{"id":62028,"date":"2018-03-09T22:49:55","date_gmt":"2018-03-09T22:49:55","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/modelo-algebro-topologico-de-representacion-de-imagenes-digitales-en-nd\/"},"modified":"2018-03-09T22:49:55","modified_gmt":"2018-03-09T22:49:55","slug":"modelo-algebro-topologico-de-representacion-de-imagenes-digitales-en-nd","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/cohomologia\/modelo-algebro-topologico-de-representacion-de-imagenes-digitales-en-nd\/","title":{"rendered":"Modelo \u00e1lgebro-topol\u00f3gico de representaci\u00f3n de im\u00e1genes digitales en nd"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Bel\u00e9n Medrano Garfia <\/strong><\/h2>\n<p>Esta tesis aborda el problema de computar caracter\u00edsticas topol\u00f3gicas en el dominio de las im\u00e1genes digitales n-dimensionales. Para ello, trabajamos con complejos celulares asociados a dichas im\u00e1genes que reflejan la misma topolog\u00eda que el objeto inicial. Esta forma de proceder nos permite aplicar t\u00e9cnicas de la topolog\u00eda algebraica y el \u00e1lgebra homol\u00f3gica y as\u00ed obtener una mejor caracterizaci\u00f3n topol\u00f3gica de las im\u00e1genes. Definimos un modelo de representaci\u00f3n de un objeto digital n-dimensional como una forma de codificar dicho objeto asoci\u00e1ndole una herramienta algebraica: una contracci\u00f3n de cadenas. El objetivo que perseguimos es conectar el complejo de cadenas can\u00f3nicamente asociado al complejo celular con un complejo de cadenas \u00abmenor\u00bb a partir del cual podamos obtener informaci\u00f3n topol\u00f3gica del objeto inicial. Actualmente, existen dos t\u00e9cnicas fundamentales para computar grupos de homolog\u00eda: una t\u00e9cnica de diagonalizaci\u00f3n consiste en la reducci\u00f3n de matrices a su forma normal de smith y una t\u00e9cnica incremental basada en el concepto de filtraci\u00f3n de un complejo simplicial. Un primer modelo de representaci\u00f3n de objetos digitales 3d sobre el mallado bcc con la (14,14)-adyacencia es el modelo at. Este modelo consiste en una traducci\u00f3n de la t\u00e9cnica incremental a contracciones de cadenas. A partir de \u00e9l obtenemos una completa informaci\u00f3n (co)homol\u00f3gica en un cuerpo zp y un nuevo invariante cohomol\u00f3gico m\u00e1s fino que los grupos de homolog\u00eda, hb1. Posteriormente, se definen dos modelos de representaci\u00f3n en el dominio de los enteros, estudiando la informaci\u00f3n nomol\u00f3gica que podemos obtener a partir de ellos. El modelo am, consistente en una traducci\u00f3n del algoritmo de reducci\u00f3n de matrices a su forma normal de smith en t\u00e9rmino de contracciones de cadenas. Y por \u00faltimo, el lambda-modelo at surgido al generalizar la t\u00e9cnica incremental del modelo at al dominio de los enteros.  finalmente, hemos probado que nuestros modelos de r<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Modelo \u00e1lgebro-topol\u00f3gico de representaci\u00f3n de im\u00e1genes digitales en nd<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Modelo \u00e1lgebro-topol\u00f3gico de representaci\u00f3n de im\u00e1genes digitales en nd <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Bel\u00e9n Medrano Garfia <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Sevilla<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 17\/12\/2007<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Rocio Gonzalez Diaz<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Armario Sampalo Jos\u00e9 Andr\u00e9s <\/li>\n<li>Julio Jes\u00fas Rubio Garc\u00eda (vocal)<\/li>\n<li>Walter Kropatsch (vocal)<\/li>\n<li>Jean-luc Mari (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Bel\u00e9n Medrano Garfia Esta tesis aborda el problema de computar caracter\u00edsticas topol\u00f3gicas en el dominio de las [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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