Descripción y análisis de forma basado en la invarianza a isometrías de los esqueletos topológicos

ilustraciones

Autores:
Patiño Cortés, Diego Alberto
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2019
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
eng
OAI Identifier:
oai:repositorio.unal.edu.co:unal/79654
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/79654
https://repositorio.unal.edu.co/
Palabra clave:
000 - Ciencias de la computación, información y obras generales::003 - Sistemas
590 - Animales
Morfología (Zoología)
Esqueleto animal
Medial Axis Transform
Isometry
Morphological Skeletonization
Shape Analysis and Description
Shape feature
Invariance and Equivariance
PointNet
Chordiogam
Shape Classification and Retrieval
Transformada del eje medio
Isometría
Esqueletos topológicos
Análisis y descripción de forma
Invarianza y equivarianza
Clasificación y recuperación de formas
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_37ad338a20dd72606f79550c0b2f4965
oai_identifier_str oai:repositorio.unal.edu.co:unal/79654
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Descripción y análisis de forma basado en la invarianza a isometrías de los esqueletos topológicos
dc.title.translated.eng.fl_str_mv Shape analysis and description based on the isometric invariances of topological skeletonization
title Descripción y análisis de forma basado en la invarianza a isometrías de los esqueletos topológicos
spellingShingle Descripción y análisis de forma basado en la invarianza a isometrías de los esqueletos topológicos
000 - Ciencias de la computación, información y obras generales::003 - Sistemas
590 - Animales
Morfología (Zoología)
Esqueleto animal
Medial Axis Transform
Isometry
Morphological Skeletonization
Shape Analysis and Description
Shape feature
Invariance and Equivariance
PointNet
Chordiogam
Shape Classification and Retrieval
Transformada del eje medio
Isometría
Esqueletos topológicos
Análisis y descripción de forma
Invarianza y equivarianza
Clasificación y recuperación de formas
title_short Descripción y análisis de forma basado en la invarianza a isometrías de los esqueletos topológicos
title_full Descripción y análisis de forma basado en la invarianza a isometrías de los esqueletos topológicos
title_fullStr Descripción y análisis de forma basado en la invarianza a isometrías de los esqueletos topológicos
title_full_unstemmed Descripción y análisis de forma basado en la invarianza a isometrías de los esqueletos topológicos
title_sort Descripción y análisis de forma basado en la invarianza a isometrías de los esqueletos topológicos
dc.creator.fl_str_mv Patiño Cortés, Diego Alberto
dc.contributor.advisor.none.fl_str_mv Branch Bedoya, John William
dc.contributor.author.none.fl_str_mv Patiño Cortés, Diego Alberto
dc.contributor.researchgroup.spa.fl_str_mv GIDIA - Grupo de Investigación en Inteligencia Artificial
dc.subject.ddc.spa.fl_str_mv 000 - Ciencias de la computación, información y obras generales::003 - Sistemas
590 - Animales
topic 000 - Ciencias de la computación, información y obras generales::003 - Sistemas
590 - Animales
Morfología (Zoología)
Esqueleto animal
Medial Axis Transform
Isometry
Morphological Skeletonization
Shape Analysis and Description
Shape feature
Invariance and Equivariance
PointNet
Chordiogam
Shape Classification and Retrieval
Transformada del eje medio
Isometría
Esqueletos topológicos
Análisis y descripción de forma
Invarianza y equivarianza
Clasificación y recuperación de formas
dc.subject.lemb.none.fl_str_mv Morfología (Zoología)
Esqueleto animal
dc.subject.proposal.eng.fl_str_mv Medial Axis Transform
Isometry
Morphological Skeletonization
Shape Analysis and Description
Shape feature
Invariance and Equivariance
PointNet
Chordiogam
Shape Classification and Retrieval
dc.subject.proposal.spa.fl_str_mv Transformada del eje medio
Isometría
Esqueletos topológicos
Análisis y descripción de forma
Invarianza y equivarianza
Clasificación y recuperación de formas
description ilustraciones
publishDate 2019
dc.date.issued.none.fl_str_mv 2019-06
dc.date.accessioned.none.fl_str_mv 2021-06-19T13:52:39Z
dc.date.available.none.fl_str_mv 2021-06-19T13:52:39Z
dc.type.spa.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TD
format http://purl.org/coar/resource_type/c_db06
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/79654
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/79654
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv eng
language eng
