This repository contains the variance/error/Fourier analysis code developed as part of the SIGGRAPH course

Fourier analysis of numerical integration in Monte Carlo rendering: Theory and Practice
Kartic Subr, Gurprit Singh, Wojciech Jarosz
In SIGGRAPH Courses July 2016
Project page

If you use this source code in your research, please cite the code using the following entry:

@inproceedings{subr16fourier,
author = {Kartic Subr and Gurprit Singh and Wojciech Jarosz},
title = {Fourier Analysis of Numerical Integration in Monte Carlo Rendering: Theory and Practice},
booktitle = {ACM SIGGRAPH Courses},
year = {2016},
month = jul,
publisher = {ACM},
address = {New York, NY, USA},
location = {Anaheim, California},
isbn = {978-1-4503-4289-6},
doi = {10.1145/2897826.2927356}
}

• List of dependencies:
• CGAL is made optional. If you happen to use integrands that depend on CGAL (PWConstIntegrand & QPIntegrand) then use set(MYCGAL_ENABLED 1) in the CMakeLists.txt and Install CGAL (only Main library required with basic functionalities) prior to cmake...
• GMP (While installing CGAL, GMP gets installed as a dependency)
• TBB (for parallel computation of Fourier analysis) made optional for those who are only interested in the variance/mse analysis. Simply set TBB_ENABLED flag to zero in the CMakeLists.txt file to disable TBB. After that, you don't even need an installation of TBB on your system.
• Python (only required for PBRTIntegrand, the source code still compiles and run for other integrands without Python)

• Use recursive tag to clone from git to add the Openexr submodule:

git clone --recursive https://github.com/sinbag/EmpiricalErrorAnalysis.git
cd EmpiricalErrorAnalysis
mkdir build
cd build
cmake ..
make -j4

• If you accidentally already cloned the repo without the recursive tag, run the following command to also fetch the OpenEXR dependency:

git submodule update --init --recursive

• The interface supports different types of integrand. You can hit:

./build/eea or ./build/eea -h

to see the command line usage. Example to call Disk Integrand for variance analysis is as follows:

./build/exec -S --stype Jittered -I Disk --rad 0.25 --center 0.5 0.5 -A --atype var --nsamps  9 36 100 512  --nreps 1000 -G --ofile testDisk

• Detailed description of all the parameters is added in the recent version of the course notes provided on the project page.

Pbrt-v3 Error Analyzer

• The interface also allow user to call PBRT-v3 code directly via python script (Make sure you have a cropwindow defined in the .pbrt scene file to select the region you are interested in):
  • To perform Variance analysis for pbrt-v3 generated images, user can directly call pbrt from the provided Analysis code (look for PBRTIntegrand in the code). Make sure you have a cropwindow defined in the .pbrt scene file to select the region you are interested in. Variance is computed in an online fashion without any reference image. To save time use --refnspp 1. Example to call PBRTIntegrand (all in one line):

./build/eea -S --stype Random 
-I --itype Pbrt 
--epath path-to-pbrt-v3-executable/pbrt 
--spath path-to-pbrt-v3-scenes/anim-killeroos.pbrt 
--pypath path-to-FAS2016/code/Analysis/python/pbrt-cl.py 
--crop 0.25 0.75 0.25 0.75 
--pbrtstype stratified
--refnspp 1
--img pbrt-eea.exr 
-A --atype var --nsamps 9 16 25 36 64 --nreps 200 
-G --ofile pbrt-killeroos

• The Pbrt Integrand directly calls the integrators that are called from the SamplerIntegrator::Render(const Scene &scene){...} function. That includes: directlighting, whitted, path, volpath integrators. However, it would be straight forward to use this error analysis source code for other integrators (with minor tweaks by the user).
• Note: In Pbrt, the seed for random number generator for all samplers is set to be deterministic. As a result, for each call to Pbrt the same set of random numbers will be generated resulting in zero variance. To obtain variance we need to randomize the seed, one way to randomize the seed is by using the following snippet in the function call SamplerIntegrator::Render(const Scene &scene){...} in the integrator.cppfile :

...
ProgressReporter reporter(nTiles.x * nTiles.y, "Rendering");
    {
        //StatTimer timer(&renderingTime);
        ParallelFor2D([&](Point2i tile){
...

std::random_device rd;
static thread_local std::mt19937 generator(rd());
std::uniform_int_distribution<long> dis(1, 100000000);
unsigned int randomseed = dis(gen);

...

///comment out lrandseed to use default PBRT seed.
int seed = tile.y * nTiles.x + tile.x + randomseed;
...

• MSE analyzer works the same as variance analyzer but you need a reference value. For pbrt-v3, you need to compute the reference image (ReferenceSampler used Halton) with huge number of samples per pixel (--refnspp 1000). Example to call PBRTIntegrand (all in one line):

./build/eea -S --stype Random 
-I --itype Pbrt 
--epath path-to-pbrt-v3-executable/pbrt 
--spath path-to-pbrt-v3-scenes/anim-killeroos.pbrt 
--pypath path-to-FAS2016/code/Analysis/python/pbrt-cl.py 
--crop 0.25 0.75 0.25 0.75 
--pbrtstype stratified
--refnspp 1000
--img pbrt-eea.exr 
-A --atype var --nsamps 9 16 25 36 64 --nreps 200 
-G --ofile pbrt-killeroos