Hierarchical Variance Reduction Techniques for Monte Carlo Rendering
(2012) Abstract
 Ever since the first threedimensional computer graphics appeared half a century ago, the goal has been to model and simulate how light interacts with materials and objects to form an image. The ultimate goal is photorealistic rendering, where the created images reach a level of accuracy that makes them indistinguishable from photographs of the real world. There are many applications ñ visualization of products and architectural designs yet to be built, special effects, computergenerated films, virtual reality, and video games, to name a few. However, the problem has proven tremendously complex; the illumination at any point is described by a recursive integral to which a closedform solution seldom exists. Instead, computer simulation... (More)
 Ever since the first threedimensional computer graphics appeared half a century ago, the goal has been to model and simulate how light interacts with materials and objects to form an image. The ultimate goal is photorealistic rendering, where the created images reach a level of accuracy that makes them indistinguishable from photographs of the real world. There are many applications ñ visualization of products and architectural designs yet to be built, special effects, computergenerated films, virtual reality, and video games, to name a few. However, the problem has proven tremendously complex; the illumination at any point is described by a recursive integral to which a closedform solution seldom exists. Instead, computer simulation and Monte Carlo methods are commonly used to statistically estimate the result. This introduces undesirable noise, or variance, and a large body of research has been devoted to finding ways to reduce the variance. I continue along this line of research, and present several novel techniques for variance reduction in Monte Carlo rendering, as well as a few related tools.
The research in this dissertation focuses on using importance sampling to pick a small set of welldistributed point samples. As the primary contribution, I have developed the first methods to explicitly draw samples from the product of distant highfrequency lighting and complex reflectance functions. By sampling the product, low noise results can be achieved using a very small number of samples, which is important to minimize the rendering times. Several different hierarchical representations are explored to allow efficient product sampling. In the first publication, the key idea is to work in a compressed wavelet basis, which allows fast evaluation of the product. Many of the initial restrictions of this technique were removed in followup work, allowing higherresolution uncompressed lighting and avoiding precomputation of reflectance functions. My second main contribution is to present one of the first techniques to take the triple product of lighting, visibility and reflectance into account to further reduce the variance in Monte Carlo rendering. For this purpose, control variates are combined with importance sampling to solve the problem in a novel way. A large part of the technique also focuses on analysis and approximation of the visibility function. To further refine the above techniques, several useful tools are introduced. These include a fast, lowdistortion map to represent (hemi)spherical functions, a method to create highquality quasirandom points, and an optimizing compiler for analyzing shaders using interval arithmetic. The latter automatically extracts bounds for importance sampling of arbitrary shaders, as opposed to using a priori known reflectance functions.
In summary, the work presented here takes the field of computer graphics one step further towards making photorealistic rendering practical for a wide range of uses. By introducing several novel Monte Carlo methods, more sophisticated lighting and materials can be used without increasing the computation times. The research is aimed at domainspecific solutions to the rendering problem, but I believe that much of the new theory is applicable in other parts of computer graphics, as well as in other fields. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/3158641
 author
 Clarberg, Petrik ^{LU}
 supervisor

 Tomas AkenineMöller ^{LU}
 opponent

 Lawrence, Jason, Department of Computer Science, University of Virginia, USA
 organization
 publishing date
 2012
 type
 Thesis
 publication status
 published
 subject
 keywords
 computer graphics, Monte Carlo methods, importance sampling, hierarchical techniques, rendering
 pages
 301 pages
 defense location
 Lecture hall E:1406, Ebuilding,Ole Römers väg 3, Lund University Faculty of Engineering
 defense date
 20121207 10:00
 ISSN
 14041219
 ISBN
 9789197693998
 language
 English
 LU publication?
 yes
 id
 09ccbe0f74dc463daca121cff4b818fa (old id 3158641)
 date added to LUP
 20121108 08:18:28
 date last changed
 20181121 20:53:18
@phdthesis{09ccbe0f74dc463daca121cff4b818fa, abstract = {Ever since the first threedimensional computer graphics appeared half a century ago, the goal has been to model and simulate how light interacts with materials and objects to form an image. The ultimate goal is photorealistic rendering, where the created images reach a level of accuracy that makes them indistinguishable from photographs of the real world. There are many applications ñ visualization of products and architectural designs yet to be built, special effects, computergenerated films, virtual reality, and video games, to name a few. However, the problem has proven tremendously complex; the illumination at any point is described by a recursive integral to which a closedform solution seldom exists. Instead, computer simulation and Monte Carlo methods are commonly used to statistically estimate the result. This introduces undesirable noise, or variance, and a large body of research has been devoted to finding ways to reduce the variance. I continue along this line of research, and present several novel techniques for variance reduction in Monte Carlo rendering, as well as a few related tools.<br/><br> <br/><br> The research in this dissertation focuses on using importance sampling to pick a small set of welldistributed point samples. As the primary contribution, I have developed the first methods to explicitly draw samples from the product of distant highfrequency lighting and complex reflectance functions. By sampling the product, low noise results can be achieved using a very small number of samples, which is important to minimize the rendering times. Several different hierarchical representations are explored to allow efficient product sampling. In the first publication, the key idea is to work in a compressed wavelet basis, which allows fast evaluation of the product. Many of the initial restrictions of this technique were removed in followup work, allowing higherresolution uncompressed lighting and avoiding precomputation of reflectance functions. My second main contribution is to present one of the first techniques to take the triple product of lighting, visibility and reflectance into account to further reduce the variance in Monte Carlo rendering. For this purpose, control variates are combined with importance sampling to solve the problem in a novel way. A large part of the technique also focuses on analysis and approximation of the visibility function. To further refine the above techniques, several useful tools are introduced. These include a fast, lowdistortion map to represent (hemi)spherical functions, a method to create highquality quasirandom points, and an optimizing compiler for analyzing shaders using interval arithmetic. The latter automatically extracts bounds for importance sampling of arbitrary shaders, as opposed to using a priori known reflectance functions.<br/><br> <br/><br> In summary, the work presented here takes the field of computer graphics one step further towards making photorealistic rendering practical for a wide range of uses. By introducing several novel Monte Carlo methods, more sophisticated lighting and materials can be used without increasing the computation times. The research is aimed at domainspecific solutions to the rendering problem, but I believe that much of the new theory is applicable in other parts of computer graphics, as well as in other fields.}, author = {Clarberg, Petrik}, isbn = {9789197693998}, issn = {14041219}, keyword = {computer graphics,Monte Carlo methods,importance sampling,hierarchical techniques,rendering}, language = {eng}, pages = {301}, school = {Lund University}, title = {Hierarchical Variance Reduction Techniques for Monte Carlo Rendering}, year = {2012}, }