Publication: Un nuevo modelo autoorganizado aplicado a la resolución de problemas de geometría computacional
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2008-07
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2008-10-16
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Abstract
Los Mapas Autoorganizados constituyen un modelo de reconocida solvencia a la hora de generar clasificadores, en los que se logra obtener proyecciones que conservan las propiedades topológicas de la distribución de datos. En este trabajo se propone un nuevo modelo autoorganizado en el que se aúnan estas características con otras relacionadas con la generación de subgrafos de la triangulación de Delaunay, con la posibilidad de realizar aproximaciones poligonales elásticas y con la capacidad de reorganizar su estructura en función de la distribución de datos. Esto permite su aplicación a problemas relacionados con la Geometría Computacional, en concreto a la extracción de estructuras lineales en figuras bidimensionales, ya sean densas o no, y a curvas unidimensionales. La caracterización y validación del modelo se realiza sobre dos dominios de aplicación, como son la extracción de esqueletos vectoriales en textos digitalizados (manuscritos y tipográficos), y en la extracción de minucias en huellas dactilares digitalizadas. _________________________________________
Self-Organizing Maps are a well known neural model, which are able to provide topology preserving classifiers. In this work we propose a new self-organizing model, which combines these properties with others related to the generation of sub-graphs of the Delaunaytriangulation, with the possibility of generating elastic polygonal approximations and the capacity to reconfigure the models structure in a data driven way. These properties allow us to apply the model to some applications related to Computational Geometry, specifically with the extraction of linear structures from two-dimensional figures (which can be dense or not), and from one-dimensional curves. Two applications serve as validation domains, in particular, the construction of skeletal descriptions in digitized texts (with handwritten or typographic fonts), and for detecting minutiae from digitized fingerprints.
Self-Organizing Maps are a well known neural model, which are able to provide topology preserving classifiers. In this work we propose a new self-organizing model, which combines these properties with others related to the generation of sub-graphs of the Delaunaytriangulation, with the possibility of generating elastic polygonal approximations and the capacity to reconfigure the models structure in a data driven way. These properties allow us to apply the model to some applications related to Computational Geometry, specifically with the extraction of linear structures from two-dimensional figures (which can be dense or not), and from one-dimensional curves. Two applications serve as validation domains, in particular, the construction of skeletal descriptions in digitized texts (with handwritten or typographic fonts), and for detecting minutiae from digitized fingerprints.
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Matemáticas computacionales, Geometría computacional