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Journals

Meshless Helmholtz-Hodge Decomposition. (pdf)
F. Petronetto, A. Paiva, M. Lage, G. Tavares, H. Lopes and T. Lewiner.
Accepted on IEEE Transactions on Visualization and Computer Graphics, 2009.

Abstract: Vector fields analysis traditionally distinguishes conservative (curl-free) from mass preserving (divergence-free) components. The Helmholtz-Hodge decomposition allows separating any vector field into the sum of three uniquely defined components: curlfree, divergence-free and harmonic. This decomposition is usually achieved by using mesh-based methods such as finite differences or finite elements. This work presents a new meshless approach to the Helmholtz-Hodge decomposition for the analysis of 2D discrete vector fields. It embeds into the SPH particle-based framework. The proposed method is efficient and can be applied to extract features from a 2D discrete vector field and to multiphase fluid flow simulation to ensure incompressibility..

Regularized implicit surface reconstruction from points and normals. (pdf)
B. Mederos, M. Lage, S. Arouca, F. Petronetto, L. Velho, T. Lewiner and H. Lopes.
In Journal of the Brazilian Computer Society, v.13, pp. 7-16, 2007

Abstract: We consider the problem of surface reconstruction of a geometric object from a finite set of sample points with normals. Our contribution is to present a new scheme for implicit surface reconstruction. Similarly to the multilevel partition of unity (MPU) method we hierarchically divide the domain obtaining local approximation for the object on each part, and then patch all together obtaining a global description of the object. Our new scheme uses ridge regression and weighted gradient one fitting techniques to get better stability on local approximations. The method behaves reasonably on sparse set of points and data with holes as those which comes from 3D scanning of real objects.

Conferences

Random Walks on Vector Fields Denoising. (pdf)
J. Paixao, M. Lage, F. Petronetto, A. Laier, S. Pesco, G. Tavares, T. Lewiner, H. Lopes.
To appear in Proceedings of SIBGRAPI 2009.

Abstract: In recent years, several devices allow to directly measure real vector fields, leading to a better understanding of fundamental phenomena such as fluid simulation or brain water movement. This turns vector field visualization and analysis important tools for many applications in engineering and in medicine. However, real data is generally corrupted by noise, puzzling the understanding provided by those tools. Those tools thus need a denoising step as preprocessing, although usual denoising removes discontinuities, which are fundamental for vector field analysis. This paper proposes a novel method for vector field denoising based on random walks which preserve those discontinuities. It works in a meshless setting; it is fast, simple to implement, and shows a better performance than the traditional gaussian denoising technique.

Support Vectors Learning for Vector Field Reconstruction (pdf)
M. Lage, R. Castro, F. Petronetto, G. Tavares, T. Lewiner and H. Lopes
To appear in Proceedings of SIBGRAPI 2009.

Abstract: Sampled vector fields generally appear as measurements of real phenomena. They can be obtained by the use of a Particle Image Velocimetry acquisition device, or as the result of a physical simulation, such as a fluid flow simulation, among many examples. This paper proposes a novel technique for reconstructing a vector field from unstructured samples, formulating the reconstructions a Machine-Learning problem. The machine learns from the samples a global vector field estimation function that is then evaluable at arbitrary points from the whole domain. Using an adaptation of the Support Vector Regression method for multi-scale analysis, the proposed method provides a global, analytical expression for the reconstructed vector field through an efficient nonlinear optimization. Experiments on artificial and real data show a statistically robust behavior of the proposed technique.

A hybrid chain ladder and gaussian process regression method for IBNR estimation. (pdf)
J. Kubrusly, M. Dias, M. Lage and H. Lopes.
In Proceedings of the Fourth Brazilian Conference on Statistical Modelling in Insurance and Finance.

Abstract: This work presents a hybrid model that improves the Chain Ladder method for IBNR reserve computation by learning the residuals of its estimations by the use of a Gaussian Process Regression technique.

