Károly Zsolnai-Fehér explains Wenzel Jakob's Manifold Exploration, an extension to Metropolis Light Transport that samples difficult light paths by solving for directions at diffuse vertices. On scenes with specular bounces like a glass egg, it converges faster than PSSMLT and original MLT.
This is the work of Wenzel Jakob. He's a super smart, really brilliant guy. He extended the Veatch Metropolis algorithm to handle SDS transport better. Now how is this possible? What I have written here is the very scientific way of stating what is really happening. The most difficult paths form a manifold in path space and you can grab this manifold and sample this exhaustively with an equation solving system. Let's take a look at the intuition. This is super useful, but very challenging to understand and implement for ordinary people. And what is exactly happening here? So we have a diffuse bounce, this is xb and we hit the light source after that, which is XC on the upper right. And between the B and the C we have two specular bounces. And imagine that I am fixing the XB and xc, these are two fixed vertices. And if I have this glass egg in between that is perfectly specular, then I can write an algorithm that computes what should be the exact outgoing direction from this diffuse vertex in order to exactly hit that XZ point. There is only one possible path because we have perfectly smart specular interreflections in between. So what should be this outgoing direction from xb? This is the equation solving system that we're interested in. How do the results look like? Well, you can compare it to Metropolis Light Transport. That is either very noisy or it misses some of the light paths completely. In these very difficult test cases, the manifold exploration path tracer outperforms all of the existing algorithms. PSSMLT is the Kalamanstein mlt. MLT is the original Veatch Metropolis. One more example. A Veach Metropolis B erpt. I'll tell you in a second what that is. C Kellerman's Metropolis Light Transport algorithm and D Manifold exploration path tracing. Vensal was kind enough to put I think 20 minute talk about this work on his website. So make sure to check it out. It is really well illustrated. It is really well explained. Make sure to check it out. Let's take a look how the algorithm converges each time. Take a look at this beauty. Lots of SDS light paths and in the first 10 minutes you already have some degree of convergence that would take days or possibly forever with other algorithms. Pretty amazing. Pretty amazing. One of my favorites out there. Here you can see side by side Kalamans Metropolis Light transport versus manifold exploration path tracing. It's difficult not to get excited about this right.
