Variance of two in nite path length random walk radiosity estimators

The error in an unbiased Monte Carlo method is characterized by the variance. By knowing the variance of different Monte Carlo estimators for Radiosity (and also their cost) we should be able to obtain the most efficient of them. This paper gives the variances for two such estimators, the shooting and gathering infinite path length random walk estimators. This completes a previous work of the author on finite path length estimators

Thermal radiation view factor: Methods, accuracy and computer-aided procedures

The computer aided thermal analysis programs which predicts the result of predetermined acceptable temperature range prior to stationing of these orbiting equipment in various attitudes with respect to the Sun and the Earth was examined. Complexity of the surface geometries suggests the use of numerical schemes for the determination of these viewfactors. Basic definitions and standard methods which form the basis for various digital computer methods and various numerical methods are presented. The physical model and the mathematical methods on which a number of available programs are built are summarized. The strength and the weaknesses of the methods employed, the accuracy of the calculations and the time required for computations are evaluated. The situations where accuracies are important for energy calculations are identified and methods to save computational times are proposed. Guide to best use of the available programs at several centers and the future choices for efficient use of digital computers are included in the recommendations

Information theoretic refinement criteria for image synthesis

Aquest treball està enmarcat en el context de gràfics per computador partint de la intersecció de tres camps: rendering, teoria de la informació, i complexitat.Inicialment, el concepte de complexitat d'una escena es analitzat considerant tres perspectives des d'un punt de vista de la visibilitat geomètrica: complexitat en un punt interior, complexitat d'una animació, i complexitat d'una regió. L'enfoc principal d'aquesta tesi és l'exploració i desenvolupament de nous criteris de refinament pel problema de la il·luminació global. Mesures de la teoria de la informació basades en la entropia de Shannon i en la entropia generalitzada de Harvda-Charvát-Tsallis, conjuntament amb les f-divergències, són analitzades com a nuclis del refinement. Mostrem com ens aporten una rica varietat d'eficients i altament discriminatòries mesures que són aplicables al rendering en els seus enfocs de pixel-driven (ray-tracing) i object-space (radiositat jeràrquica).Primerament, basat en la entropia de Shannon, es defineixen un conjunt de mesures de qualitat i contrast del pixel. S'apliquen al supersampling en ray-tracing com a criteris de refinement, obtenint un algorisme nou de sampleig adaptatiu basat en entropia, amb un alt rati de qualitat versus cost. En segon lloc, basat en la entropia generalitzada de Harvda-Charvát-Tsallis, i en la informació mutua generalitzada, es defineixen tres nous criteris de refinament per la radiositat jeràrquica. En correspondencia amb tres enfocs clàssics, es presenten els oracles basats en la informació transportada, el suavitzat de la informació, i la informació mutua, amb resultats molt significatius per aquest darrer. Finalment, tres membres de la familia de les f-divergències de Csiszár's (divergències de Kullback-Leibler, chi-square, and Hellinger) son analitzats com a criteris de refinament mostrant bons resultats tant pel ray-tracing com per la radiositat jeràrquica.This work is framed within the context of computer graphics starting out from the intersection of three fields: rendering, information theory, and complexity.Initially, the concept of scene complexity is analysed considering three perspectives from a geometric visibility point of view: complexity at an interior point, complexity of an animation, and complexity of a region. The main focus of this dissertation is the exploration and development of new refinement criteria for the global illumination problem. Information-theoretic measures based on Shannon entropy and Harvda-Charvát-Tsallis generalised entropy, together with f-divergences, are analysed as kernels of refinement. We show how they give us a rich variety of efficient and highly discriminative measures which are applicable to rendering in its pixel-driven (ray-tracing) and object-space (hierarchical radiosity) approaches.Firstly, based on Shannon entropy, a set of pixel quality and pixel contrast measures are defined. They are applied to supersampling in ray-tracing as refinement criteria, obtaining a new entropy-based adaptive sampling algorithm with a high rate quality versus cost. Secondly, based on Harvda-Charvát-Tsallis generalised entropy, and generalised mutual information, three new refinement criteria are defined for hierarchical radiosity. In correspondence with three classic approaches, oracles based on transported information, information smoothness, and mutual information are presented, with very significant results for the latter. And finally, three members of the family of Csiszár's f-divergences (Kullback-Leibler, chi-square, and Hellinger divergences) are analysed as refinement criteria showing good results for both ray-tracing and hierarchical radiosity

