UCLA Electronic Theses and Dissertations

UCLA UCLA Electronic Theses and Dissertations Title A Comprehensive Study of the Seminal Monte-Carlo-Based Image Synthesis Algorithms Permalink https://escholarship.org/uc/item/3968c9k5 Author Kouhzadi, Ali Publication Date 2016 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA Los Angeles A Comprehensive Study of the Seminal Monte-Carlo-Based Image Synthesis Algorithms A thesis submitted in partial satisfaction of the requirements for the degree Master of Science in Computer Science by Ali Kouhzadi 2016 ABSTRACT OF THE THESIS A Comprehensive Study of the Seminal Monte-Carlo-Based Image Synthesis Algorithms by Ali Kouhzadi Master of Science in Computer Science University of California, Los Angeles, 2016 Professor Demetri Terzopoulos, Chair This thesis presents an in-depth study of the problem of photorealistic image synthesis in the field of computer graphics. To better understand the proposed solutions to this problem, we first briefly overview several relevant fundamental topics, such as probability, Monte Carlo integration, sampling methods, reflection methods, etc. We then review some of the most influential Monte-Carlo-Based image synthesis methods introduced over the past four decades. Finally, to better understand the advantages and weaknesses of each method, we evaluate the reviewed methods using the Mitsuba Renderer, an open-source, research- oriented rendering system. ii The thesis of Ali Kouhzadi is approved. Song-Chun Zhu Joseph M. Teran Demetri Terzopoulos, Committee Chair University of California, Los Angeles 2016 iii Contents List of Figures vi List of Tables vii 1 Introduction1 1.1 Global Illumination and Photorealistic Image Synthesis............1 1.2 Objectives.....................................3 1.3 Outline.......................................4 2 Background5 2.1 Basic Probability Concepts............................5 2.2 Estimators and Their Properties.........................8 2.3 Monte Carlo Integration.............................9 2.4 Geometrical Optics and Light Rays....................... 10 2.5 Heckbert's Light Transport Notation...................... 11 2.6 Radiometry.................................... 11 2.7 Surface Reflection and Transmission....................... 14 2.7.1 Reflection Types............................. 14 2.7.2 Transmission or Internal Reflection................... 15 2.7.3 Bidirectional Reflectance Distribution Function (BRDF)....... 16 2.8 Light Transport Equation............................ 17 2.9 Sampling Methods................................ 18 2.9.1 Uniform Sampling............................ 18 2.9.2 Stratified Sampling............................ 19 2.9.3 Importance Sampling........................... 20 iv 2.9.4 Multiple Importance Sampling...................... 21 3 Monte Carlo Ray Tracing Methods 23 3.1 Precursors to MCRT............................... 23 3.2 Path Tracing and The Rendering Equation................... 26 3.3 Bidirectional Path Tracing............................ 30 3.4 Photon Mapping................................. 34 3.5 Metropolis Light Transport........................... 39 3.6 Progressive Photon Mapping........................... 44 4 Sample Results and Comparison of MCRT Algorithms 48 5 Conclusion 56 5.1 Outlook...................................... 56 6 Bibliography 58 v List of Figures 2.1 Interaction of light with diffuse and specular surfaces.............. 15 2.2 Stratified sampling illustration.......................... 20 3.1 Example scenario for Bidirectional Path Tracing................ 31 3.2 Path construction in bidirectional path tracing................. 31 3.3 Use visibility rays to connect all the points on the subpaths in BPT...... 33 3.4 Rendering caustics................................ 36 4.1 Cornell Box scene rendered by Path Tracing, Bidirectional Path Tracing, and Metropolis Light Transport........................... 50 4.2 Torus scene rendered by Path Tracing, Bidirectional Path Tracing, and Metropo- lis Light Transport................................. 51 4.3 Room scene rendered by Path Tracing, Bidirectional Path Tracing, and Metropo- lis Light Transport................................. 52 4.4 Cornell Box scene rendered by Photon Mapping and Progressive Photon Map- ping......................................... 53 4.5 Torus scene rendered by Photon Mapping and Progressive Photon Mapping. 54 4.6 Room scene rendered by Photon Mapping and Progressive Photon Mapping. 55 vi List of Tables 4.1 Rendering times for unbiased algorithms (Cornell Box scene)......... 50 4.2 Rendering times for unbiased algorithms (torus scene with caustics)..... 51 4.3 Rendering times for unbiased algorithms (room scene with indirect illumination) 52 4.4 Rendering times for biased algorithms (Cornell box scene).......... 