Anisotropic Gaussian Mutations for Metropolis Light Transport through Hessian-Hamiltonian Dynamics

Anisotropic Gaussian Mutations for Metropolis Light Transport
through Hessian-Hamiltonian Dynamics

Tzu-Mao Li	Jaakko Lehtinen	Ravi Ramamoorthi	Wenzel Jakob	Frédo Durand
MIT CSAIL	Aalto University NVIDIA	University of California, San Diego	ETH Zürich	MIT CSAIL

Abstract

The simulation of light transport in the presence of multi-bounce glossy effects and motion is challenging because the integrand is high dimensional and areas of high-contribution tend to be narrow and hard to sample. We present a Markov Chain Monte Carlo (MCMC) rendering algorithm that extends Metropolis Light Transport by automatically and explicitly adapting to the local shape of the integrand, thereby increasing the acceptance rate. Our algorithm characterizes the local behavior of throughput in path space using its gradient as well as its Hessian. In particular, the Hessian is able to capture the strong anisotropy of the integrand. We obtain the derivatives using automatic differentiation, which makes our solution general and easy to extend to additional sampling dimensions such as time.

However, the resulting second order Taylor expansion is not a proper distribution and cannot be used directly for importance sampling. Instead, we use ideas from Hamiltonian Monte-Carlo and simulate the Hamiltonian dynamics in a flipped version of the Taylor expansion where gravity pulls particles towards the high-contribution region. Whereas such methods usually require numerical integration, we show that our quadratic landscape leads to a closed-form anisotropic Gaussian distribution for the final particle positions, and it results in a standard Metropolis-Hastings algorithm. Our method excels at rendering glossy-to-glossy reflections on small and highly curved surfaces. Furthermore, unlike previous work that derives sampling anisotropy with pen and paper and only considers specific effects such as specular BSDFs, we characterize the local shape of throughput through automatic differentiation. This makes our approach very general. In particular, our method is the first MCMC rendering algorithm that is able to resolve the anisotropy in the time dimension and render difficult moving caustics.

Publication

Tzu-Mao Li, Jaakko Lehtinen, Ravi Ramamoorthi, Wenzel Jakob, Frédo Durand. Anisotropic Gaussian Mutations for Metropolis Light Transport through Hessian-Hamiltonian Dynamics.
ACM Transactions on Graphics 34(6) (Proceedings of ACM SIGGRAPH Asia 2015)
BibTeX

Errata

See here for errata of the equations in the paper.

Downloads

SIGGRAPH Asia 2015 paper

Supplemental images

SIGGRAPH Asia 2015 presentation slides (Keynote)

SIGGRAPH Asia 2015 presentation slides (Powerpoint)

Code

https://github.com/BachiLi/dpt

Talk video

Acknowledgement

We are grateful to the anonymous reviewers for their valuable comments. This work is funded by NSF grants 1451830 and Academy of Finland grant 277833. Wenzel Jakob was supported by an ETH/Marie Curie fellowship.