Self-Organized Maps

Se han obtenido los siguientes resultados: (1) Estudio de topologías bidimensionales alternativas: se muestra la importancia de topologías alternativas basadas en áreas ajenas como las teselaciones. (2) Estudio comparativo de topologías en una, dos y tres dimensiones: se revela la influencia de la dimensión en el funcionamiento de una SOM a escala local y global. (3) Estudio de alternativas al movimiento euclídeo: se propone y presenta la alternativa FRSOM al algoritmo SOM clásico. En FRSOM, las neuronas esquivan barreras predefinidas en su movimiento. Las conclusiones más relevantes que emanan de esta Tesis Doctoral son las siguientes: (1) La calidad del clustering y de la preservación topológica de una SOM puede ser mejorada mediante el uso de topologías alternativas y también evitando regiones prohibidas que no contribuyan significativamente al Error Cuadrático Medio (ECM). (2) La dimensióon de la SOM que obtiene mejores resultados es la propia dimensión intrínseca de los datos. Además, en general, valores bajos para la dimensión de la SOM producen mejores resultados en términos del ECM, y valores altos ocasionan mejor aprendizaje de la estructura de los datos.Los mapas auto-organizados o redes de Kohonen (SOM por sus siglas en inglés, self-organizing map) fueron introducidos por el profesor finlandés Teuvo Kalevi Kohonen en los años 80. Un mapa auto-organizado es una herramienta que analiza datos en muchas dimensiones con relaciones complejas entre ellos y los reduce o representa en, usualmente, una, dos o tres dimensiones. La propiedad más importante de una SOM es que preserva las propiedades topológicas de los datos, es decir, que datos próximos aparecen próximos en la representación. La literatura relacionada con los mapas auto-organizados y sus aplicaciones es muy diversa y numerosa. Las neuronas en un mapa auto-organizado clásico están distribuidas en una topología (o malla) bidimensional cuadrada o hexagonal y las distancias entre ellas son distancias euclídeas. Una de las disciplinas de investigación en SOM consiste en la modificación y generalización del algoritmo SOM. Esta Tesis Doctoral por compendio de publicaciones se centra en esta línea de investigación. En concreto, los objetivos desarrollados han sido el estudio de topologías bidimensionales alternativas, el estudio comparativo de topologías de una, dos y tres dimensiones y el estudio de variaciones para la distancia y movimientos euclídeos. Estos objetivos se han abordado mediante el método científico a través de las siguientes fases: aprehensión de resultados conocidos, planteamiento de hipótesis, propuesta de métodos alternativos, confrontación de métodos mediante experimentación, aceptación y rechazo de las diversas hipótesis mediante métodos estadísticos

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

Unsupervised Learning of Category-Specific Symmetric 3D Keypoints from Point Sets

Automatic discovery of category-specific 3D keypoints from a collection of objects of a category is a challenging problem. The difficulty is added when objects are represented by 3D point clouds, with variations in shape and semantic parts and unknown coordinate frames. We define keypoints to be category-specific, if they meaningfully represent objects’ shape and their correspondences can be simply established order-wise across all objects. This paper aims at learning such 3D keypoints, in an unsupervised manner, using a collection of misaligned 3D point clouds of objects from an unknown category. In order to do so, we model shapes defined by the keypoints, within a category, using the symmetric linear basis shapes without assuming the plane of symmetry to be known. The usage of symmetry prior leads us to learn stable keypoints suitable for higher misalignments. To the best of our knowledge, this is the first work on learning such keypoints directly from 3D point clouds for a general category. Using objects from four benchmark datasets, we demonstrate the quality of our learned keypoints by quantitative and qualitative evaluations. Our experiments also show that the keypoints discovered by our method are geometrically and semantically consistent

Model figging of articulated objects

本稿では人体や手などに代表される多関節物体の三次元姿勢を画像から推定するモデルフィッティングの技術についてサーベイする。画像によるモデルフィッティングの枠組みを,1)推定に利用される画像特徴,2)画像と照合するモデルの表現と照合のパラメータ空間,3)照合時の評価関数と最適解の探索手法,にわけて多関節物体の三次元姿勢推定に特徴的な要素を上記三つの観点から比較整理することを試みる。In this paper, we present a survey report for the model fitting method to estimate3-D posture of articulated objects such as human body and hand. We decompose the model fitting framework into the following threee lements: 1)image feature, 2)model description and parameter space for model-image matching and 3)matching function and its optimization. From the viewpoint of these three issues, we try to compare the various methods of model fitting to each other and summarize them