Generating Radiosity Maps on the GPU

Global illumination algorithms are used to render photorealistic images of 3D scenes taking into account both direct lighting from the light source and light reflected from other surfaces in the scene. Algorithms based on computing radiosity were among the first to be used to calculate indirect lighting, although they make assumptions that work only for diffusely reflecting surfaces. The classic radiosity approach divides a scene into multiple patches and generates a linear system of equations which, when solved, gives the values for the radiosity leaving each patch. This process can require extensive calculations and is therefore very slow. An alternative to solving a large system of equations is to use a Monte Carlo method of random sampling. In this approach, a large number of rays are shot from each patch into its surroundings and the irradiance values obtained from these rays are averaged to obtain a close approximation to the real value. This thesis proposes the use of a Monte Carlo method to generate radiosity texture maps on graphics hardware. By storing the radiosity values in textures, they are immediately available for rendering, making this algorithm useful for interactive implementations. We have built a framework to run this algorithm and using current graphics cards (NV6800 or higher) it is possible to execute it almost interactively for simple scenes and within relatively low times for more complex scenes

Efficient Many-Light Rendering of Scenes with Participating Media

We present several approaches based on virtual lights that aim at capturing the light transport without compromising quality, and while preserving the elegance and efficiency of many-light rendering. By reformulating the integration scheme, we obtain two numerically efficient techniques; one tailored specifically for interactive, high-quality lighting on surfaces, and one for handling scenes with participating media

Efficient representations of large radiosity matrices

The radiosity equation can be expressed as a linear system, where light interactions between patches of the scene are considered. Its resolution has been one of the main subjects in computer graphics, which has lead to the development of methods focused on different goals. For instance, in inverse lighting problems, it is convenient to solve the radiosity equation thousands of times for static geometries. Also, this calculation needs to consider many (or infinite) light bounces to achieve accurate global illumination results. Several methods have been developed to solve the linear system by finding approximations or other representations of the radiosity matrix, because the full storage of this matrix is memory demanding. Some examples are hierarchical radiosity, progressive refinement approaches, or wavelet radiosity. Even though these methods are memory efficient, they may become slow for many light bounces, due to their iterative nature. Recently, efficient methods have been developed for the direct resolution of the radiosity equation. In this case, the challenge is to reduce the memory requirements of the radiosity matrix, and its inverse. The main objective of this thesis is exploiting the properties of specific problems to reduce the memory requirements of the radiosity problem. Hereby, two types of problems are analyzed. The first problem is to solve radiosity for scenes with a high spatial coherence, such as it happens to some architectural models. The second involves scenes with a high occlusion factor between patches. For the high spatial coherence case, a novel and efficient error-bounded factorization method is presented. It is based on the use of multiple singular value decompositions along with a space filling curve, which allows to exploit spatial coherence. This technique accelerates the factorization of in-core matrices, and allows to work with out-of-core matrices passing only one time over them. In the experimental analysis, the presented method is applied to scenes up to 163K patches. After a precomputation stage, it is used to solve the radiosity equation for fixed geometries and infinite bounces, at interactive times. For the high occlusion problem, city models are used. In this case, the sparsity of the radiosity matrix is exploited. An approach for radiative exchange computation is proposed, where the inverse of the radiosity matrix is approximated. In this calculation, near-zero elements are removed, leading to a highly sparse result. This technique is applied to simulate daylight in urban environments composed by up to 140k patches.La ecuación de radiosidad tiene por objetivo el cálculo de la interacción de la luz con los elementos de la escena. Esta se puede expresar como un sistema lineal, cuya resolución ha derivado en el desarrollo de diversos métodos gráficos para satisfacer propósitos específicos. Por ejemplo, en problemas inversos de iluminación para geometrías estáticas, se debe resolver la ecuación de radiosidad miles de veces. Además, este cálculo debe considerar muchos (infinitos) rebotes de luz, si se quieren obtener resultados precisos de iluminación global. Entre los métodos desarrollados, se destacan aquellos que generan aproximaciones u otras representaciones de la matriz de radiosidad, debido a que su almacenamiento requiere grandes cantidades de memoria. Algunos ejemplos de estas técnicas son la radiosidad jerárquica, el refinamiento progresivo y la radiosidad basada en wavelets. Si bien estos métodos son eficientes en cuanto a memoria, pueden ser lentos cuando se requiere el cálculo de muchos rebotes de luz, debido a su naturaleza iterativa. Recientemente se han desarrollado métodos eficientes para la resolución directa de la ecuación de radiosidad, basados en el pre-cómputo de la inversa de la matriz de radiosidad. En estos casos, el desafío consiste en reducir los requerimientos de memoria y tiempo de ejecución para el cálculo de la matriz y de su inversa. El principal objetivo de la tesis consiste en explotar propiedades específicas de ciertos problemas de iluminación para reducir los requerimientos de memoria de la ecuación de radiosidad. En este contexto, se analizan dos casos diferentes. El primero consiste en hallar la radiosidad para escenas con alta coherencia espacial, tal como ocurre en algunos modelos arquitectónicos. El segundo involucra escenas con un elevado factor de oclusión entre parches. Para el caso de alta coherencia espacial, se presenta un nuevo método de factorización de matrices que es computacionalmente eficiente y que genera aproximaciones cuyo error es configurable. Está basado en el uso de múltiples descomposiciones en valores singulares (SVD) junto a una curva de recubrimiento espacial, lo que permite explotar la coherencia espacial. Esta técnica acelera la factorización de matrices que entran en memoria, y permite trabajar con matrices que no entran en memoria, recorriéndolas una única vez. En el análisis experimental, el método presentado es aplicado a escenas de hasta 163 mil parches. Luego de una etapa de precómputo, se logra resolver la ecuación de radiosidad en tiempos interactivos, para geométricas estáticas e infinitos rebotes. Para el problema de alta oclusión, se utilizan modelos de ciudades. En este caso, se aprovecha la baja densidad de la matriz de radiosidad, y se propone una técnica para el cálculo aproximado de su inversa. En este cálculo, los elementos cercanos a cero son eliminados. La técnica es aplicada a la simulación de la luz natural en ambientes urbanos compuestos por hasta 140 mil parches

