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Metropolis Light Transport is an application of the Metropolis-Hastings algorithm. Its variants differ only in the used "mutation strategy".

Is there ongoing research on other Markov Chain Monte Carlo algorithms (with faster convergence rates) for use in ray tracing?

If so, I'm interested in any paper.

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Overview

Here is a short overview of the most used space representations, MLT variants and mutation strategies for these MLT variants. As you can see, there are quite some papers dating back to 2017 (e.g., three papers explore combining the Path Space and the Primary Sample Space by jumping back and forth between the two).

Path Space (PS) representation, Metropolis Light Transport (MLT)

[Example implementation available in Mitsuba]

Primary Sample Space (PSS) representation, PSSMLT

Extended Primary Sample Space (EPSS) representation, Multiplexed MLT (MMLT)

Note that MMLT improves upon PSSMLT.

[Example implementation available in pbrt-v3]

Manifold Exploration MLT (MEMLT)

[Example implementation available in Mitsuba]

Half Vector Space representation, Half Vector Space Light Transport (HSLT)

Note that HSLT is more general than MEMLT: MEMLT is an optional add-on mutation for MLT, whereas HSLT replaces the complete Path Space representation.

Gradient Domain representation, GDMLT

Note that there are variants for path tracing and bidirectional path tracing exploiting the Gradient Domain representation as well.

Path Space <-> Primary Sample Space representations

Reversible Jump MLT (RJMLT)

Charted MLT (CMLT)

Fusing State Spaces

Genetic operators in Path Space and Extended Primary Sample Space, Genetic MLT (GMLT)

  • Delabie M.: Genetic Operators in Metropolis Light Transport. Master’s thesis, KU Leuven, Belgium, 2018.

Note that the Path Space is represented via 3D path vertex positions instead of directions to facilitate crossovers (compared to MLT).

Post Scriptum

Its variants differ only in the used "mutation strategy".

Different mutation strategies and space representations are used. Furthermore, GMLT replaces and extends Markov states representing single paths to complete path populations (Evolutionary Monte Carlo, Evolutionary Markov Chain Monte Carlo <> Markov Chain Monte Carlo).

Some references to Evolutionary Monte Carlo:

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  • $\begingroup$ Is the thesis "Genetic Operators in Metropolis Light Transport" anywhere available? $\endgroup$ – 0xbadf00d Aug 26 '18 at 19:55
  • $\begingroup$ @0xbadf00d As the mentor of that thesis student, I know that this thesis is available for the complete KU Leuven association. The availability for an external audience depends on the optional self-archiving of the author which is not done (yet?) at this time of writing. So my apologies, but I cannot point to a public archive for that one (yet?). With regard to the performance: in the best case it is quite similar to MMLT, but only works for pure diffuse scenes. $\endgroup$ – Matthias Aug 26 '18 at 20:14
  • $\begingroup$ @0xbadf00d I will add tomorrow some mathematics references to Evolutionary MCMC if you want. $\endgroup$ – Matthias Aug 26 '18 at 20:17
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    $\begingroup$ @0xbadf00d Added them at the end ;-) $\endgroup$ – Matthias Aug 27 '18 at 8:07

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