Improvements in the ray tracing of implicit surfaces based on interval arithmetic

Las superfícies implícitas son útiles en muchas áreasde los gráficos por ordenador. Una de sus principales ventajas es que pueden ser fácilmente usadas como primitivas para modelado. Aun asi, no son muy usadas porque su visualización toma bastante tiempo. Cuando se necesita una visualización precisa, la mejor opción es usar trazado de rayos. Sin embargo, pequeñas partes de las superficies desaparecen durante la visualización. Esto ocurre por la truncación que se presenta en la representación en punto flotante de los ordenadores; algunos bits se puerden durante las operaciones matemáticas en los algoritmos de intersección. En este tesis se presentan algoritmos para solucionar esos problemas. La investigación se basa en el uso del Análisis Intervalar Modal el cual incluye herramientas para resolver problemas con incertidumbe cuantificada. En esta tesis se proporcionan los fundamentos matemáticos necesarios para el desarrollo de estos algoritmos.

Refinement criteria for global illumination using convex funcions

In several computer graphics areas, a refinement criterion is often needed to decide whether to go on or to stop sampling a signal. When the sampled values are homogeneous enough, we assume that they represent the signal fairly well and we do not need further refinement, otherwise more samples are required, possibly with adaptive subdivision of the domain. For this purpose, a criterion which is very sensitive to variability is necessary. In this paper, we present a family of discrimination measures, the f-divergences, meeting this requirement. These convex functions have been well studied and successfully applied to image processing and several areas of engineering. Two applications to global illumination are shown: oracles for hierarchical radiosity and criteria for adaptive refinement in ray-tracing. We obtain significantly better results than with classic criteria, showing that f-divergences are worth further investigation in computer graphics. Also a discrimination measure based on entropy of the samples for refinement in ray-tracing is introduced. The recursive decomposition of entropy provides us with a natural method to deal with the adaptive subdivision of the sampling region

Visual SLAM for underwater vehicles using video velocity log and natural landmarks

A visual SLAM system has been implemented and optimised for real-time deployment on an AUV equipped with calibrated stereo cameras. The system incorporates a novel approach to landmark description in which landmarks are local sub maps that consist of a cloud of 3D points and their associated SIFT/SURF descriptors. Landmarks are also sparsely distributed which simplifies and accelerates data association and map updates. In addition to landmark-based localisation the system utilises visual odometry to estimate the pose of the vehicle in 6 degrees of freedom by identifying temporal matches between consecutive local sub maps and computing the motion. Both the extended Kalman filter and unscented Kalman filter have been considered for filtering the observations. The output of the filter is also smoothed using the Rauch-Tung-Striebel (RTS) method to obtain a better alignment of the sequence of local sub maps and to deliver a large-scale 3D acquisition of the surveyed area. Synthetic experiments have been performed using a simulation environment in which ray tracing is used to generate synthetic images for the stereo system