Application des surfaces de Bézier pour la reconstruction 3-D

Dans ce travail, nous présentons une méthode de reconstruction 3-D basée sur l’utilisation des surfaces de Bézier, combinée au lissage tridimensionnel. L’idée principale est de générer, à partir d’un nuage de points issus de la numérisation d’un objet 3-D, une représentation de surfaces à partir de la quelle nous procédons à la reconstruction 3-D de l’objet en question. Ensuite nous présentons les résultats de notre méthode appliquées à quelques objets

Ajuste con nurbs a una malla cuadrilateral regularizada

Este artículo propone un método de ajuste de superficies con NURBS a partir de la regularización de una malla cuadrilateral mediante Geodésicas y BSplines, de tal manera que se aproxime precisa y continuamente la geometría de la superficie del objeto físico desconocido. La primera fase del método propuesto, consiste de los siguientes pasos: 1. Selección de un cuadrilátero ; 2. Selección de un lado del cuadrilátero escogido y su opuesto ; 3. Regularización utilizando Bsplines con densidad lambda ; 4. Emparejamiento de puntos regular izados mediante geodésicas FMM; y 5. Generación de puntos par a cada línea de Bspline con densidad lambda. La malla cuadrilateral regularizada obtenida de la fase anterior, sirve como base par a el posterior trazado de superficies NURBS (Non Uniform Rational B-Splines), las cuales son un estándar de los sistemas CAD/CAM. Finalmente, los parches NURBS son optimizados mediante Estrategias Evolutivas

Automatic construction of nurbs surfaces from unorganized points

Modeling with Non Uniform Rational B-Splines (NURBS) surfaces has become a standard in CAD/CAM systems due to its stability, flexibility, and local modification properties. The advantage of fitting with NURBS surfaces is well known, but it is also known that NURBS surfaces have several deficiencies. A NURBS surface cannot be fitted over an unorganized and scattered set of points and the representation of sharp features like edges, corners, and high curvatures is poor. This paper presents a new method for fitting a NURBS surface over an unorganized and scattered cloud of points, preserving its sharp features. In contrast with other methods, ours does not need either to construct a network of NURBS patches or polygon meshes. By reducing the dimensionality of the point cloud using ISOMAP algorithms, our method detects both regions with lacking points, and regions where the cloud is too dense. Then, the cloud is regularized by inserting and removing points, and it is approximated by a NURBS surface. An evolutionary strategy obtains the weights of the NURBS surface in order to improve the representation of sharp features

Multiresolution editing for B-spline curves and surfaces

Since 1980 surface modeling has been used in industrial design, CAD and entertainment to create and represent complex forms. Even with this comparatively long history of development, challenges remain in free-form surface modeling. One such challenge is building surface creation and editing techniques that effectively balance the need for local control with the need to control the overall global shape, or sweep of the surface. This dissertation presents a multiresolution approach to the creation of surfaces that allows a designer to more easily manage this balance between local and global control. The techniques presented in this dissertation utilize a wavelet decomposition of B-spline curves and surfaces to allow a designer to easily develop the basic shape using lower level representations, and then seamlessly switch to higher level representations to achieve fine control over local features. The algorithms described in the dissertation are implemented in an interactive software system that is used to demonstrate their effectiveness in comparison to existing methods

Construction of C\u3csup\u3e∞\u3c/sup\u3e Surfaces From Triangular Meshes Using Parametric Pseudo-Manifolds

We present a new constructive solution for the problem of fitting a smooth surface to a given triangle mesh. Our construction is based on the manifold-based approach pioneered by Grimm and Hughes. The key idea behind this approach is to define a surface by overlapping surface patches via a gluing process, as opposed to stitching them together along their common boundary curves. The manifold based approach has proved to be well-suited to fit with relative ease, Ck-continuous parametric surfaces to triangle and quadrilateral meshes, for any arbitrary finite k or even k = ∞. Smooth surfaces generated by the manifold-based approach share some of the most important properties of splines surfaces, such as local shape control and fixed-sized local support for basis functions. In addition, the differential structure of a manifold provides us with a natural setting for solving equations on the surface boundary of 3D shapes. Our new manifold-based solution possesses most of the best features of previous constructions. In particular, our construction is simple, compact, powerful, and flexible in ways of defining the geometry of the resulting surface. Unlike some of the most recent manifold-based solutions, ours has been devised to work with triangle meshes. These meshes are far more popular than any other kind of mesh encountered in computer graphics and geometry processing applications. We also provide a mathematically sound theoretical framework to undergird our solution. This theoretical framework slightly improves upon the one given by Grimm and Hughes, which was used by most manifold-based constructions introduced before

