<h1>Overview</h1>

<p>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 <strong>2017</strong> (e.g., three papers explore combining the <em>Path Space</em> and the <em>Primary Sample Space</em> by jumping back and forth between the two).</p>

<h2>Path Space (PS) representation, Metropolis Light Transport (MLT)</h2>

<ul>
<li><a href="https://dl.acm.org/citation.cfm?id=258775" rel="nofollow noreferrer">Veach E., Guibas L. J.: Metropolis Light Transport. In Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 1997), SIGGRAPH ’97, ACM Press/Addison-Wesley Publishing Co.</a></li>
<li><a href="http://graphics.stanford.edu/papers/veach_thesis/" rel="nofollow noreferrer">Veach E.: Robust monte carlo methods for light transport simulation. Stanford University PhD thesis, 1997.</a></li>
<li><a href="http://graphics.cs.kuleuven.be/publications/WFBD2017TCFMLT/" rel="nofollow noreferrer">Van de Woestijne J., Frederickx R., Billen N., Dutré P.: Temporal Coherence for Metropolis Light Transport. Eurographics Symposium on Rendering - Experimental Ideas &amp; Implementations 2017.</a></li>
</ul>

<p>[Example implementation available in <a href="https://github.com/mitsuba-renderer/mitsuba" rel="nofollow noreferrer">Mitsuba</a>]</p>

<h2>Primary Sample Space (PSS) representation, PSSMLT</h2>

<ul>
<li><a href="https://onlinelibrary.wiley.com/doi/pdf/10.1111/1467-8659.t01-1-00703" rel="nofollow noreferrer">Kelemen C., Szirmay-Kalos L., Antal G., Csonka F.: A Simple and Robust Mutation Strategy for the Metropolis Light Transport Algorithm.</a></li>
</ul>

<h2>Extended Primary Sample Space (EPSS) representation, Multiplexed MLT (MMLT)</h2>

<ul>
<li><a href="https://dl.acm.org/citation.cfm?id=2601138" rel="nofollow noreferrer">Hachisuka T., Kaplanyan A. S., Dachsbacher C.: Multiplexed Metropolis Light Transport. ACM Trans. Graph. 33, 4 (July 2014).</a></li>
</ul>

<p><strong>Note</strong> that MMLT improves upon PSSMLT. </p>

<p>[Example implementation available in <a href="https://github.com/mmp/pbrt-v3" rel="nofollow noreferrer">pbrt-v3</a>]</p>

<h2>Manifold Exploration MLT (MEMLT)</h2>

<ul>
<li><a href="https://dl.acm.org/citation.cfm?id=2185554" rel="nofollow noreferrer">Jakob W., Marschner S.: Manifold Exploration: A Markov Chain Monte Carlo Technique for Rendering Scenes with Difficult Specular Transport. ACM Trans. Graph. 31, 4 (July 2012).</a></li>
<li><a href="https://ecommons.cornell.edu/handle/1813/34189" rel="nofollow noreferrer">Jakob W.: Light Transport On Path-Space Manifolds. Cornell University PhD thesis, 2013.</a></li>
</ul>

<p>[Example implementation available in <a href="https://github.com/mitsuba-renderer/mitsuba" rel="nofollow noreferrer">Mitsuba</a>]</p>

<h2>Half Vector Space representation, Half Vector Space Light Transport (HSLT)</h2>

<ul>
<li><a href="https://dl.acm.org/citation.cfm?id=2601108" rel="nofollow noreferrer">Kaplanyan A. S., Hanika J., Dachsbacher C.: The Natural-constraint Representation of the Path Space for Efficient Light Transport Simulation. ACM Trans. Graph. 33, 4 (July 2014).</a></li>
<li><a href="https://dl.acm.org/citation.cfm?id=2853798" rel="nofollow noreferrer">Hanika J., Kaplanyan A., Dachsbacher C.: Improved half vector space light transport. In Computer Graphics Forum (2015), vol. 34, Wiley Online Library.</a></li>
</ul>

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

<h2>Gradient Domain representation, GDMLT</h2>

<ul>
<li><a href="https://dl.acm.org/citation.cfm?id=2461943" rel="nofollow noreferrer">Lehtinen J., Karras T., Laine S., Aittala M., Durand F., Aila T.: Gradient-domain Metropolis Light Transport. ACM Trans. Graph. 32, 4 (July 2013).</a></li>
<li><a href="https://dl.acm.org/citation.cfm?id=2661291" rel="nofollow noreferrer">Manzi M., Rousselle F., Kettunen M., Lehtinen J., Zwicker M.: Improved Sampling for Gradient-domain Metropolis Light Transport. ACM Trans. Graph. 33, 6 (Nov. 2014).</a></li>
</ul>

