A bidirectional formulation for Walk on Spheres

Poisson’s equations and Laplace’s equations are important linear partial differential equations (PDEs)widely used in many applications. Conventional methods for solving PDEs numerically often need todiscretize the space first, making them less efficient for complex shapes. The random walk on spheresmethod (WoS) is a grid-free Monte-Carlo method for solving PDEs that does not need to discrete thespace. We draw analogies between WoS and classical rendering algorithms, and find that the WoSalgorithm is conceptually identical to forward path tracing.We show that solving the Poisson’s equation is equivalent to solving the Green’s function for everypair of points in the domain. Inspired by similar approaches in rendering, we propose a novel WoSreformulation that operates in the reverse direction. Besides this, using the corrector function enablesus to use control variates to estimate the Green’s function. Implementations of this algorithm showimprovement over classical WoS in solving Poisson’s equation with sparse sources. Our approachopens exciting avenues for future algorithms for PDE estimation which, analogous to light transport,connect WoS walks starting from sensors and sources and combine different strategies for robustsolution algorithms in all cases

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

Modeling of Reverberant Radio Channels Using Propagation Graphs

In measurements of in-room radio channel responses an avalanche effect can be observed: earliest signal components, which appear well separated in delay, are followed by an avalanche of components arriving with increasing rate of occurrence, gradually merging into a diffuse tail with exponentially decaying power. We model the channel as a propagation graph in which vertices represent transmitters, receivers, and scatterers, while edges represent propagation conditions between vertices. The recursive structure of the graph accounts for the exponential power decay and the avalanche effect. We derive a closed form expression for the graph's transfer matrix. This expression is valid for any number of interactions and is straightforward to use in numerical simulations. We discuss an example where time dispersion occurs only due to propagation in between vertices. Numerical experiments reveal that the graph's recursive structure yields both an exponential power decay and an avalanche effect.Comment: 11 pages, Submitted to IEEE Transactions on Antennas and Propagatio

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

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

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

Go with the winners strategy in path tracing

This paper proposes a new random walk strategy that minimizes the variance of the estimate using statistical estimations of local and global features of the scene. Based on the local and global properties, the algorithm decides at each point whether a Russian-roulette like random termination is worth performing, or on the contrary, we should split the path into several child paths. In this sense the algorithm is similar to the go-with-the-winners strategy invented in general Monte Carlo context. However, instead of establishing thresholds to make decisions, we compute the number of child paths on a continuous level and show that Russian roulette can be interpreted as a kind of splitting using fractional number of children. The new method is built into a path tracing algorithm, and a minimum cost heuristic is proposed for choosing the number of rejected rays. Comparing it with the classical path tracing approach we concluded that the new method reduced the variance significantly

Efficient From-Point Visibility for Global Illumination in Virtual Scenes with Participating Media

Sichtbarkeitsbestimmung ist einer der fundamentalen Bausteine fotorealistischer Bildsynthese. Da die Berechnung der Sichtbarkeit allerdings äußerst kostspielig zu berechnen ist, wird nahezu die gesamte Berechnungszeit darauf verwendet. In dieser Arbeit stellen wir neue Methoden zur Speicherung, Berechnung und Approximation von Sichtbarkeit in Szenen mit streuenden Medien vor, die die Berechnung erheblich beschleunigen, dabei trotzdem qualitativ hochwertige und artefaktfreie Ergebnisse liefern

A Study of Bi-Directional Reflectance Distribution Functions and Their Effects on Infrared Signature Models

Since 2004, AFIT has been developing a trend-analysis tool to assess large commercial aircraft infrared (LCAIR) signatures. In many cases, this code predicted signatures to within 10% of measured data. However, other results indicated that the single-bounce, specular-reflection algorithm being used failed to adequately simulate interactions between aircraft parts where either the specular component is dominated by diffuse reflection or part-to-part multiple-bounce reflections contribute significantly to the signature. This research incorporates Bi-Directional Reflectance Distribution Functions (BRDF\u27s) and multiple-bounce calculations into the LCAIR model. A physical aircraft model was constructed from aluminum, and measurements were taken before and after a surface treatment in gloss black paint. The Sandford-Robertson model is used to parameterize the BRDF\u27s of both the bare aluminum and gloss black paint. Since the most efficient method of integrating a BRDF depends upon the reflectance distribution of the aircraft material, the sampling resolution of the BRDF integral is crucial to an accurate simulation. Additionally, care is taken to ensure that the integration of the hemispherical irradiance onto each facet of the computational model is sampled at a sufficient resolution to achieve convergence in the solution. Simulations in the mid-wave infrared (MWIR) and long-wave infrared (LWIR) bands validate both the previous specular reflectance simplification for the gloss black simulations and the failure of the previous algorithm for the highly reflective bare aluminum. The necessity of considering multiple bounces in the simulation is also demonstrated amongst part-to-part reflections near the wing root, where three or four bounces are required for the solution to converge. Finally, three scenarios simulating a man-portable air defense system (MAN-PADS) system engaging an Airbus A340-300 aircraft landing at a generic airport are performed