![[IMAGE -- the pyramid]](figure9a.jpg)
Optimally Combining Sampling Techniques for Monte Carlo Rendering
Reference:
Images too
Figure 9(x) (JPEG, 312K)
Row $i$ shows techniques that sample transport paths of length $i+1$.
The $m$-th image in the $i$-th row uses the distribution $p_{i+1,m-1}$
described in Sec. 4.3 (this distribution chooses $m-1$ vertices using
the light subpath, and the other $i+3-m$ vertices using the eye subpath).
Images in row $i$ have been overexposed by $i$ f-stops so that
details can be seen.
Relative to Figure 9(a), we have added one extra column to the left
of each row (these images are nearly black, as mentioned in the
text), and one row along the bottom (showing transport paths of
length 6). We have still omitted one image from the right side of
each row, corresponding to the sampling distribution $p_{i+1,i+2}$
(zero vertices in the light subpath). These images are truly
black, since this particular scene has a pinhole lens.
Figure 9(y) (JPEG, 530K)
There is also more
information on gamma correction.
Abstract
Monte Carlo integration is a powerful technique for the
evaluation of difficult integrals. Applications in rendering include
distribution ray tracing, Monte Carlo path tracing, and form-factor
computation for radiosity methods. In these cases variance can often be
significantly reduced by drawing samples from several
distributions, each designed to sample well some difficult aspect of the
integrand. Normally this is done by explicitly partitioning the
integration domain into regions that are sampled differently. We
present a powerful alternative for constructing robust Monte
Carlo estimators, by combining samples from several distributions in a
way that is provably good. These estimators are unbiased, and can
reduce variance significantly at little additional cost. We present
experiments and measurements from several areas in rendering:
calculation of glossy highlights from area light sources, the ``final
gather'' pass of some radiosity algorithms, and direct solution of the
rendering equation using bidirectional path tracing.
Additional information
If the images are too
Extra images (in the electronic SIGGRAPH proceedings)
Figure 2(x) (JPEG, 22K)
A false-color image showing the weights used to compute Figure
2(c). Green represents samples from Figure 2(a), red from Figure
2(b). Yellow indicates that both types of samples are assigned a
significant weight. Notice that some of the highlights are yellow
in the center and green around the edges---the weights are not
just a function of the light source size and surface roughness.
This is an extension of Figure 9(a). Each image shows the weighted
contribution made by one of the bidirectional sampling techniques
to Figure 9(b), using the power heuristic with $\beta=2$. In this
case, paths of up to length $k=6$ were sampled.
This image shows what the various bidirectional sampling
techniques look like when used alone. This is similar to
Fig. 2(a) and Fig. 2(b), where we used two different sampling
techniques in attempting to compute the same image. In this case,
the $m$-th image of row $i$ uses the distribution $p_{i+1,m-1}$
to make an image of the light flowing on paths of length $i+1$.
Standard path tracing is equivalent to summing the second image
from the left on each row (except for caustic paths, which get
their contribution from the first image on each row).
Last modified: May 16, 1995
