Fundamentals of Pattern Recognition
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Table of contents:The fundamental problem of pattern recognition; images, fibre images and shapes - the topological framework; objects or images structures or patterns, classification and recognition - the structural or syntactic framework; general formalization of the pattern recognition problem - the categorical framework.Revised, updated, and expanded throughout, this edition of Fundamentals of Pattern Recognition addresses the field of PR from a basic mathematical view-point - treating algebraic, topological, and categorical approaches of PR using concepts from homotopy, shape, and fibre s...
Table of contents:
The fundamental problem of pattern recognition; images, fibre images and shapes - the topological framework; objects or images structures or patterns, classification and recognition - the structural or syntactic framework; general formalization of the pattern recognition problem - the categorical framework.
Revised, updated, and expanded throughout, this edition of Fundamentals of Pattern Recognition addresses the field of PR from a basic mathematical view-point - treating algebraic, topological, and categorical approaches of PR using concepts from homotopy, shape, and fibre spaces theories as well as computational topology.;Maintaining the features of the first edition, this resource: provides a new section on fibrewise topology that formalizes, for the first time, multicoloured, different gray level pictures and other complex signals consisting of base and value spaces and their interconnections; explores new artificial intelligence problems on the possible interplay between recursion theory and fibrewise image topology in connection with effectiveness and decidability problems; develops original techniques and results, such as the study of extremely irregular shapes by means of the mathematical theory of shape, finite topological spaces, and category theory's applications to PR; exhibits new figures of panoramic hierarchical classifications of all mathematical approaches to PR discussed; and presents five appendices that give quick overviews of dominant concepts in PR and related fields.;Containing open research and development problems to reinforce important methodologies, this second edition of Fundamentals of Pattern Recognition is a guide for applied mathematicians; electrical and electronics, systems, and computer engineers; computer scientists; and upper-level undergraduate and graduate students in applied mathematics and computer science courses in pattern recognition theory and artificial intelligence.
The fundamental problem of pattern recognition; images, fibre images and shapes - the topological framework; objects or images structures or patterns, classification and recognition - the structural or syntactic framework; general formalization of the pattern recognition problem - the categorical framework.
Revised, updated, and expanded throughout, this edition of Fundamentals of Pattern Recognition addresses the field of PR from a basic mathematical view-point - treating algebraic, topological, and categorical approaches of PR using concepts from homotopy, shape, and fibre spaces theories as well as computational topology.;Maintaining the features of the first edition, this resource: provides a new section on fibrewise topology that formalizes, for the first time, multicoloured, different gray level pictures and other complex signals consisting of base and value spaces and their interconnections; explores new artificial intelligence problems on the possible interplay between recursion theory and fibrewise image topology in connection with effectiveness and decidability problems; develops original techniques and results, such as the study of extremely irregular shapes by means of the mathematical theory of shape, finite topological spaces, and category theory's applications to PR; exhibits new figures of panoramic hierarchical classifications of all mathematical approaches to PR discussed; and presents five appendices that give quick overviews of dominant concepts in PR and related fields.;Containing open research and development problems to reinforce important methodologies, this second edition of Fundamentals of Pattern Recognition is a guide for applied mathematicians; electrical and electronics, systems, and computer engineers; computer scientists; and upper-level undergraduate and graduate students in applied mathematics and computer science courses in pattern recognition theory and artificial intelligence.