05788nam 2200757 450 991013218380332120230803203829.01-118-98455-21-118-98457-91-118-98456-0(CKB)3710000000205240(EBL)1752710(OCoLC)885122545(SSID)ssj0001412513(PQKBManifestationID)11774063(PQKBTitleCode)TC0001412513(PQKBWorkID)11408535(PQKB)11773412(MiAaPQ)EBC1752710(MiAaPQ)EBC4040336(Au-PeEL)EBL1752710(CaPaEBR)ebr10899804(CaONFJC)MIL632018(Au-PeEL)EBL4040336(CaPaEBR)ebr11113568(OCoLC)927509250(EXLCZ)99371000000020524020140908h20142014 uy 0engur|n|---|||||txtccrMathematical foundations of image processing and analysis 2 /Jean-Charles Pinoli ; series editor, Jean-Pierre Goure1st ed.London, England ;Hoboken, New Jersey :iSTE :Wiley,2014.©20141 online resource (492 p.)Digital Signal and Image Processing SeriesDescription based upon print version of record.1-84821-748-X Includes bibliographical references and index.Cover; Title Page; Copyright; Contents; Preface; Introduction; PART 5: Twelve Main Geometrical Frameworks for Binary Images; Chapter 21: The Set-Theoretic Framework; 21.1. Paradigms; 21.2. Mathematical concepts and structures; 21.2.1. Mathematical disciplines; 21.3. Main notions and approaches for IPA; 21.3.1. Pixels and objects; 21.3.2. Pixel and object separation; 21.3.3. Local finiteness; 21.3.4. Set transformations; 21.4. Main applications for IPA; 21.4.1. Object partition and object components; 21.4.2. Set-theoretic separation of objects and object removal21.4.3. Counting of separate objects21.4.4. Spatial supports border effects; 21.5. Additional comments; Historical comments and references; Bibliographic notes and additional readings; Further topics and readings; Some references on applications to IPA; Chapter 22: The Topological Framework; 22.1. Paradigms; 22.2. Mathematical concepts and structures; 22.2.1. Mathematical disciplines; 22.2.2. Special classes of subsets of Rn; 22.2.3. Fell topology for closed subsets; 22.2.4. Hausdorff topology for compact subsets; 22.2.5. Continuity and semi-continuity of set transformations22.2.6. Continuity of basic set-theoretic and topological operations22.3. Main notions and approaches for IPA; 22.3.1. Topologies in the spatial domain Rn; 22.3.2. The Lebesgue-(Čech) dimension; 22.3.3. Interior and exterior boundaries; 22.3.3.1. Topologically regular objects; 22.3.4. Path-connectedness; 22.3.5. Homeomorphic objects; 22.4. Main applications to IPA; 22.4.1. Topological separation of objects and object removal; 22.4.1.1. (Path)-connected components; 22.4.2. Counting of separate objects; 22.4.3. Contours of objects; 22.4.4. Metric diameter; 22.4.5. Skeletons of proper objects22.4.6. Dirichlet-Voronoi's diagrams22.4.7. Distance maps; 22.4.8. Distance between objects; 22.4.9. Spatial support's border effects; 22.5. Additional comments; Historical comments and references; Bibliographic notes and additional readings; Further topics and readings; Some references on applications to IPA; Chapter 23: The Euclidean Geometric Framework; 23.1. Paradigms; 23.2. Mathematical concepts and structures; 23.2.1. Mathematical disciplines; 23.2.2. Euclidean dimension; 23.2.3. Matrices; 23.2.4. Determinants; 23.2.5. Eigenvalues, eigenvectors and trace of a matrix23.2.6. Matrix norms23.3. Main notions and approaches for IPA; 23.3.1. Affine transformations; 23.3.2. Special groups of affine transformations; 23.3.3. Linear and affine sub-spaces and Grassmannians; 23.3.4. Linear and affine spans; 23.4. Main applications to IPA; 23.4.1. Basic spatial transformations; 23.4.1.1. Reflected objects; 23.4.2. Hyperplanes; 23.4.3. Polytopes; 23.4.4. Minkowski addition and subtraction; 23.4.5. Continuity and semi-continuities of Euclidean transformations; 23.5. Additional comments; Historical comments and references; Commented bibliography and additional readingsFurther topics and readingsMathematical Imaging is currently a rapidly growing field in applied mathematics, with an increasing need for theoretical mathematics. This book, the second of two volumes, emphasizes the role of mathematics as a rigorous basis for imaging sciences. It provides a comprehensive and convenient overview of the key mathematical concepts, notions, tools and frameworks involved in the various fields of gray-tone and binary image processing and analysis, by proposing a large, but coherent, set of symbols and notations, a complete list of subjects and a detailed bibliography. It establishes a bridgeDigital signal and image processing series.Image processingMathematical modelsConvolutions (Mathematics)MathematicsImage processingMathematical models.Convolutions (Mathematics)Mathematics.621.367015118Pinoli Jean-Charles860410Goure J.-PMiAaPQMiAaPQMiAaPQBOOK9910132183803321Mathematical foundations of image processing and analysis 22157618UNINA