Implementation and Analysis of an Image-Based Global Illumination Framework for Animated Environments

We describe a new framework for efficiently computing and storing global illumination effects for complex, animated environments. The new framework allows the rapid generation of sequences representing any arbitrary path in a view space within an environment in which both the viewer and objects move. The global illumination is stored as time sequences of range-images at base locations that span the view space. We present algorithms for determining locations for these base images, and the time steps required to adequately capture the effects of object motion. We also present algorithms for computing the global illumination in the base images that exploit spatial and temporal coherence by considering direct and indirect illumination separately. We discuss an initial implementation using the new framework. Results and analysis of our implementation demonstrate the effectiveness of the individual phases of the approach; we conclude with an application of the complete framework to a complex environment that includes object motion

Artistic Path Space Editing of Physically Based Light Transport

Die Erzeugung realistischer Bilder ist ein wichtiges Ziel der Computergrafik, mit Anwendungen u.a. in der Spielfilmindustrie, Architektur und Medizin. Die physikalisch basierte Bildsynthese, welche in letzter Zeit anwendungsübergreifend weiten Anklang findet, bedient sich der numerischen Simulation des Lichttransports entlang durch die geometrische Optik vorgegebener Ausbreitungspfade; ein Modell, welches für übliche Szenen ausreicht, Photorealismus zu erzielen. Insgesamt gesehen ist heute das computergestützte Verfassen von Bildern und Animationen mit wohlgestalteter und theoretisch fundierter Schattierung stark vereinfacht. Allerdings ist bei der praktischen Umsetzung auch die Rücksichtnahme auf Details wie die Struktur des Ausgabegeräts wichtig und z.B. das Teilproblem der effizienten physikalisch basierten Bildsynthese in partizipierenden Medien ist noch weit davon entfernt, als gelöst zu gelten. Weiterhin ist die Bildsynthese als Teil eines weiteren Kontextes zu sehen: der effektiven Kommunikation von Ideen und Informationen. Seien es nun Form und Funktion eines Gebäudes, die medizinische Visualisierung einer Computertomografie oder aber die Stimmung einer Filmsequenz -- Botschaften in Form digitaler Bilder sind heutzutage omnipräsent. Leider hat die Verbreitung der -- auf Simulation ausgelegten -- Methodik der physikalisch basierten Bildsynthese generell zu einem Verlust intuitiver, feingestalteter und lokaler künstlerischer Kontrolle des finalen Bildinhalts geführt, welche in vorherigen, weniger strikten Paradigmen vorhanden war. Die Beiträge dieser Dissertation decken unterschiedliche Aspekte der Bildsynthese ab. Dies sind zunächst einmal die grundlegende Subpixel-Bildsynthese sowie effiziente Bildsyntheseverfahren für partizipierende Medien. Im Mittelpunkt der Arbeit stehen jedoch Ansätze zum effektiven visuellen Verständnis der Lichtausbreitung, die eine lokale künstlerische Einflussnahme ermöglichen und gleichzeitig auf globaler Ebene konsistente und glaubwürdige Ergebnisse erzielen. Hierbei ist die Kernidee, Visualisierung und Bearbeitung des Lichts direkt im alle möglichen Lichtpfade einschließenden "Pfadraum" durchzuführen. Dies steht im Gegensatz zu Verfahren nach Stand der Forschung, die entweder im Bildraum arbeiten oder auf bestimmte, isolierte Beleuchtungseffekte wie perfekte Spiegelungen, Schatten oder Kaustiken zugeschnitten sind. Die Erprobung der vorgestellten Verfahren hat gezeigt, dass mit ihnen real existierende Probleme der Bilderzeugung für Filmproduktionen gelöst werden können