[Paper Review] Reversible Jump Metropolis Light Transport using Inverse Mappings

Benedikt Bitterli, Wenzel Jakob+2 more|arXiv (Cornell University)|Apr 22, 2017

Visual perception and processing mechanismsNeuroscience5 references3 citations

TL;DR

This paper introduces Reversible Jump Metropolis Light Transport (RJMLT), a novel MCMC rendering method that uses inverse sampling techniques to transition between different light transport sampling strategies without altering path geometry. By formulating perturbations within the Reversible Jump MCMC framework, RJMLT achieves higher acceptance rates, improved temporal coherence, reduced artifacts, and faster convergence than existing methods like MMLT.

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.

Motivation & Objective

• To address the instability and low acceptance rates in Multiplexed Metropolis Light Transport (MMLT) caused by disruptive path changes during sampling technique transitions.
• To enable local, geometry-preserving transitions between different sampling strategies in primary sample space MCMC rendering.
• To develop a mathematically sound framework using Reversible Jump MCMC that ensures detailed balance and unbiased sampling.
• To generalize inverse sampling to non-invertible techniques via probabilistic inverses, extending applicability to real-world rendering scenarios.
• To improve temporal coherence and convergence speed in complex scenes with caustics, subsurface scattering, and hard-edged shadows.

Proposed method

• Reformulates MMLT within the Reversible Jump MCMC (RJMCMC) framework to allow dimensionally consistent transitions between sampling techniques.
• Introduces inverse sampling functions that map light paths back to the random numbers that generated them, enabling path-geometry-preserving perturbations.
• Derives correct acceptance probabilities using RJMCMC detailed balance, ensuring unbiased sampling despite non-reversible transitions.
• Constructs probabilistic inverses for non-invertible sampling schemes (e.g., rejection sampling, Box-Muller) to extend the method to practical rendering pipelines.
• Employs sample Jacobians to quantify sensitivity of paths to random number perturbations, enabling adaptive step size control.
• Enables novel perturbations that transition between path space and primary sample space, combining benefits of both frameworks.

Experimental results

Research questions

• RQ1 Can Reversible Jump MCMC be effectively applied to light transport rendering to enable smooth transitions between sampling strategies?
• RQ2 How can inverse mappings be constructed to recover the random numbers that produce a given light path, even for non-invertible sampling techniques?
• RQ3 What is the correct acceptance probability for transitions between different sampling techniques in primary sample space MCMC?
• RQ4 Can the proposed method reduce structured noise and improve temporal coherence compared to MMLT and PSSMLT?
• RQ5 How do inverse mappings and Jacobian determinants affect mixing rates and convergence in MCMC rendering?

Key findings

• RJMLT achieves significantly higher acceptance rates than MMLT by avoiding disruptive path geometry changes during technique transitions.
• The method reduces temporal instability and structured artifacts, particularly in scenes with caustics, hard-edged shadows, and complex materials.
• In the Kitchen scene, RJMLT eliminates visible streaks on pots and the cutting board present in MMLT renderings.
• In the Living Room scene, RJMLT reduces streaky reflections and hard-edge shadows that mar MMLT results.
• In the Salle de Bain scene, RJMLT correctly renders caustics that are missing or misplaced in MMLT.
• The Glass of Water scene shows reduced splotchy noise in RJMLT compared to MMLT, with improved convergence and visual consistency.