibliography
2 GridsandDigitization
2.1 TheGridPointandGridCellModels
2.2 ConnectedComponents
2.3 DigitizationModels
2.4 PropertyEstimation
2.5 Exercises
2.6 CommentedBibliography
3 Metrics
3.1 BasicsAboutMetrics
3.2 GridPointMetrics
3.3 GridCellMetrics
3.4 MetricsonPictures
3.5 Exercises
3.6 CommentedBibliography
4 AdjacencyGraphs
4.1 Graphs,AdjacencyStructures,andAdjacencyGraphs
4.2 SomeBasicsofGraphTheory
4.3 OrientedAdjacencyGraphs
4.4 CombinatorialMaps
4.5 Exercises
4.6 CommentedBibliography
5 IncidencePseudographs
5.1 IncidenceStructures
5.2 Boundaries,Frontiers,andtheELderCharacteristic
5.3 TheRegularCase
5.4 PicturesonIncidenceGrids
5.5 Exercises
5.6 CommentedBibliography
6 Topology
6.1 TopologicSpaces
6.2 DigitalTopologies
6.3 TopologicConcepts
6.4 CombinatorialTopology
6.5 Exercises
6.6 CommentedBibliography
7 CurvesandSurfaces:Topology
7.1 CurvesintheEuclideanTopology
7.2 CurvesinIncidenceGrids
7.3 CurvesinAdjacencyGrids
7.4 SurfacesintheEuclideanTopology
7.5 SurfacesandSeparationsin3DGrids
7.6 Exercises
7.7 CommentedBibliography
8 CurvesandSurfaces:Geometry
8.1 PlanarCurvesandArcs
8.2 SpaceCurvesandArcs
8.3 SurfacesandSolids
8.4 SurfaceTracingandApproximation
8.5 Exercises
8.6 CommentedBibliography
9 2DStraightness
10 2DArcLength;CurvatureandCorners
11 3DStraightnessandPtanarity
12 3DAreLength,SurfaceArea,andCurvature
13 HullsandDiagrans
14 Transformations
15 MorphologicOperations
16 Deformations
17 PicturePropertiesandSpatialRelations
ListofAlgorithms
ListofSymbols
ListofAxioms
Bibliography
Index
前言/序言
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