Generalized Higher-Order Voronoi Diagrams on Polyhedral Surfaces

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex polyhedral surface in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) on a polyhedral surface with obstacles. To obtain the discrete Voronoi diagrams our algorithms, exploiting hardware graphics capabilities, compute shortest path distances defined by the sites

View-dependent information theory quality measures for pixel sampling and scene discretization in flatland

In this paper, we present view-dependent information theory quality measures for pixel sampling and scene discretization in flatland. The measures are based on a definition for the mutual information of a line, and have a purely geometrical basis. Several algorithms exploiting them are presented and compare well with an existing one based on depth differences

An information theoretic framework for image segmentation

In this paper, an information theoretic framework for image segmentation is presented. This approach is based on the information channel that goes from the image intensity histogram to the regions of the partitioned image. It allows us to define a new family of segmentation methods which maximize the mutual information of the channel. Firstly, a greedy top-down algorithm which partitions an image into homogeneous regions is introduced. Secondly, a histogram quantization algorithm which clusters color bins in a greedy bottom-up way is defined. Finally, the resulting regions in the partitioning algorithm can optionally be merged using the quantized histogram

Point sampling with uniformly distributed lines

In this paper we address the problem of extracting representative point samples from polygonal models. The goal of such a sampling algorithm is to find points that are evenly distributed. We propose star-discrepancy as a measure for sampling quality and propose new sampling methods based on global line distributions. We investigate several line generation algorithms including an efficient hardware-based sampling method. Our method contributes to the area of point-based graphics by extracting points that are more evenly distributed than by sampling with current algorithms

Algorismes per a la resolució de problemes de proximitat en terrenys

El modelatge, visualització i anàlisi de terrenys és de gran importància en els Sistemes d’Informació Geogràfica (GIS). Actualment és de gran interès per a aquesta comunitat disposar de software que permeti analitzar terrenys. L’objectiu principal del projecte és desenvolupar una aplicació per a la resolució de diversos problemes de proximitat en terrenys. Una part important ha d’ésser la de poder generar, visualitzar i modificar un model 3D d’un terreny a partir de dades introduïdes per l’usuari o obtingudes des d’un fitxer. Per tal de poder construir l’aplicació desitjada ha calgut dissenyar una interfície gràfica d’usuari que permetés realitzar de forma interactiva la introducció, modificació i esborrat de les diferents seus (punts, segments, polígons, poligonals...) o restriccions del terreny, així com la seva visualització