Image sampling

[kephrenz]

Hi,

Lastweek I was doing some experimets on monte-carlo and variance reduction techniques. Importance sampling especially.

I did come up with an idea, so I have tried ( this could have been done before of course )

So what I did was,

1) I got an image, greyscaled it (intensitiy value), then i took a kernel size of NxN,
2) then for every pixel on the image I calculated the variance in kernel (where pixel is in the middle) and put that value on pixel.
3) Then I have normalized the image bu dividing the sum of all pixels. Now I have a normalized space, that looks like a 2D, discrete, probability density function
4) I have calculated marginal along -x- side, and calculated the marginal. Then cumulative sum. Voila. I have a distribution function.
5) I took uniform random numbers and sampled from the dist function find place on -x-.
6) I took the x,x+1 columns of image, and summed them, and divided by sum. This is the conditional probablity function. Then the same operation on 5, and took I found the -y- position.

I wrote a matlab code, and tested it, I have the results below.

Test Image

Variance Image

Sampled Image

I haven't did any research for it yet. But I could get more samples where frequencies seem higher.

Ahmet,

[jeanphi]

Hi,

I seem to remember this is how the infinitesample light works (using the intensity instead of the variance of course), or using a similar scheme.

Jeanphi

[Radiance]

Hey,

i moved this post to 'architecture and design' as there's usually all discussion regarding algorithms etc...

on a side note, karlvb has already provided some interesting information regarding these techniques (including interesting papers),
i've asked him to comment here too

greetz,
radiance

[Karl vom Berge]

I'm very happy there is growing interest in the forum regarding variance reduction techniques such as important sampling.

I thnink we should go in the direction of adaptive sampling combined with a perceptual framework: this could vastly improve rendertimes.

See my post in this thread for more technical info:http://www.luxrender.net/forum/viewtopic.php?f=8&t=451#p3037

But adaptive sampling can also introduce bias, if not implemented carefully, see my post in this thread: http://www.luxrender.net/forum/viewtopic.php?f=8&t=692#p5195

Karl

[jeanphi]

Hi,

As noticed with the usevariance feature of the MLT sampler, a minimum sampling probability should be ensured so that the coverage of the image plane is not too slow. In order to go further, the Film class should have a new method to return a given pixel intensity and number of samples so that samplers could compute a proper estimate of the variance for the value to be added.

Jeanphi

[Karl vom Berge]

I haven't did any research for it yet. But I could get more samples where frequencies seem higher.

Actually this is not always what you want. A human will notice less noise on a high frequent texture than on a smooth low frequent texture. So during rendering, you can allow for more noise, or variance (or less computation time) in areas that have e.g. high frequent textures.

An example is the persian mat in the examples in the paper of Mahesh Ramasubramanian.

Page 8 in the paper, fig 7 (d) visualizes the sample density that was used to compute the image. You clearly see that less samples are used on highfrequent areas than on smooth regions, especially shadowed regions.

I included these images for convenience.

Persian mat scene computed using path tracing, reference image.

Persian mat scene sample density used in the perceptual adaptive sampler.

Persian mat scene computed using path tracing with the perceptual adaptive sampler, using only 5%-10% of the samples that where used in the reference image: huge speed increase!

Karl

[kephrenz]

Hi,

I am researching BRDF, global illumination ( infinite lights in this condition ). First I thought this example to be used in multiple importance sampling (MIS) of BRDF and global light. In the MIS you try to find a good probability densitiy function (pdf) for brdf and the image. But my example forgets about the intensity, where there could be variance but colors may be darker. As in this cat example.

But I would try some variances of this only using this, intensitiy added, multiplied, or some other operation. ( Just to see I am wrong )

Thanks for the papers and interest.

Ahmet,

[Karl vom Berge]

I am researching BRDF, global illumination ( infinite lights in this condition )

I though you where thinking in the direction of adaptive sampling using the variance, so that's why I added my comments. Any ideas are of course useful!

Specific techniques must always be used depending on the signal that you want to sample.

Ameth, this technique that have source code included could also be useful to experiment with, when you are interested in Importance sampling:
http://www.iro.umontreal.ca/~ostrom/ImportanceSampling/

The above technique is not very efficient in generating large amounts of well distributed points with constant density. For doing this, look at this paper:

http://www.cs.virginia.edu/~gfx/pubs/antimony/

Importance sampling is however not easy in this last technique.

Karl

[kephrenz]

Hi,

I haven't seen those papers before. I am on my way , downloaded and ready to dig

Thanks Karl,

Ahmet