Anisotropic Gaussian mutations for metropolis light transport through Hessian-Hamiltonian dynamics

Tzu-Mao Li, Jaakko Lehtinen, Ravi Ramamoorthi, Wenzel Jakob, Frédo Durand
2015 ACM Transactions on Graphics  
OURS REF OURS MEMLT MMLT BDPT Figure 1: CARS: Equal-time (20 minutes) comparison on the cars scene, with a static car and a moving car lit by an area light. The direct lighting is computed separately. The interior of the car is enclosed by near-specular glass windows, which gives rise to specular-diffusespecular (SDS) paths that are challenging to sample. The three insets show the renderings of our method (H 2 M C), Manifold Exploration Metropolis Light Transport (MEMLT), Multiplexed Metropolis
more » ... tiplexed Metropolis Light Transport (MMLT), and Bidirectional Path Tracing (BDPT). The reference (REF) is rendered by our method in roughly 15 hours. BDPT cannot efficiently sample the sparse contribution function and suffers from severe noise. MMLT tends to get trapped in the hard-to-find features and produces correlated noise. MEMLT specializes in finding difficult static specular paths, but does not consider the anisotropy in the time domain, resulting in ghosting artifacts. Our method can efficiently resolve the hard-to-find SDS paths like the specialized method, and is more general so that it can resolve moving caustic paths in the window by capturing the correlation between the time domain and path space. 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. In-stead, 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.
doi:10.1145/2816795.2818084 fatcat:iokusej2yzdu7bdt3rdohovh2e