53 4.5 Rendering times for biased algorithms (torus scene with caustics)...... 54 4.6 Rendering times for biased algorithms (room scene with indirect illumination) 54 vii 1. Introduction 1.1 Global Illumination and Photorealistic Image Syn- thesis Global Illumination refers to a group of algorithms concerned with simulating the interaction of light with surfaces and volumes [10, p. 470], also called light transport simulation. The purpose of global illumination is in synthesizing photorealistic images based on a scene description. In the context of computer graphics, geometrical optics is almost exclusively used for simulating the behavior of light [13, 20] and other theoretical frameworks (e.g., light as waves or particles) are usually ignored, since they are either too complex and negatively affect efficiency, or do not have noticeable visual effects at macroscopic scales. The first attempt at approaching image synthesis using geometrical optics can be traced back to Appel's 1968 paper [2], which laid the foundations for Goldstein and Nagel's 1971 milestone paper that introduced the first method for simulating the physical process of photography and synthesizing fully computer-generated perspective images by \geometric ray tracing". These two seminal papers paved the way for the introduction of recursive ray tracing by Whitted in 1979 [36], ray casting by Roth in 1982 [28], and radiosity by Goral et al. in 1984 [9]. In turn, the introduction of Whitted's recursive ray tracing and Goral's radiosity were arguably the start of a wave of scholarly interest in global illumination and physically-based image synthesis. As was discussed in [2], the most obvious method for simulating light transport is to trace rays emitted from a light source through the scene until they reach the observer, but in practice this method is not feasible since it is most likely that a small number, or even none, of the selected rays reach the observer (e.g., in outdoor scenes). Tracing infinite beams of 1 light emitted from a light source is also impractical for obvious reasons. The more practical alternative is to trace light rays or beams of light backward, from the observer through the image plane, and from there through the scene until some of them reach some sort of light source. This is essentially the basis of all the global illumination methods in computer graphics. There are two types of widely-used light transport models: 1. Local Illumination and 2. Global Illumination. In the local illumination approach, only direct lighting is taken into account|light rays that are directly emitted from the light source and bounce off a single surface directly towards the observer [10, p. 140]. Using this approach, all the inter-reflections between different surfaces in a scene are ignored in exchange for performance, which makes it well- suited for realtime application (e.g., video games, virtual reality). In realtime rendering, a local lighting model is used by default, and numerous \hacks and tricks" and ad-hoc methods are used to efficiently synthesize natural-looking images. Global illumination methods, by contrast, take into account direct lighting as well as indirect lighting, so that the process of shading a point on a surface takes into account the direct light rays coming from the light sources, the reflected light rays coming from other objects in the scene (inter-reflection), and refracted light rays passing through the object itself, as well as the effects of participating media, etc., thus producing photorealistic images. Using global illumination, one can simulate optical phenomena such as caustics, color-bleeding, soft shadows, motion blur, etc. Subsequent improvements on recursive ray tracing and radiosity resulted in one of the most important contributions to the field in 1986 by Kajiya|the Rendering Equation, also referred to as the Light Transport Equation (LTE), which was introduced in his seminal paper [20] and was the starting point of Monte Carlo Ray Tracing (MCRT), methods that 2 involve evaluating the rendering equation using Monte Carlo integration. These methods can be categorized into two groups of algorithms (to be discussed in more detail in Chapter 2): 1. Biased and 2. Unbiased. In general, we can categorize global illumination algorithms into two groups: 1. Algorithms based on point sampling and Monte Carlo integration (e.g., path tracing, bidirectional path tracing, Metropolis light transport, etc.) 2. Algorithms based on the Finite Element Method (FEM) (e.g., radiosity) Over time and through the introduction of new methods, it is now widely accepted that the most general and robust approach to the global illumination problem is MCRT [13, p. vi]. 1.2 Objectives

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