The natural-constraint representation of the path space for efficient light transport simulation

Abstract

The path integral formulation of light transport is the basis for (Markov chain) Monte Carlo global illumination methods. In this paper we present half vector space light transport (HSLT) , a novel approach to sampling and integrating light transport paths on surfaces. The key is a partitioning of the path space into subspaces in which a path is represented by its start and end point constraints and a sequence of generalized half vectors. We show that this representation has several benefits. It enables importance sampling of all interactions along paths in between two endpoints. Based on this, we propose a new mutation strategy, to be used with Markov chain Monte Carlo methods such as Metropolis light transport (MLT), which is well-suited for all types of surface transport paths (diffuse/glossy/specular interaction). One important characteristic of our approach is that the Fourier-domain properties of the path integral can be easily estimated. These can be used to achieve optimal correlation of the samples due to well-chosen mutation step sizes, leading to more efficient exploration of light transport features. We also propose a novel approach to control stratification in MLT with our mutation strategy.

Physically based computer graphics for realistic image formation to simulate optical measurement systems

“…Numerous variants exist, e.g., sampling in primary space (Kelemen et al, 2002) or in path space (Veach, 1998), as well as modern extensions such as energy redistribution path tracing (ERPT, Cline et al, 2005), manifold exploration (Jakob and Marschner, 2012), half-vector space transport (Kaplanyan et al, 2014), and gradient domain methods (Kettunen et al, 2015).…”

Selective application of Metropolis Light Transport for hard sampling illumination phenomena

“…Развивая MLT в пространстве путей, работа [24] предлагает специфиче-ские стратегии предложений переходов (называемых пертурбациями) для зер-кальных отражений, а работа [25] -для глянцевых (glossy) поверхностей. Наи-более существенным недостатком MLT в пространстве путей является то, что под каждый феномен освещённости необходимо не только тщательно проекти-ровать специфические стратегии пертурбаций, но и уметь вычислять плотности вероятности переходов -…”

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

“…Unlike their method, which requires a specially designed mutation, we treat the time dimension the same as the other dimensions, and handle the correlation between coordinates using the Hessian. Jakob and Marschner [2012], Kaplanyan et al [2014], and Hanika et al [2015] use the first derivatives of the half-vectors of a specular light path to guide the MCMC sampling. These methods apply a form of Newton-iteration to sample new light paths satisfying certain constraints.…”

“…Previous work has focused on model-based characterizations of anisotropy that are tied to specific effects (specular transfer, motion, etc.) [Jakob and Marschner 2012;Belcour et al 2013;Kaplanyan et al 2014], and combining them is not easy. Closest to our work is Manifold Exploration [Jakob and Marschner 2012] and Half-vector Space Light Transport Hanika et al 2015] which use assumptions about the mirror direction and specular reflection to derive major directions of anisotropy (Figure 2(e)), and walk along a lower-dimensional manifold.…”