LEADER 05491nam 2200673Ia 450 001 9910145959803321 005 20230721005136.0 010 $a1-282-03141-4 010 $a9786612031410 010 $a0-470-82309-7 010 $a0-470-82308-9 035 $a(CKB)1000000000719457 035 $a(EBL)427594 035 $a(OCoLC)476269258 035 $a(SSID)ssj0000302759 035 $a(PQKBManifestationID)11232682 035 $a(PQKBTitleCode)TC0000302759 035 $a(PQKBWorkID)10274512 035 $a(PQKB)10293493 035 $a(MiAaPQ)EBC427594 035 $a(Au-PeEL)EBL427594 035 $a(CaPaEBR)ebr10301348 035 $a(CaONFJC)MIL203141 035 $a(EXLCZ)991000000000719457 100 $a20071218d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematics of shape description$b[electronic resource] $ea morphological approach to image processing and computer graphics /$fPijush K. Ghosh, Koichiro Deguchi 210 $aSingapore ;$aHoboken, NJ $cWiley$dc2008 215 $a1 online resource (272 p.) 300 $aDescription based upon print version of record. 311 $a0-470-82307-0 320 $aIncludes bibliographical references (p. [247]-250) and index. 327 $aMATHEMATICS OF SHAPE DESCRIPTION; Contents; Foreword; Preface; 1 In Search of a Framework for Shape Description; 1.1 Shape Description: What It Means to Us; 1.2 Pure versus Pragmatic Approaches; 1.3 The In.uence of the Digital Computer on Our Approach to Shape Description; 1.4 A Metamodel for Shape Description; 1.4.1 A Mathematical Model for Shape Description and Associated Problems; 1.4.2 The Need for a Metamodel; 1.4.3 Reformulating the Metamodel to Adapt to the Pragmatic Approach; 1.5 The Metamodel within the Framework of Formal Language 327 $a1.5.1 An Introduction to Formal Languages and Grammars1.5.2 A Grammar for the Constructive Part of the Metamodel; 1.5.3 An Exploration of Shape Description Schemes in Terms of Formal Language Theory; 1.6 The Art of Model Making; 1.6.1 What is the Meaning of "Model"?; 1.6.2 A Few Guiding Principles; 1.7 Shape Description Schematics and the Tools of Mathematics; 1.7.1 Underlying Assumptions when Mapping from the Real World to a Mathematical System; 1.7.2 Fundamental Mathematical Structures and Their Various Compositions; 2 Sets and Functions for Shape Description; 2.1 Basic Concepts of Sets 327 $a2.1.1 De.nition of Sets2.1.2 Membership; 2.1.3 Speci.cations for a Set to Describe Shapes; 2.1.4 Special Sets; 2.2 Equality and Inclusion of Sets; 2.3 Some Operations on Sets; 2.3.1 The Power Set; 2.3.2 Set Union; 2.3.3 Set Intersection; 2.3.4 Set Difference; 2.3.5 Set Complement; 2.3.6 Symmetric Difference; 2.3.7 Venn Diagrams; 2.3.8 Cartesian Products; 2.4 Relations in Sets; 2.4.1 Fundamental Concepts; 2.4.2 The Properties of Binary Relations in a Set; 2.4.3 Equivalence Relations and Partitions; 2.4.4 Order Relations; 2.5 Functions, Mappings, and Operations; 2.5.1 Fundamental Concepts 327 $a2.5.2 The Graphical Representations of a Function2.5.3 The Range of a Function, and Various Categories of Function; 2.5.4 Composition of Functions; 2.5.5 The Inverse Function; 2.5.6 The One-to-One Onto Function and Set Isomorphism; 2.5.7 Equivalence Relations and Functions; 2.5.8 Functions of Many Variables, n-ary Operations; 2.5.9 A Special Type of Function: The Analytic Function; 3 Algebraic Structures for Shape Description; 3.1 What is an Algebraic Structure?; 3.1.1 Algebraic Systems with Internal Composition Laws; 3.1.2 Algebraic Systems with External Composition Laws 327 $a3.2 Properties of Algebraic Systems3.2.1 Associativity; 3.2.2 Commutativity; 3.2.3 Distributivity; 3.2.4 The Existence of the Identity/Unit Element; 3.2.5 The Existence of an Inverse Element; 3.3 Morphisms of Algebraic Systems; 3.4 Semigroups and Monoids: Two Simple Algebraic Systems; 3.5 Groups; 3.5.1 Fundamentals; 3.5.2 The Advantages of Identifying a System as a Group; 3.5.3 Transformation Groups; 3.6 Symmetry Groups; 3.6.1 The Action of a Group on a Set; 3.6.2 Translations and the Euclidean Group; 3.6.3 The Matrix Group; 3.7 Proper Rotations of Regular Solids 327 $a3.7.1 The Symmetry Groups of the Regular Solids 330 $aImage processing problems are often not well defined because real images are contaminated with noise and other uncertain factors. In Mathematics of Shape Description, the authors take a mathematical approach to address these problems using the morphological and set-theoretic approach to image processing and computer graphics by presenting a simple shape model using two basic shape operators called Minkowski addition and decomposition. This book is ideal for professional researchers and engineers in Information Processing, Image Measurement, Shape Description, Shape Representation and 606 $aGeometry, Algebraic 606 $aMinkowski geometry 606 $aImage processing$xMathematical models 615 0$aGeometry, Algebraic. 615 0$aMinkowski geometry. 615 0$aImage processing$xMathematical models. 676 $a516.3/5 700 $aGhosh$b Pijush K$0936808 701 $aDeguchi$b Koichiro$0936809 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910145959803321 996 $aMathematics of shape description$92110032 997 $aUNINA