Approximations by Smooth Transitions in Binary Space Partitions (pdf)
M. Lage, A. Bordignon, F. Petronetto, A. Veiga, G. Tavares, T. Lewiner, H. Lopes
In Proceedings of SIBGRAPI 2008, IEEE Press, pp. 230-336, 2008.

Abstract: This work proposes a simple approximation scheme for discrete data that leads to an infinitely smooth result without global optimization. It combines the flexibility of Binary Space Partitions Trees with the statistical robustness of Smooth Transition Regression Trees. The construction of the tree is straightforward and easily controllable, using errordriven metrics or external constraints. Moreover, it leads to a concise representation. Applications on synthetic and real data, both scalar and vector-valued demonstrated the effectiveness of this approach.

Vector field reconstruction from sparse samples with applications (pdf)
M. Lage, F. Petronetto, A. Paiva, H. Lopes, T. Lewiner and G. Tavares
In Proceedings of SIBGRAPI 2006, IEEE Press, pp. 297-304, 2006.

Abstract: This work presents a novel algorithm for 2D vector field reconstruction from sparse set of points-vectors pairs. Our approach subdivides the domain adaptively in order to make local piecewise polynomial approximations for the field. It uses partition of unity to blend those local approximations together, generating a global approximation for the field. The flexibility of this scheme allows handling data from very different sources. In particular, this work presents important applications of the proposed method to velocity and acceleration fields analysis, in particular for fluid dynamics visualization.

CHF: A scalable topological data-structure for tetrahedral meshes (pdf)
M. Lage, T. Lewiner, H. Lopes, L. Velho
In Proceedings of SIBGRAPI 2005, IEEE Press, pp. 349-356, 2005.

Abstract: This work introduces a scalable topological data structure for manifold tetrahedral meshes called Compact Half-edge (CHF). It provides a high degree of scalability, which means it is able to optimize the memory consumption / execution time ratio for different applications and data. An object-oriented API using class inheritance and virtual instantiation enables a unique and simple interface of the same functions for every scale. CHF requires very few memory, is simple to implement and easy to use, since it substitutes pointers by containers of integers and basic bitwise rules.

Preprints

CHE: A scalable topological data-structure for triangular meshes (pdf)
M. Lage, T. Lewiner, H. Lopes, L. Velho
Preprint number Mat.13/2005 Puc-Rio de Janeiro

Abstract: This work introduces a scalable topological data structure for manifold triangular meshes called Compact Half–Edge (CHE). It provides a high degree of scalability, since it is able to optimize the memory consumption / execution time ratio for different applications and data by using features of its different levels. An object–oriented API using class inheritance and virtual instantiation enables a unique interface for each function at any level. CHE requires very few memory, is simple to implement and easy to use, since it substitutes pointers by container of integers and basic bitwise rules.

M.Sc. Thesis

Estruturas de dados escalonáveis para variedades de dimensão 2 e 3. (pdf) (pdf-short version) (pdf banner)
M. Lage, Advisor - Prof. H. Lopes (in Pourtuguese)
Thesis number 8176 on PUC-Rio digital Library.

Resumo: Pesquisas na área de estrutura de dados são fundamentais para aumentar a generalidade e eficiência computacional da representação de modelos geométricos. Neste trabalho, apresentamos duas estruturas de dados topológicas escalonáveis, uma para superfícies trianguladas, chamada CHE (Compact Half–Edge), e outra para malhas de tetraedros, chamada CHF (Compact Half–Face). Tais estruturas são compostas de diferentes níveis, que nos possibilitam alterar a quantidade de dados armazenados com objetivo de melhorar sua eficiência computacional. O uso de APIs baseadas no conceito de objeto, e de herança de classes, possibilitam uma interface única para cada função em todos os níveis das estruturas. A CHE e a CHF requerem pouca memória e são simples de implementar já que substituem o uso de ponteiros pelo de contêineres genéricos e regras aritméticas.