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spelling Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Branch Bedoya, John William7e38ec86da58a9547c188086b39efee8600Patiño Cortés, Diego Albertoa93635a0fd4f153bc64dd192648d57b0600GIDIA - Grupo de Investigación en Inteligencia Artificial2021-06-19T13:52:39Z2021-06-19T13:52:39Z2019-06https://repositorio.unal.edu.co/handle/unal/79654Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustracionesIn this dissertation, we explore the problem of how to describe the shape of an object in 2D and 3D with a set of features that are invariant to isometric transformations. We focus to based our approach on the well-known Medial Axis Transform and its topological properties. We aim to study two problems. The first is how to find a shape representation of a segmented object that exhibits rotation, translation, and reflection invariance. The second problem is how to build a machine learning pipeline that uses the isometric invariance of the shape representation to do both classification and retrieval. Our proposed solution demonstrates competitive results compared to state-of-the-art approaches. We based our shape representation on the medial axis transform (MAT), sometimes called the topological skeleton. Accepted and well-studied properties of the medial axis include: homotopy preservation, rotation invariance, mediality, one pixel thickness, and the ability to fully reconstruct the object. These properties make the MAT a suitable input to create shape features; however, several problems arise because not all skeletonization methods satisfy all the above-mentioned properties at the same time. In general, skeletons based on thinning approaches preserve topology but are noise sensitive and do not allow a proper reconstruction. They are also not invariant to rotations. Voronoi skeletons also preserve topology and are rotation invariant, but do not have information about the thickness of the object, making reconstruction impossible. The Voronoi skeleton is an approximation of the real skeleton. The denser the sampling of the boundary, the better the approximation; however, a denser sampling makes the Voronoi diagram more computationally expensive. In contrast, distance transform methods allow the reconstruction of the original object by providing the distance from every pixel in the skeleton to the boundary. Moreover, they exhibit an acceptable degree of the properties listed above, but noise sensitivity remains an issue. Therefore, we selected distance transform medial axis methods as our skeletonization strategy, and focused on creating a new noise-free approach to solve the contour noise problem. To effectively classify an object, or perform any other task with features based on its shape, the descriptor needs to be a normalized, compact form: $\Phi$ should map every shape $\Omega$ to the same vector space $\mathrm{R}^{n}$. This is not possible with skeletonization methods because the skeletons of different objects have different numbers of branches and different numbers of points, even when they belong to the same category. Consequently, we developed a strategy to extract features from the skeleton through the map $\Phi$, which we used as an input to a machine learning approach. After developing our method for robust skeletonization, the next step is to use such skeleton into the machine learning pipeline to classify object into previously defined categories. We developed a set of skeletal features that were used as input data to the machine learning architectures. We ran experiments on MPEG7 and ModelNet40 dataset to test our approach in both 2D and 3D. Our experiments show results comparable with the state-of-the-art in shape classification and retrieval. Our experiments also show that our pipeline and our skeletal features exhibit some degree of invariance to isometric transformations. In this study, we sought to design an isometric invariant shape descriptor through robust skeletonization enforced by a feature extraction pipeline that exploits such invariance through a machine learning methodology. We conducted a set of classification and retrieval experiments over well-known benchmarks to validate our proposed method. (Tomado de la fuente)En esta disertación se explora el problema de cómo describir la forma de un objeto en 2D y 3D con un conjunto de características que sean invariantes a transformaciones isométricas. La metodología propuesta en este documento se enfoca en la Transformada del Eje Medio (Medial Axis Transform) y sus propiedades topológicas. Nuestro objetivo es estudiar dos problemas. El primero es encontrar una representación matemática de la forma de un objeto que exhiba invarianza a las operaciones de rotación, translación y reflexión. El segundo problema es como construir un modelo de machine learning que use esas invarianzas para las tareas de clasificación y consulta de objetos a través de su forma. El método propuesto en esta tesis muestra resultados competitivos en comparación con otros métodos del estado del arte. En este trabajo basamos nuestra representación de forma en la transformada del eje medio, a veces llamada esqueleto topológico. Algunas propiedades conocidas y bien