Cornellbox: Monte Carlo Sampling the Light Transportation Intergral on Path Space

Top Previous Next

Not recursive evaluation anymore. The image synthesis is regarded as solving an explicit integral problem with Monte Carlo sampling. This integral, as detailed in Eric Veach's PhD thesis, is the light transportation integral formaulation with measure on path space.

The following rgb cornell box images are synthesized under the following assumptions.

all surfaces are ideal diffuse, including the light src (with uniform direction distribution), and the 'sensor' for each pixel (the importance directional distribution is uniform).
box filter
the calculated measure is
(incident power) / [ lens_area * pixel_area_at_image_plane / square_dist_of_pixel_to_lens ]
the light src is 3.14 W/sq(m).
thin lens; however the lens area is small enough compared to the distance to the image plane.
all sampling is uniform, either respect to area surface(as lens, and lights), or respect to solid angle.

For the following iamges, 'sntm' means sampling n light vertices and m eye vertices.
Because light src value directly seen from pixel is about 0.9, and the maximal pixel value of one bounce is about 0.023, and even less for two and three bounces (0.016 and 0.006), almost all the following images are scaled and furthermore, sqaure rooted twice.

Physically correct rendering is my main concern, and to this end I designed two experiments on the central pixel value. The first one is to compare analytical value with rendered value by Monte Carlo sampling (s1t2 strategy) the light transport integral of path length 2. The second one is to compare the variance of two different sampling strategies. In both experiments I removed the two boxes, and for the first one, I changed the light size to be 1 by 1, so that a good approximate analytical value can be obtained.
Uniform (with repsect to solid angle) sampling is used through all these experiments.

Comparsion of analytic value with s1t2 sampling strategy. scene file.

Analytic Value	s1t2 9 samples	s1t2 100 samples	s1t2 10,000 samples	s1t2 1000,000 samples	s1t2 4000,000 samples	s1t2 9000,000 samples
~1.0e-06	9.38197e-07	9.39712e-07	9.39662e-07	9.42307e-07	9.49878e-07	9.51933e-07

convergence of s1t2 sampling strategy. scene file.

Analytic Value	1 samples	4 samples	9 samples	16 samples	25 samples	100 samples	10,000 samples
~~~0.01	0.0116471	0.0122869	0.0125904	0.0125964	0.0125451	0.0126007	0.0125995

convergence of s0t3 sampling strategy. (same scene file as above)

Analytic Value	400 samples	10,000 samples	40,000 samples	90,000 samples	1000,000 samples
~~~0.01	0.00982598	0.0122769	0.012786	0.0121666	0.0124256

These images are the monte carlo sampled result of the integral, with path space constrained to specific path length. scene file. All images except the first two, are scaled by 30 and then square root-ed twice.

	s0t2, 100 samples	s1t1, 100 samples
stratified uniform sampling respect to solid angle

	s0t3, 100 samples	s0t3, 900 samples	s1t2, 100 samples	s2t1, 100 samples
stratified uniform sampling respect to solid angle

	s0t4, 100 samples	s0t4, 900 samples	s1t3, 100 samples	s2t2, 100 samples	s2t2, 900 samples	s2t2, 2500 samples	s3t1, 100 samples
stratified uniform sampling respect to solid angle

	s0t5, 100 samples	s0t5, 900 samples	s1t4, 100 samples	s2t3, 100 samples	s2t3, 400 samples	s3t2, 100 samples	s3t2, 400 samples	s4t1, 100 samples
stratified uniform sampling respect to solid angle
stratified uniform sampling respect to projected solid angle

These three images are rendered by domain partition with a single sampling strategy(s0t2, s1t2-5 respectively) to solve the light transportation integral (within path length 5) of cornell box scene. I simply use the same samples for each domain, which is actually not necessary. Stratified uniform(respect to projected solid angle) sampling is used. All the images are scaled by 20, sqrt-ed once.

64X5 samples	225X5 samples	900X5 samples

Cornellbox: Monte Carlo Sampling the Light Transportation Intergral on Path Space

CS 6650: Image Synthesis

Instructor Peter Shirley

XianMing Chen, xchen AT cs DOT utah DOT edu