E. Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. Ph.D. thesis, Department of Computer Science, Katholieke Universitiet Leuven, Leuven, Belgium, Feb. 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of the first pass. In order to accomplish this, we have used two view dependent methods: a Monte Carlo path tracing algorithm using next event estimation [24, 25] and a ray tracer incorporating final gather [21, 22] Importance sampling is usually performed based on the BRDF term for surfaces [16], and on the phase function for participating media [3] but not taking into account the incoming radiance. During the second pass the incoming light at a certain point can be estimated using the results of the first pass. This permits the creation of discrete probability density functions (PDFs) ....

Eric Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. Ph.D. thesis, Leuven, Belgium, February 1996. 8

....Hierarchical Monte Carlo image synthesis is a fundamental procedure which can be applied whenever the shader function L S can be provided. In consequence it directly applies to distribution ray tracing [CPC84] the photon map [JC98] with all its extensions, and bidirectional path tracing [Laf96] [VG94] 12 In order to take advantage of the speedup for multiple light sources, the new algorithm is applied separately for each light source by separating the integrals. Otherwise artifacts may appear due to the high variance in pixels with low sampling rate that randomly include only a ....

E. Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. PhD thesis, Katholieke Universitiet Leuven, Belgium, 1996. 5

....the right border describes the paths started from the detectors. The inner terms of the pyramid scheme are functionals linking segments independently started on the light sources and the detectors. The original stochastic algorithm for bidirectional path tracing has been introduced in [VG95, Laf96] For the deterministic simulation, the Halton vector x i = u i,1 , u i,4j 2 ) is used in an interleaved way to exploit the good discrepancy in the lower dimensions: Choosing the pixel functional (1.6) y # 0 is the first point hit when shooting a ray from the eye point through a point ....

....is shown in figure 3b. Note, that this scheme is a single pass algorithm, working without discretization error. Due to the scene complexity, a very high sampling rate (N 1000) Printer: Opaque this is required for each pixel of the image, which can be reduced by techniques proposed in [VG95, Laf96] Nevertheless this very expensive method is useful for reference calculations, when testing fast multi pass algorithms as proposed in [Kel96a] in combination with unidirectional quasi random walk preprocessing. FIGURE 4. Photorealistic rendering of a conference room using the quasi random walk ....

E. Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. PhD thesis, Katholieke Universitiet Leuven, Belgium, 1996. 4.2

....The efficiency of path tracing algorithms can be improved by using sophisticated sampling schemes such as importance sampling, stratified sampling or Metropolis sampling. An excellent overview of these techniques can be found in the dissertations of Veach [Vea97] Dutre [Dut96] and Lafortune [Laf96] Ultimately however, all these techniques rely on the law of large numbers for converging to the accurate global illumination solution and therefore, the error in the computed image at any given time is inversely proportional to the square root of time. This results in a very poor convergence ....

Eric Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. Ph.D. thesis, Leuven, Belgium, February 1996.

....procedure. Note that links to clusters must be taken into account too. 5 Our Monte Carlo step is currently an extended path tracing algorithm. It uses next event estimation and the usual importance sampling based on the BRDF term for surfaces without information about the incoming radiance [14], and on the phase function for participating media [4] For now our implementation sets pdf s taking into account the incoming light at lambertian surfaces (based on L i ( w i ) cosq i ) The pdf s of volume elements containing participating media can be set taking into account the incoming ....

....into our system. Probably a better sampling strategy for a reflected scattered direction would be to interpolate the pdf s of the elements near the interaction point, as is done in [16, 8] at the expense of increasing the computation time. 5. 3 Path tracer Our path tracer follows the work of [14], using importance sampling and (optionally) next event estimation. Several enhancements have been made that allow better functionality and produce more accurate images: ffl Adaptive control of the number of required samples per pixel. We implemented a stopping criterion based on the estimation ....

E. Lafortune, Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering, PhD thesis, Department of Computer Science, Katholieke Universitiet Leuven, 1996.

.... based methods (further discussed in Chapters 7 and 8) introduced in the computer graphics literature by Goral et al. 94] The introduction of these methods is considered the first step towards a more accurate approach to the global illumination problem, known as physically based rendering [136]. INTRODUCTION 3 There are phenomena at the level of electromagnetism, such as interference, diffraction and polarization [113, 198] that cannot be explained by geometrical optics or radiative transfer theory. These phenomena are addressed by physical optics [113, 149] which involves the study ....

....normalized, i.e. conserve energy. This means that the total energy propagated in response to some irradiation must be no more than the energy received [86] In other words, for any incoming direction the radiant power propagated over the hemisphere can never be more than the incident radiant power [136]. Any radiant power that is not propagated is absorbed. Formally, in the case of reflection of light, the so called directionalhemispherical reflectance [5] should therefore be less than or at most equal to 1: ae ( x; i ; 2; Z outgoing f r (x; i ; cos d 1; 8 i 2 incoming ....

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Lafortune, E. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. PhD thesis, Department of Computer Science, Faculty of Engineering, Katholieke Universiteit Leuven, 1996.