Expressive Knowledge Resources in Probabilistic Models

Understanding large collections of unstructured documents remains a persistent problem. Users need to understand the themes of a corpus and to explore documents of interest. Topic models are a useful and ubiquitous tool to discover the main themes (namely topics) of the corpus. Topic models have been successfully applied in natural language processing, computer vision, information retrieval, cognitive science, etc. However, the discovered topics are not always meaningful: some topics confuse two or more themes into one topic; two different topics can be near duplicates; and some topics make no sense at all. Adding knowledge resources into topic models can improve the topics. However, how to encode knowledge into topic models and where to find these knowledge resources remain two scientific challenges. To address these problems, this thesis presents tree-based topic models to encode prior knowledge, a mechanism incorporating knowledge from untrained users, a polylingual tree-based topic model based on existing dictionaries as knowledge resources, an exploration of regularizing spectral methods to encode prior knowledge into topic models, and a model for automatically building hierarchies of prior knowledge for topic models. To encode knowledge resources into topic models, we first present tree-based topic models, where correlations between word types are modeled as a prior tree and applied to topic models. We also develop more efficient inference algorithms for tree- based topic models. Experiments on multiple corpora show that efficiency is greatly improved on different number of topics, number of correlations and vocabulary size. Because users decide whether the topics are useful or not, users' feedback is necessary for effective topic modeling. We thus propose a mechanism for giving normal users a voice to topic models by encoding users' feedback as correlations between word types into tree-based topic models. This framework, interactive topic modeling (ITM), allows untrained users to encode their feedback easily and iteratively into the topic models. We validate the framework both with simulated and real users and discuss strategies for improving the user experience to adapt models to what users need. Existing knowledge resources such as dictionaries can also improve the model. We propose polylingual tree-based topic models based on bilingual dictionaries and apply this model to domain adaptation for statistical Machine Translation. We derive three different inference schemes and evaluate the efficacy of our model on a Chinese to English translation system, and obtain up to 1.2 BLEU improvement over the machine translation baseline. This thesis further explores an alternative way--regularizing spectral methods for topic models--to encode prior knowledge into topic models. Spectral methods offer scalable alternatives to Markov chain Monte Carlo and expectation maximization. However, these new methods lack the priors that are associated with probabilistic models. We examine Arora et al.'s anchor algorithm for topic models and encode prior knowledge by regularizing the anchor algorithm to improve the interpretability and generalizability of topic models. Because existing knowledge resources are limited and because obtaining the knowledge from users is expensive and time-consuming, automatic techniques should also be considered to extract knowledge from the corpus. This thesis further presents a Bayesian hierarchical clustering technique with the Beta coalescent, which provides a possible way to build up the prior tree automatically. Because of its computational complexity, we develop new sampling schemes using sequential Monte carlo and Dirichlet process mixture models, which render the inference practical and efficient. This thesis explores sources of prior knowledge, presents different ways to encode these expressive knowledge resources into probabilistic topic models, and also applies these models in translation domain adaptation. We also discuss further extensions in a bigger picture of interactive machine learning techniques and domain adaptation for downstream tasks

Génération et édition de textures géométriques représentées par des ensembles de points

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Hierarchical Triangular Splines

International audienceSmooth parametric surfaces interpolating triangular meshes are very useful for modeling surfaces of arbitrary topology. Several interpolants based on this kind of surfaces have been developed over the last fifteen years. However, with current 3D acquisition equipments, models are becoming more and more complex. Since previous interpolating methods lack a local refinement property, there is no way to locally adapt the level of detail. In this paper, we introduce a hierarchical triangular surface model. The surface is overall tangent plane continuous and is defined parametrically as a piecewise quintic polynomial. It can be adaptively refined while preserving the overall tangent plane continuity. This model enables designers to create a complex smooth surface composed of a small number of patches, to which details can be added by locally refining the patches until an arbitrary small size is reached. It is implemented as a hierarchical data structure where the top layer describes a coarse, smooth base surface, and the lower levels encode the details in local frame coordinates

G.P.: Smooth adaptive fitting of 3d models using hierarchical triangular splines

The recent ability to measure quickly and inexpensively dense sets of points on physical objects has deeply influenced the way engineers used to represent shapes in CAD systems, animation software or in the game industry. Many researchers advocated to completely bypass smooth surface representations, and to stick to a dense mesh model throughout the design process. Yet smooth analytic representations are still required in standard CAD systems and animation software, for reasons of compactness, control, appearance and manufacturability. In this paper we present a method for fitting a smooth adaptively refinable triangular spline surface of arbitrary topology to an arbitrary dense triangular mesh. The final surface is composed of low-degree polynomial patches that join with G1-continuity. The ability to adaptively refine the model allows to achieve a given approximation error with a minimal number of patches. 1