商品簡介
本書的作者是數碼幾何學的開創者。本書是第一部詳盡介紹數碼幾何概念、算法和實際應用的專著,書中全面而系統提供了數碼幾何最重要的數學思想和方法,其中某些思想源于古代數學。 全書共有17章。第1章簡單介紹了一些幾何學的基本概念。第2—8章詳細論述了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章詳細論述了直線、曲線、平面和曲面等重要幾何概念。13—16章重點論述了Hull算子、圖和三種重要變換。最后一章是圖像的其它特性及其相互關係。 本書適應于從事數碼圖像、圖像傳輸、醫療影像、模式識別和機器人技術等相關領域的研究人員和研究生。
目次
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