....Hierarchical Monte Carlo image synthesis is a fundamental procedure which can be applied whenever the shader function L S can be provided. In consequence it directly applies to distribution ray tracing [CPC84] the photon map [JC98] with all its extensions, and bidirectional path tracing [Laf96] [VG94] 12 In order to take advantage of the speedup for multiple light sources, the new algorithm is applied separately for each light source by separating the integrals. Otherwise artifacts may appear due to the high variance in pixels with low sampling rate that randomly include only a ....

E. Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. PhD thesis, Katholieke Universitiet Leuven, Belgium, 1996.

....not be analytically integrated, the probability distribution function P (x) can be computed and tabulated. A complete description of methods needed to sample the initial state of a particle is given in [Pat93] A study of some variance reduction techniques and their combinations is conducted in [Laf96]. A very detailed presentation of the mathematical framework of the variance reduction techniques is presented in [Fis96] Sampling frequency, location and direction of propagation independently allow the particle tracing method to deal with many kinds of sources fairly easily. 1 The initial ....

Eric Lafortune. Mathematical models and Monte-Carlo algorithms for physically based rendering. PhD thesis, Dept. of Computer Science, Faculty of engineering, Katholieke Universiteit Leuven, Leuven, Belgium, February 1996.

.... the most notable of these have been Shirley and Wang s work on using Monte Carlo Methods to provide physically accurate evaluation of direct lighting[18] the introduction of path tracing as a means of solving the rendering equation[10] Dutre s work on light tracing[3] bidirectional path tracing [14][21] and Veach s more recent application of Metropolis sampling[24] In this report we will provide an overview of various Monte Carlo methods for carrying out photorealistic rendering. We will describe these techniques, describe our implementation of these techniques, and present results which ....

....as the above and hence the whole process is recursive. Traditional image synthesis techniques simplify the equation above in order to make it com 1 There are many di erent mathematical formulations of this material. In this report we choose to follow most of the conventions used by Lafortune [14] putationally tractable. In classical ray tracing [25] the BRDF is replaced with the simple Phong model and the hemisphere of directions along which incoming radiance is calculated is replaced by a nite set of directions. This nite set is comprised of the set of directions towards visible ....

E.P.Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. Ph.D. thesis. 1996

....method is presented to estimate the actual bias. This provides a technique for bias correction and it shows that the bias is most significant in areas with indirect illumination. 1 Introduction Monte Carlo based global illumination methods such as path tracing [6] and bidirectional path tracing [10, 9, 17] are very powerful techniques when highly complex scenes with complex reflection models are rendered. The main disadvantage of Monte Carlo based ray tracing is the high variance of the result which is seen as noise in the rendered images. This noise can be eliminated by increasing the number of ....

E. Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. Ph.D. thesis, Department of Computer Science, Katholieke Universitiet Leuven, Leuven, Belgium, February 1996.

....each frame, and the polygons are drawn as is. In contrast, scenes containing glossy surfaces cannot yet be treated in an interactive context. To generate images with glossy surfaces, ray tracing based approaches are typically used, such as the RADIANCE system [27] or pathtracing algorithms (e.g. [11, 23]) Some finite element approaches have been presented, but can only treat trivial scenes (e.g. 13, 1] or require a second, ray casting pass to generate an image [3] Two approaches have been proposed which are capable of interactive viewing [16, 25] but they are limited in their capacity to ....

....raytracing [28, 5] and the rendering equation [9] in the late eighties. A large body of research ensued focusing on Monte Carlo stochastic algorithms. The goal of this research was to reduce the noise in the solutions, introduced by the stochastic nature of the Monte Carlo methods (e.g. [22, 11, 14]) Monte Carlo algorithms that proved to be useful in other research areas were successfully trans ferred to the global illumination problem [10, 24] In parallel, several multi pass methods have been developed which combine the advantages of ray tracing and radiosity style calculations [17] ....

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E. Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. PhD thesis, Katholieke Universiteit Leuven, 1996.

....means of shadow rays. Each shadow ray that is not intercepted by an object in the scene contributes to the estimated flux or average radiance through the pixel. The algorithm has proven to be particularly effective for rendering scenes with indirect illumination, compared to ordinary path tracing [18]. The different illumination transport paths present different estimators for the flux, each one with its own potential strength. A judicious combination of the estimators [17] yields a robust estimator with a generally lower variance. For this purpose the alternative estimators for illumination ....

E. Lafortune, Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. PhD thesis, Katholieke Universiteit Leuven, Belgium, Feb. 1996.

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E. Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. Ph.D. thesis, Department of Computer Science, Katholieke Universitiet Leuven, Leuven, Belgium, Feb. 1996.

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Eric Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. Ph.D. thesis, Department of Computer Science, Katholieke Universitiet Leuven. Leuven, Belgium, February 1996.

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Eric Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. Ph.D. thesis, Leuven, Belgium, February 1996.

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E. Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. PhD thesis, Katholieke Universitiet Leuven, Belgium, 1996. 1

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Lafortune, E., Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. PhD thesis, Department of Computer Science, Katholieke Universitiet Leuven, 1996.

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Lafortune E.; Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering; Ph.D. Thesis, Katholieke Universiteit Leuven, 1996.

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Eric Lafortune. Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. PhD thesis, Katholieke Universiteit Leuven, 1996.

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Lafortune, Eric P.: "Mathematical Models and Monte Carlo Algorithms for Physcially Based Rendering". Ph.d. thesis, Katholieke University, Leuven, Belgium 1995.

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