Reversible Jump Metropolis Light Transport using Inverse Mappings

Benedikt Bitterli, Wenzel Jakob, Jan Novák, and Wojciech Jarosz

ACM Transactions on Graphics (presented at SIGGRAPH 2018), vol. 37, no. 1

Fundamental issues of path sampling using primary sample space: (a) Perturbations in PSSMLT cause a ripple change that propagates to later vertices: here, a perturbation of the outgoing direction at the camera causes a large-scale change of the vertex on the light source. In such cases, it can be advantageous to switch to a different sampling strategy, for instance one that explicitly samples a position on a light source rather than intersecting it by chance. (b) Such strategy changes are possible using a multiplexed primary sample space such as that of MMLT. However, changing strategies generally leads to a large-scale change to the path geometry that causes the proposed path to be rejected with high probability. The RJMLT technique proposed in this paper introduces efficient strategy perturbations that leave the path geometry intact.

abstract

We study Markov Chain Monte Carlo (MCMC) methods operating in primary sample space and their interactions with multiple sampling techniques. We observe that incorporating the sampling technique into the state of the Markov Chain, as done in Multiplexed Metropolis Light Transport (MMLT), impedes the ability of the chain to properly explore the path space, as transitions between sampling techniques lead to disruptive alterations of path samples. To address this issue, we reformulate Multiplexed MLT in the Reversible Jump MCMC framework (RJMCMC) and introduce inverse sampling techniques that turn light paths into the random numbers that would produce them. This allows us to formulate a novel perturbation that can locally transition between sampling techniques without changing the geometry of the path, and we derive the correct acceptance probability using RJMCMC. We investigate how to generalize this concept to non-invertible sampling techniques commonly found in practice, and introduce probabilistic inverses that extend our perturbation to cover most sampling methods found in light transport simulations. Our theory reconciles the inverses with RJMCMC yielding an unbiased algorithm, which we call Reversible Jump MLT (RJMLT). We verify the correctness of our implementation in canonical and practical scenarios and demonstrate improved temporal coherence, decrease in structured artifacts, and faster convergence on a wide variety of scenes.

note

This work is concurrent with Fusing State Spaces for Markov Chain Monte Carlo Rendering by Otsu et al. and Charted Metropolis Light Transport by Jacopo Pantaleoni.

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bibtex

@article{Bitterli2017reversible,
    author = {Bitterli, Benedikt and Jakob, Wenzel and Nov{\'a}k, Jan and Jarosz, Wojciech},
    title = {Reversible Jump Metropolis Light Transport Using Inverse Mappings},
    journal = {ACM Transactions on Graphics},
    volume = {37},
    number = {1},
    year = {2017},
    month = oct,
    doi = {10.1145/3132704},
    keywords = {Ray tracing, photorealistic rendering},
}