<p><strong>Note</strong> that there are variants for path tracing and bidirectional path tracing exploiting the Gradient Domain representation as well.</p>

<h2>Path Space &lt;-> Primary Sample Space representations</h2>

<h3>Reversible Jump MLT (RJMLT)</h3>

<ul>
<li><a href="https://benedikt-bitterli.me/master-thesis/" rel="nofollow noreferrer">Bitterli B.: Informed Choices In Primary Sample Space. Master’s thesis, Swiss Federal Institute of Technology Zurich, 2015.</a></li>
<li><a href="https://dl.acm.org/citation.cfm?id=3132704" rel="nofollow noreferrer">Bitterli B., Jakob W., Novák J., Jarosz W.: Reversible Jump Metropolis Light Transport Using Inverse Mappings. ACM Transactions on Graphics 37, 1 (Oct. 2017).</a></li>
</ul>

<h3>Charted MLT (CMLT)</h3>

<ul>
<li><a href="https://dl.acm.org/citation.cfm?id=3073677" rel="nofollow noreferrer">Pantaleoni J.: Charted Metropolis Light Transport. ACM Trans. Graph. 36, 4 (July 2017).</a></li>
</ul>

<h3>Fusing State Spaces</h3>

<ul>
<li><a href="https://dl.acm.org/citation.cfm?id=3073691" rel="nofollow noreferrer">Otsu H., Kaplanyan A. S., Hanika J., Dachsbacher C., Hachisuka T.: Fusing State Spaces for Markov Chain Monte Carlo Rendering. ACM Transactions on Graphics (Proc. of SIGGRAPH) 36, 4 (2017).</a></li>
</ul>

<h2>Genetic operators in Path Space and Extended Primary Sample Space, Genetic MLT (GMLT)</h2>

<ul>
<li>Delabie M.: Genetic Operators in Metropolis Light Transport. Master’s thesis, KU Leuven, Belgium, 2018.</li>
</ul>

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

<h1>Post Scriptum</h1>

<blockquote>
  <p>Its variants differ only in the used "mutation strategy".</p>
</blockquote>

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

<p>Some references to <em>Evolutionary Monte Carlo</em>:</p>

<ul>
<li><a href="https://www.jstor.org/stable/24306722?seq=1#page_scan_tab_contents" rel="nofollow noreferrer">Liang F., Wong W. H.: Evolutionary Monte Carlo: Applications to Cp Model Sampling and Change Point Problem. STATISTICA SINICA 10 (2000).</a></li>
<li><a href="https://www.jstor.org/stable/2670304?seq=1#page_scan_tab_contents" rel="nofollow noreferrer">Liang F., Wong W. H.: Real-Parameter Evolutionary Monte Carlo With Applications to Bayesian Mixture Models. Journal of the American Statistical Association 96, 454 (2001).</a></li>
</ul>

CC BY-SA 4.0
2018-08-26T19:55:49.767Z
Is the thesis "Genetic Operators in Metropolis Light Transport" anywhere available?
0xbadf00d
CC BY-SA 4.0
2018-08-26T20:14:53.480Z
@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.
Matthias
CC BY-SA 4.0
2018-08-26T20:17:54.097Z
@0xbadf00d I will add tomorrow some mathematics references to Evolutionary MCMC if you want.
Matthias
CC BY-SA 4.0
2018-08-27T08:07:07.870Z
@0xbadf00d Added them at the end ;-)
Matthias
CC BY-SA 4.0
2018-08-26T17:51:07.630Z
2018-08-27T08:04:15.833Z
2018-08-27T08:04:15.833Z
Matthias
<p>Metropolis Light Transport is an application of the Metropolis-Hastings algorithm. Its variants differ only in the used "mutation strategy".</p>

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

<p>If so, I'm interested in any paper.</p>

<raytracing><rendering><pathtracing><global-illumination><monte-carlo>
Is there ongoing research on Markov Chain Monte Carlo algorithms (other than Metropolis-Hastings) for use in ray tracing?
0xbadf00d
# Is there ongoing research on Markov Chain Monte Carlo algorithms (other than Metropolis-Hastings) for use in ray tracing?

(Asked by: username_0 on 2018-08-26)

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.

