Irregular graph pyramids and representative cocycles of cohomology generators
Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than d...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/30786 |
| Acceso en línea: | http://hdl.handle.net/11441/30786 https://doi.org/10.1007/978-3-642-02124-4_27 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph pyramids Representative cocycles of cohomology generators |
| Sumario: | Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. Extension to nD and application in the context of pattern recognition are discussed. |
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