estudiadas de la transformada del eje medio son: conservación de la homotopía, invarianza a la rotación, su grosor consiste en un solo pixel (1D), y la habilidad para reconstruir el objeto original a través de ella. Estas propiedades hacen de la transformada del eje medio un punto de partida adecuado para crear características de forma. Sin embargo, en este punto surgen varios problemas dado que no todos los métodos de esqueletización satisfacen, al mismo tiempo, todas las propiedades mencionadas anteriormente. En general, los esqueletos basados en enfoques de erosión morfológica conservan la topología del objeto, pero son sensibles al ruido y no permiten una reconstrucción adecuada. Además, no son invariantes a las rotaciones. Otro método de esqueletización son los esqueletos de Voronoi. Los esqueletos de Voronoi también conservan la topología y son invariantes a la rotación, pero no tienen información sobre el grosor del objeto, lo que hace imposible su reconstrucción. Cuanto más denso sea el muestreo del contorno del objeto, mejor será la aproximación. Sin embargo, un muestreo más denso hace que el diagrama de Voronoi sea más costoso computacionalmente. Por el contrario, los métodos basados en la transformada de la distancia permiten la reconstrucción del objeto original, ya que proporcionan la distancia desde cada píxel del esqueleto hasta su punto más cercano en el contorno. Además, exhiben un grado aceptable de las propiedades enumeradas anteriormente, aunque la sensibilidad al ruido sigue siendo un problema. Por lo tanto, en este documento seleccionamos los métodos basados en la transformada de la distancia como nuestra estrategia de esqueletización, y nos enfocamos en crear un nuevo enfoque que resuelva el problema del ruido en el contorno. Para clasificar eficazmente un objeto o realizar cualquier otra tarea con características basadas en su forma, el descriptor debe ser compacto y estar normalizado: $\Phi$ debe relacionar cada forma $\Omega$ al mismo espacio vectorial $\mathrm{R}^{n}$. Esto no es posible con los métodos de esqueletización en el estado del arte, porque los esqueletos de diferentes objetos tienen diferentes números de ramas y diferentes números de puntos incluso cuando pertenecen a la misma categoría. Consecuentemente, en nuestra propuesta desarrollamos una estrategia para extraer características del esqueleto a través de la función $\Phi$, que usamos como entrada para un enfoque de aprendizaje automático. % TODO completar con resultados. Después de desarrollar nuestro método de esqueletización robusta, el siguiente paso es usar dicho esqueleto en un modelo de aprendizaje de máquina para clasificar el objeto en categorías previamente definidas. Para ello se desarrolló un conjunto de características basadas en el eje medio que se utilizaron como datos de entrada para la arquitectura de aprendizaje automático. Realizamos experimentos en los conjuntos de datos: MPEG7 y ModelNet40 para probar nuestro enfoque tanto en 2D como en 3D. Nuestros experimentos muestran resultados comparables con el estado del arte en clasificación y consulta de formas (retrieval). Nuestros experimentos también muestran que el modelo desarrollado junto con nuestras características basadas en el eje medio son invariantes a las transformaciones isométricas. (Tomado de la fuente)Beca para Doctorados Nacionales de Colciencias, convocatoria 725 de 2015DoctoradoDoctor en IngenieríaVisión por computadora y aprendizaje automático104 páginasapplication/pdfengUniversidad Nacional de ColombiaMedellín - Minas - Doctorado en Ingeniería - SistemasDepartamento de la Computación y la DecisiónFacultad de MinasMedellínUniversidad Nacional de Colombia - Sede Medellín000 - Ciencias de la computación, información y obras generales::003 - Sistemas590 - AnimalesMorfología (Zoología)Esqueleto animalMedial Axis TransformIsometryMorphological SkeletonizationShape Analysis and DescriptionShape featureInvariance and EquivariancePointNetChordiogamShape Classification and RetrievalTransformada del eje medioIsometríaEsqueletos topológicosAnálisis y descripción de formaInvarianza y equivarianzaClasificación y recuperación de formasDescripción y análisis de forma basado en la invarianza a isometrías de los esqueletos topológicosShape analysis and description based on the isometric invariances of topological skeletonizationTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDAtabay, H. 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GVyZWNob3MgZGUgYXV0b3IgcXVlIGNvbmxsZXZlIGxhIGRpc3RyaWJ1Y2nDs24gZGUgZXN0b3MgYXJjaGl2b3MgeSBtZXRhZGF0b3MuCkFsIGhhY2VyIGNsaWMgZW4gZWwgc2lndWllbnRlIGJvdMOzbiwgdXN0ZWQgaW5kaWNhIHF1ZSBlc3TDoSBkZSBhY3VlcmRvIGNvbiBlc3RvcyB0w6lybWlub3MuCgpVTklWRVJTSURBRCBOQUNJT05BTCBERSBDT0xPTUJJQSAtIMOabHRpbWEgbW9kaWZpY2FjacOzbiAyNy8yMC8yMDIwCg==

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