數(shù)碼幾何

內(nèi)容概要

本書的作者是數(shù)碼幾何學(xué)的開創(chuàng)者。本書是第一部詳盡介紹數(shù)碼幾何概念、算法和實(shí)際應(yīng)用的專著，書中全面而系統(tǒng)提供了數(shù)碼幾何最重要的數(shù)學(xué)思想和方法，其中某些思想源于古代數(shù)學(xué)。全書共有17章。第1章簡單介紹了一些幾何學(xué)的基本概念。第2—8章詳細(xì)論述了數(shù)碼幾何學(xué)的基礎(chǔ)理論，包括格點(diǎn)、度規(guī)、圖、拓?fù)浜蛶缀危约叭绾卧跀?shù)碼幾何中應(yīng)用這些理論。第9—12章詳細(xì)論述了直線、曲線、平面和曲面等重要幾何概念。13—16章重點(diǎn)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(guān)系。    本書適應(yīng)于從事數(shù)碼圖像、圖像傳輸、醫(yī)療影像、模式識別和機(jī)器人技術(shù)等相關(guān)領(lǐng)域的研究人員和研究生。

書籍目錄

1 Introduction  1.1 Pictures  1.2 DigitalGeometryandRelatedDisciplines  1.3 Exercises  1.4 CommentedBibliography2 GridsandDigitization  2.1 TheGridPointandGridCellModels  2.2 ConnectedComponents  2.3 DigitizationModels  2.4 PropertyEstimation  2.5 Exercises  2.6 CommentedBibliography3 Metrics  3.1 BasicsAboutMetrics  3.2 GridPointMetrics  3.3 GridCellMetrics  3.4 MetricsonPictures  3.5 Exercises  3.6 CommentedBibliography4 AdjacencyGraphs  4.1 Graphs,AdjacencyStructures,andAdjacencyGraphs  4.2 SomeBasicsofGraphTheory  4.3 OrientedAdjacencyGraphs  4.4 CombinatorialMaps  4.5 Exercises  4.6 CommentedBibliography5 IncidencePseudographs  5.1 IncidenceStructures  5.2 Boundaries,Frontiers,andtheELderCharacteristic  5.3 TheRegularCase  5.4 PicturesonIncidenceGrids  5.5 Exercises  5.6 CommentedBibliography6 Topology  6.1 TopologicSpaces  6.2 DigitalTopologies  6.3 TopologicConcepts  6.4 CombinatorialTopology  6.5 Exercises  6.6 CommentedBibliography7 CurvesandSurfaces:Topology  7.1 CurvesintheEuclideanTopology  7.2 CurvesinIncidenceGrids  7.3 CurvesinAdjacencyGrids  7.4 SurfacesintheEuclideanTopology  7.5 SurfacesandSeparationsin3DGrids  7.6 Exercises  7.7 CommentedBibliography8 CurvesandSurfaces:Geometry  8.1 PlanarCurvesandArcs  8.2 SpaceCurvesandArcs  8.3 SurfacesandSolids  8.4 SurfaceTracingandApproximation  8.5 Exercises  8.6 CommentedBibliography9 2DStraightness10 2DArcLength;CurvatureandCorners11 3DStraightnessandPtanarity12 3DAreLength,SurfaceArea,andCurvature13 HullsandDiagrans14 Transformations15 MorphologicOperations16 Deformations17 PicturePropertiesandSpatialRelationsListofAlgorithmsListofSymbolsListofAxiomsBibliographyIndex

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