Manifold Learning for Natural Image Sets, Doctoral Dissertation August 2006

The field of manifold learning provides powerful tools for parameterizing high-dimensional data points with a small number of parameters when this data lies on or near some manifold. Images can be thought of as points in some high-dimensional image space where each coordinate represents the intensity value of a single pixel. These manifold learning techniques have been successfully applied to simple image sets, such as handwriting data and a statue in a tightly controlled environment. However, they fail in the case of natural image sets, even those that only vary due to a single degree of freedom, such as a person walking or a heart beating. Parameterizing data sets such as these will allow for additional constraints on traditional computer vision problems such as segmentation and tracking. This dissertation explores the reasons why classical manifold learning algorithms fail on natural image sets and proposes new algorithms for parameterizing this type of data

Data-driven shape analysis and processing

Data-driven methods serve an increasingly important role in discovering geometric, structural, and semantic relationships between shapes. In contrast to traditional approaches that process shapes in isolation of each other, data-driven methods aggregate information from 3D model collections to improve the analysis, modeling and editing of shapes. Through reviewing the literature, we provide an overview of the main concepts and components of these methods, as well as discuss their application to classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing

Geometric deep learning for shape analysis: extending deep learning techniques to non-Euclidean manifolds

The past decade in computer vision research has witnessed the re-emergence of artificial neural networks (ANN), and in particular convolutional neural network (CNN) techniques, allowing to learn powerful feature representations from large collections of data. Nowadays these techniques are better known under the umbrella term deep learning and have achieved a breakthrough in performance in a wide range of image analysis applications such as image classification, segmentation, and annotation. Nevertheless, when attempting to apply deep learning paradigms to 3D shapes one has to face fundamental differences between images and geometric objects. The main difference between images and 3D shapes is the non-Euclidean nature of the latter. This implies that basic operations, such as linear combination or convolution, that are taken for granted in the Euclidean case, are not even well defined on non-Euclidean domains. This happens to be the major obstacle that so far has precluded the successful application of deep learning methods on non-Euclidean geometric data. The goal of this thesis is to overcome this obstacle by extending deep learning tecniques (including, but not limiting to CNNs) to non-Euclidean domains. We present different approaches providing such extension and test their effectiveness in the context of shape similarity and correspondence applications. The proposed approaches are evaluated on several challenging experiments, achieving state-of-the- art results significantly outperforming other methods. To the best of our knowledge, this thesis presents different original contributions. First, this work pioneers the generalization of CNNs to discrete manifolds. Second, it provides an alternative formulation of the spectral convolution operation in terms of the windowed Fourier transform to overcome the drawbacks of the Fourier one. Third, it introduces a spatial domain formulation of convolution operation using patch operators and several ways of their construction (geodesic, anisotropic diffusion, mixture of Gaussians). Fourth, at the moment of publication the proposed approaches achieved state-of-the-art results in different computer graphics and vision applications such as shape descriptors and correspondence

On Motion Parameterizations in Image Sequences from Fixed Viewpoints

This dissertation addresses the problem of parameterizing object motion within a set of images taken with a stationary camera. We develop data-driven methods across all image scales: characterizing motion observed at the scale of individual pixels, along extended structures such as roads, and whole image deformations such as lungs deforming over time. The primary contributions include: a) fundamental studies of the relationship between spatio-temporal image derivatives accumulated at a pixel, and the object motions at that pixel,: b) data driven approaches to parameterize breath motion and reconstruct lung CT data volumes, and: c) defining and offering initial results for a new class of Partially Unsupervised Manifold Learning: PUML) problems, which often arise in medical imagery. Specifically, we create energy functions for measuring how consistent a given velocity vector is with observed spatio-temporal image derivatives. These energy functions are used to fit parametric snake models to roads using velocity constraints. We create an automatic data-driven technique for finding the breath phase of lung CT scans which is able to replace external belt measurements currently in use clinically. This approach is extended to automatically create a full deformation model of a CT lung volume during breathing or heart MRI during breathing and heartbeat. Additionally, motivated by real use cases, we address a scenario in which a dataset is collected along with meta-data which describes some, but not all, aspects of the dataset. We create an embedding which displays the remaining variability in a dataset after accounting for variability related to the meta-data