Dear Fellow Scholars, this is Two Minute Papers with Dr. Károly Zsolnai-Fehér.
I think this might be it.
This paper is called Monte Carlo Geometry Processing, and in my opinion, this may one
of the best, if not the best computer graphics paper of the year.
There will be so many amazing results, I first thought this one paper could be the topic
of ten Two Minute Papers videos, but I will attempt to cram everything into this one video.
It is quite challenging to explain, so please bear with me, I’ll try my best.
To even have a fighting chance at understanding what is going on here, first, we start out
one of the most beautiful topics in computer graphics, which is none other than light transport.
To create a beautiful light simulation, we have to solve something that we call the rendering
equation.
For practical cases, it is currently impossible to solve it like we usually solve any other
equation.
However, what we can do, is that we can choose a random ray, simulate its path as it bounces
around in the scene and compute how it interacts with the objects and material within this
scene.
As we do it with more and more rays, we get more information about what we see in the
scene, that’s good, but, look, it is noisy.
As we add even more rays, this noise slowly evens out, and in the end, we get a perfectly
clean image.
This takes place with the help of a technique that we call Monte Carlo integration, which
involves randomness.
At the risk of oversimplifying the situation, in essence, this technique says that we cannot
solve the problem, but we can take samples from the problem, and if we do it in a smart
way, eventually, we will be able to solve it.
In light transport, the problem is the rendering equation, which we cannot solve, but we can
take samples, one sample is simulating one ray.
If we have enough rays, we have a solution.
However, it hasn’t always been like this.
Before Monte Carlo integration, light transport was done through a technique called Radiosity.
The key issue with Radiosity was that the geometry of the scene had to be sliced up
into many small pieces, and the light scattering events had to be evaluated between these small
pieces.
It could not handle all light transport phenomena and the geometry processing part was a major
headache, and Monte Carlo integration was a revelation that breathed new life into this
field.
However, there are still many geometry processing problems that include these headaches, and,
hold on to your papers, because this paper shows us that we can apply Monte Carlo integration
to many of these problems too.
For instance, one, it can resolve the rich external and internal structure of this ant.
With traditional techniques, this would normally take more than 14 hours and 30 gigabytes of
memory, but, if we apply Monte Carlo integration to this problem, we can get a somewhat noisy
preview of the result in less than one minute.
Of course, over time, as we compute more samples, the noise clears up and we get this beautiful
final result.
And the concept can be used for so much more, it truly makes my head spin.
Let’s discuss six amazing applications, while noting that there are so many more in
the paper, which you can and should check out in the video description.
For instance, two, it can also compute a CT scan of the infamous shovelnose frog that
you see here, and instead of creating the full 3D solution, we only have to compute
a 2D slice of it, which is much, much cheaper.
Three, it can also edit these curves, and note that the key part is that we can do that
without the major headache of creating an intermediate triangle mesh geometry for it.
Four, it also supports denoising techniques, so we don’t have to compute too many samples
to get a clear image or piece of geometry.
Five, performing a Helmholtz-Hodge decomposition with this method is also possible.
This is a technique that is used widely in many domains, for instance, it is responsible
to ensure the stability of many fluid simulation programs, and this technique can also produce
these decompositions.
And interestingly, here it is used to represent 3D objects without the usual triangle meshes
that we use in computer graphics.
Six, it supports multiple importance sampling as well.
This means that if we have multiple sampling strategies, multiple ways to solve a problem
that have different advantages and disadvantages, it combines them in a way that we get the
best of all of them.
We had a mega-episode on multiple importance sampling, it has lots of amazing uses in light
transport simulations, so if you would like to hear more, make sure to check that video
out in the video description.
But wait, these are all difficult problems.
One surely needs a PhD and years of experience in computer graphics to implement this, right?
When seeing a work like this, we often ask, okay, it does something great, but how complex
is it?
How many days do I have to work to reimplement it?
Please take a guess and let me know what the guess was in the comments section.
And now, what you see here is none other than the source code for the core of the method,
and what’s even more, a bunch of implementations of it already exist.
And, if you see that a paper has been reimplemented around day 1, you know it’s good.
So, no wonder, this paper has been accepted to SIGGRAPH, perhaps the most prestigious
computer graphics conference.
It is immensely difficult to get a paper accepted there, and I would say this one more than
earned it.
Huge congratulations to the first author of the paper, Rohan Sawhney, he is currently
a PhD student, and note that this was his second published paper.
Unreal.
Such a great leap for the field in just one paper.
Also congratulations to professor Keenan Crane who advised this project and many other wonderful
works in the last few years.
I cannot wait to see what they will be up to next and I hope that now, you are just
as excited.
Thanks for watching and for your generous support, and I'll see you next time!