arXiv subjects

Anselmo A. Montenegro

Publications and source records attributed to Anselmo A. Montenegro.

2 recordsLinked to original sources

arXiv2020

A Robust Feature-aware Sparse Mesh Representation

The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have started emerging recently. In this paper, we investigate the problem of sparsely representing discrete surfaces and propose a new representation that is capable of providing tools for solving different geometry processing problems. The sparse discrete surface representation is obtained by combining innovative approaches into an integrated method. First, to deal with irregular mesh domains, we devised a new way to subdivide discrete meshes into a set of patches using a feature-aware seed sampling. Second, we achieve good surface approximation with over-fitting control by combining the power of a continuous global dictionary representation with a modified Orthogonal Marching Pursuit. The discrete surface approximation results produced were able to preserve the shape features while being robust to over-fitting. Our results show that the method is quite promising for applications like surface re-sampling and mesh compression.

cs.CG↗

arXiv2019

A minimalistic approach for fast computation of geodesic distances on triangular meshes

The computation of geodesic distances is an important research topic in Geometry Processing and 3D Shape Analysis as it is a basic component of many methods used in these areas. In this work, we present a minimalistic parallel algorithm based on front propagation to compute approximate geodesic distances on meshes. Our method is practical and simple to implement and does not require any heavy pre-processing. The convergence of our algorithm depends on the number of discrete level sets around the source points from which distance information propagates. To appropriately implement our method on GPUs taking into account memory coalescence problems, we take advantage of a graph representation based on a breadth-first search traversal that works harmoniously with our parallel front propagation approach. We report experiments that show how our method scales with the size of the problem. We compare the mean error and processing time obtained by our method with such measures computed using other methods. Our method produces results in competitive times with almost the same accuracy, especially for large meshes. We also demonstrate its use for solving two classical geometry processing problems: the regular sampling problem and the Voronoi tessellation on meshes.

cs.CG↗