**Tags:** raytracing, rendering, pathtracing, global-illumination, monte-carlo


---

## 1 answers

### Answer by username_1 on 2018-08-26. Score: 5

# 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)

* [Veach E., Guibas L. J.: Metropolis Light Transport. In Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 1997), SIGGRAPH ’97, ACM Press/Addison-Wesley Publishing Co.](https://dl.acm.org/citation.cfm?id=258775)
* [Veach E.: Robust monte carlo methods for light transport simulation. Stanford University PhD thesis, 1997.](http://graphics.stanford.edu/papers/veach_thesis/)
* [Van de Woestijne J., Frederickx R., Billen N., Dutré P.: Temporal Coherence for Metropolis Light Transport. Eurographics Symposium on Rendering - Experimental Ideas & Implementations 2017.](http://graphics.cs.kuleuven.be/publications/WFBD2017TCFMLT/)

[Example implementation available in [Mitsuba](https://github.com/mitsuba-renderer/mitsuba)]

## Primary Sample Space (PSS) representation, PSSMLT

* [Kelemen C., Szirmay-Kalos L., Antal G., Csonka F.: A Simple and Robust Mutation Strategy for the Metropolis Light Transport Algorithm.](https://onlinelibrary.wiley.com/doi/pdf/10.1111/1467-8659.t01-1-00703)

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

* [Hachisuka T., Kaplanyan A. S., Dachsbacher C.: Multiplexed Metropolis Light Transport. ACM Trans. Graph. 33, 4 (July 2014).](https://dl.acm.org/citation.cfm?id=2601138)

**Note** that MMLT improves upon PSSMLT.

[Example implementation available in [pbrt-v3](https://github.com/mmp/pbrt-v3)]

## Manifold Exploration MLT (MEMLT)

* [Jakob W., Marschner S.: Manifold Exploration: A Markov Chain Monte Carlo Technique for Rendering Scenes with Difficult Specular Transport. ACM Trans. Graph. 31, 4 (July 2012).](https://dl.acm.org/citation.cfm?id=2185554)
* [Jakob W.: Light Transport On Path-Space Manifolds. Cornell University PhD thesis, 2013.](https://ecommons.cornell.edu/handle/1813/34189)

[Example implementation available in [Mitsuba](https://github.com/mitsuba-renderer/mitsuba)]

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

* [Kaplanyan A. S., Hanika J., Dachsbacher C.: The Natural-constraint Representation of the Path Space for Efficient Light Transport Simulation. ACM Trans. Graph. 33, 4 (July 2014).](https://dl.acm.org/citation.cfm?id=2601108)
* [Hanika J., Kaplanyan A., Dachsbacher C.: Improved half vector space light transport. In Computer Graphics Forum (2015), vol. 34, Wiley Online Library.](https://dl.acm.org/citation.cfm?id=2853798)

**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

* [Lehtinen J., Karras T., Laine S., Aittala M., Durand F., Aila T.: Gradient-domain Metropolis Light Transport. ACM Trans. Graph. 32, 4 (July 2013).](https://dl.acm.org/citation.cfm?id=2461943)
* [Manzi M., Rousselle F., Kettunen M., Lehtinen J., Zwicker M.: Improved Sampling for Gradient-domain Metropolis Light Transport. ACM Trans. Graph. 33, 6 (Nov. 2014).](https://dl.acm.org/citation.cfm?id=2661291)

**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)

* [Bitterli B.: Informed Choices In Primary Sample Space. Master’s thesis, Swiss Federal Institute of Technology Zurich, 2015.](https://benedikt-bitterli.me/master-thesis/)
* [Bitterli B., Jakob W., Novák J., Jarosz W.: Reversible Jump Metropolis Light Transport Using Inverse Mappings. ACM Transactions on Graphics 37, 1 (Oct. 2017).](https://dl.acm.org/citation.cfm?id=3132704)

### Charted MLT (CMLT)

* [Pantaleoni J.: Charted Metropolis Light Transport. ACM Trans. Graph. 36, 4 (July 2017).](https://dl.acm.org/citation.cfm?id=3073677)

### Fusing State Spaces

* [Otsu H., Kaplanyan A. S., Hanika J., Dachsbacher C., Hachisuka T.: Fusing State Spaces for Markov Chain Monte Carlo Rendering. ACM Transactions on Graphics (Proc. of SIGGRAPH) 36, 4 (2017).](https://dl.acm.org/citation.cfm?id=3073691)

## 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*:

* [Liang F., Wong W. H.: Evolutionary Monte Carlo: Applications to Cp Model Sampling and Change Point Problem. STATISTICA SINICA 10 (2000).](https://www.jstor.org/stable/24306722?seq=1#page_scan_tab_contents)
* [Liang F., Wong W. H.: Real-Parameter Evolutionary Monte Carlo With Applications to Bayesian Mixture Models. Journal of the American Statistical Association 96, 454 (2001).](https://www.jstor.org/stable/2670304?seq=1#page_scan_tab_contents)

> **Comments:**
> **username_0**: Is the thesis "Genetic Operators in Metropolis Light Transport" anywhere available?  
> **username_1**: @username_0 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.  
> **username_1**: @username_0 I will add tomorrow some mathematics references to Evolutionary MCMC if you want.  
> **username_1**: @username_0 Added them at the end ;-)  

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