Parallel Voronoi Computation for Physics-Based Simulations

International audienceVoronoi diagrams are fundamental data structures in computational geometry, with applications in such areas as physics-based simulations. For non-Euclidean distances, the Voronoi diagram must be performed over a grid-graph, where the edges encode the required distance information. Th e major bottleneck in this case is a shortest path algorithm that must be computed multiple times during the simulation. We present a GPU algorithm for solving the shortest path problem from multiple sources using a generalized distance function. Our algorithm was designed to leverage the grid-based nature of the underlying graph that represents the deformable objects. Experimental results report speed-ups up to 65× over a current reference sequential method

Parallel Shortest Path Algorithm for Voronoi Diagrams with Generalized Distance Functions

International audienceVoronoi diagrams are fundamental data structures in computational geometry with applications on different areas. Recent soft object simulation algorithms for real time physics engines require the computation of Voronoi diagrams over 3D images with non-Euclidean distances. In this case, the computation must be performed over a graph, where the edges encode the required distance information. But excessive computation time of Voronoi diagrams prevent more sophisticated deformations that require interactive topological changes, such as cutting or stitching used in virtual surgery simulations. The major bottleneck in the Voronoi computation in this case is a shortest-path algorithm that must be computed multiple times during the deformation. In this paper, we tackle this problem by proposing a GPU algorithm of the shortest-path algorithm from multiple sources using generalized distance functions. Our algorithm was designed to leverage the grid-based nature of the underlying graph used in the simulation. Experimental results report speed-ups up to 65x over a current reference sequential method.Les Diagrammes de Voronoï sont des structures de données fondamentales de la géométrie algorithmique, avec des applications dans différents domaines. Des nouveaux algorithmes de simulation d'objets déformables, en temps réels, nécessitent le calcul des diagrammes de Voronoï sur des images 3D avec des distances non euclidiennes. Dans ce cas, le calcul doit être effectué sur un graphe, où les arêtes codent l'information de distance requise. Cependant, le temps de calcul des diagrammes de Voronoï est trop coûteux et empêche des déformations plus complexes qui nécessitent des modifications topologiques interactives, telles que la coupe ou la couture utilisée dans les simulations de chirurgie virtuelle. Le goulot d'étranglement majeur dans le calcul de Voronoï dans ce cas est un algorithme du plus court chemin qui doit être calculé plusieurs fois au cours de la déformation. Dans cet article, nous nous attaquons à ce problème en proposant un algorithme de GPU pour le probléme du plus court chemin à partir de plusieurs sources utilisant une fonctions de distance généralisées. Notre algorithme a été conçu pour tirer parti de la nature basé sur une grille du graphe sous-jacent utilisé dans la simulation. Les résultats expérimentaux indiquent des accélérations jusqu'à 65x sur une méthode séquentielle de référence

Parallel Shortest Path Algorithm for Voronoi Diagrams with Generalized Distance Functions

International audienceVoronoi diagrams are fundamental data structures in computational geometry with applications on different areas. Recent soft object simulation algorithms for real time physics engines require the computation of Voronoi diagrams over 3D images with non-Euclidean distances. In this case, the computation must be performed over a graph, where the edges encode the required distance information. But excessive computation time of Voronoi diagrams prevent more sophisticated deformations that require interactive topological changes, such as cutting or stitching used in virtual surgery simulations. The major bottleneck in the Voronoi computation in this case is a shortest-path algorithm that must be computed multiple times during the deformation. In this paper, we tackle this problem by proposing a GPU algorithm of the shortest-path algorithm from multiple sources using generalized distance functions. Our algorithm was designed to leverage the grid-based nature of the underlying graph used in the simulation. Experimental results report speed-ups up to 65x over a current reference sequential method.Les Diagrammes de Voronoï sont des structures de données fondamentales de la géométrie algorithmique, avec des applications dans différents domaines. Des nouveaux algorithmes de simulation d'objets déformables, en temps réels, nécessitent le calcul des diagrammes de Voronoï sur des images 3D avec des distances non euclidiennes. Dans ce cas, le calcul doit être effectué sur un graphe, où les arêtes codent l'information de distance requise. Cependant, le temps de calcul des diagrammes de Voronoï est trop coûteux et empêche des déformations plus complexes qui nécessitent des modifications topologiques interactives, telles que la coupe ou la couture utilisée dans les simulations de chirurgie virtuelle. Le goulot d'étranglement majeur dans le calcul de Voronoï dans ce cas est un algorithme du plus court chemin qui doit être calculé plusieurs fois au cours de la déformation. Dans cet article, nous nous attaquons à ce problème en proposant un algorithme de GPU pour le probléme du plus court chemin à partir de plusieurs sources utilisant une fonctions de distance généralisées. Notre algorithme a été conçu pour tirer parti de la nature basé sur une grille du graphe sous-jacent utilisé dans la simulation. Les résultats expérimentaux indiquent des accélérations jusqu'à 65x sur une méthode séquentielle de référence

Measuring phenology uncertainty with large scale image processing

International audienceOne standard method to capture data for phenological studies is with digital cameras, taking periodic pictures of vegetation. The large volume of digital images introduces the opportunity to enrich these studies by incorporating big data techniques. The new challenges, then, are to efficiently process large datasets and produce insightful information by controlling noise and variability. On these grounds, the contributions of this paper are the following. (a) A histogram-based visualization for large scale phenological data. (b) Phenological metrics based on the HSV color space, that enhance such histogram-based visualization. (c) A mathematical model to tackle the natural variability and uncertainty of phenological images. (d) The implementation of a parallel workflow to process a large amount of collected data efficiently. We validate these contributions with datasets taken from the Phenological Eyes Network (PEN), demonstrating the effectiveness of our approach. The experiments presented here are reproducible with the provided companion materia

Conversion of Binary Space Partitioning Trees to Boundary Representation

. Binary Space Partitioning Trees (BSP-Trees) have been proposed as an alternative way to represent polytopes based on the spatial subdivision paradigm. Algorithms that convert from Boundary Representation (BRep) to BSP-Trees have been proposed, but none is known to perform the opposite conversion. In this paper we present such an algorithm, that takes as input a BSP-Tree representation for a polytope and produces a BRep as output. The difficulty in designing such algorithm comes from the fact that the information about the boundary is not explicitly represented in the BSP-Tree. The solution we present involves a recursive traversal of the tree to compute lower dimensional information, along with a gluing algorithm that combine the convex regions defined by the BSP-Tree, removing internal features. A new data structure is proposed (a Topological BSP-Tree), that augments the traditional BSPtree with topological pointers and is used to store intermediate results used in the reconstructio..

Explorando a Multidimensionalidade da Kd-Tree para Suporte a Temporalidade em Dados Espaciais Vetoriais do Tipo Ponto

The representation of time in geographic information systems (GIS) has been subject of intense investigation in late years. Actual research involves from modeling techniques for spatio-temporal representation of reality to spatio-temporal data structures and file organizations. In this paper, we propose to explore the multidimensional structure of both the Kd-Tree and the Adaptive Kd-Tree in order to keep the validation time or transaction time of the points stored in them