Path Space Regularization
Path Space Regularization
Hello all,
Just in case if someone's interested, here is the new EG2013 paper of mine about how to deal with singularities in the light transport integrand: http://cg.ibds.kit.edu/PSR.php
Hope you'll like it.
Anton
Just in case if someone's interested, here is the new EG2013 paper of mine about how to deal with singularities in the light transport integrand: http://cg.ibds.kit.edu/PSR.php
Hope you'll like it.
Anton
Re: Path Space Regularization
Thanks for sharing, very interesting work!!
I have one little question after reading the paper:
It seems that you are using a fixed "r0" for all the (selected) paths, is it possible to generalize your previous adaptive ppm work to the regularization case so that we can have adaptive regularization bandwidth to prevent large bias?
I have one little question after reading the paper:
It seems that you are using a fixed "r0" for all the (selected) paths, is it possible to generalize your previous adaptive ppm work to the regularization case so that we can have adaptive regularization bandwidth to prevent large bias?
Re: Path Space Regularization
Great work kaplanyan! I'm quite astonished how simple the implementation is, based on the modified smallpt code you have provided!kaplanyan wrote:Hello all,
Just in case if someone's interested, here is the new EG2013 paper of mine about how to deal with singularities in the light transport integrand: http://cg.ibds.kit.edu/PSR.php
Hope you'll like it.
Anton
Re: Path Space Regularization
I wonder why you do not run into the problem of very high variance of BRDFs? Even though mollification essentially blurs out the delta function of specular materials, wouldn't it still result in a very large value (or very small value) when you apply this idea to connection paths?
Re: Path Space Regularization
But that's what is visible in the pics though.. (and the pics that don't show it, have been run for a very long time)
Re: Path Space Regularization
You are right. Maybe my question is whether directional blur has some good properties for the combination with MCMC which spatial blur does not have.toxie wrote:But that's what is visible in the pics though.. (and the pics that don't show it, have been run for a very long time)
From http://igad2.nhtv.nl/ompf2/viewtopic.ph ... t=10#p3401:
I am actually now curious if path reusing is somewhat of a side effect of using spatial blur, or path reusing can be beneficial for directional blur as well.ingenious wrote: Another difference to note here is that the MCMCPPM does still employ path reusing, whereas Anton's modified MLT does not. Therefore, I expect MCMCPPM to still perform better on your zoomed in wine glass scene from the paper, for example.
Perhaps related to my original question in this thread, I actually tried using MCMC for full path throughput with spatial blur without path reusing (essentially MCMCPPM + eye subpath throughput), but no success.
My understanding is that this is essentially the same as the Anton's method but with spatial blur. I guess the only difference is that I did not do any selective regularization
which this paper claims to be one benefit of directional blur. Maybe selective regularization is possible with spatial blur and make it work well with MCMC too.
Re: Path Space Regularization
Hello all,
Thanks a lot for warm replies! Let me address a few questions
On the other hand, as it was rightly noticed, the proposed method doesn't use any cache. However the cache seems to be not required for MCMC integration, because each Markov chain always has a cache entry, which is its current state. Thus having a lot of chains is equivalent to having a sparse yet importancesampled distribution of paths.
As for low probability of sampling regularized paths, this is less of an issue with proper mutation strategies  once it's found, e.g. manifold exploration can easily sample all nearby paths. So, yes, that obviously causes problems when used together with MC methods, like PT and BDPT. However this probability is as low as in PPM, the only reason why we don't see this issue in PPM is due to a large cache, which highly alleviates it.
Another interesting question is the regularization of hardlysampleable paths, e.g. for some fast preview rendering. But that first of all depends on the ultimate goal of the renderer itself and secondly the bias should be assessed, probably similarly to APPM or something like that. So, that's what's definitely not done yet.
PS: @Toshiya: Thanks a lot for the early discussion on your MCPPM method!

Anton
Thanks a lot for warm replies! Let me address a few questions
Yes, that is a very good question. In the end there is no conceptual (mathematical) difference between spatial and angular blur. Formulating the regularization as an angular blur is just much more convenient in terms of the integration process: you can easily show that both MC and (a bit more difficult) MCMC converges with such sort of regularization. Moreover you can control where and why to regularize  based on the actual underlying local BSDF.toshiya wrote:Maybe my question is whether directional blur has some good properties for the combination with MCMC which spatial blur does not have.
On the other hand, as it was rightly noticed, the proposed method doesn't use any cache. However the cache seems to be not required for MCMC integration, because each Markov chain always has a cache entry, which is its current state. Thus having a lot of chains is equivalent to having a sparse yet importancesampled distribution of paths.
As for low probability of sampling regularized paths, this is less of an issue with proper mutation strategies  once it's found, e.g. manifold exploration can easily sample all nearby paths. So, yes, that obviously causes problems when used together with MC methods, like PT and BDPT. However this probability is as low as in PPM, the only reason why we don't see this issue in PPM is due to a large cache, which highly alleviates it.
Another interesting question is the regularization of hardlysampleable paths, e.g. for some fast preview rendering. But that first of all depends on the ultimate goal of the renderer itself and secondly the bias should be assessed, probably similarly to APPM or something like that. So, that's what's definitely not done yet.
PS: @Toshiya: Thanks a lot for the early discussion on your MCPPM method!

Anton
Re: Path Space Regularization
BTW,
How can we compare your work with the one of [Georgiev & Al], Vertex Merging (http://www.iliyan.com/publications/VertexMerging).
There is a brief comparison in your paper, but what I see is that your method :
1) Simple to integrate
2) Introduce a bias... but what is the effect of this bias, is it really visible ? Does the VM introduce a bias ?
3) Request less computations and has faster convergence
Thanks
How can we compare your work with the one of [Georgiev & Al], Vertex Merging (http://www.iliyan.com/publications/VertexMerging).
There is a brief comparison in your paper, but what I see is that your method :
1) Simple to integrate
2) Introduce a bias... but what is the effect of this bias, is it really visible ? Does the VM introduce a bias ?
3) Request less computations and has faster convergence
Thanks

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Re: Path Space Regularization
I am very interested in this.
So what's the conclusion? is this method better than BDPT? VCM? SPPM?
So what's the conclusion? is this method better than BDPT? VCM? SPPM?
Re: Path Space Regularization
The conclusion is that now MLT can also sample some complex light paths, like reflected caustics from point light, prior nonsampleable by unbiased methods. The price for that of course is the bias, which occurs on such light paths (and only on them). This bias appears similarly to PPM. MLT was demonstrated on a highly occluded scene, where all ordinary Monte Carlo methods produce noisier image.shiqiu1105 wrote:I am very interested in this.
So what's the conclusion? is this method better than BDPT? VCM? SPPM?