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Rank‐1 Lattices for Efficient Path Integral Estimation
Author(s) -
Liu Hongli,
Han Honglei,
Jiang Min
Publication year - 2021
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.142617
Subject(s) - rendering (computer graphics) , computer science , vertex (graph theory) , curse of dimensionality , lattice (music) , algorithm , ray tracing (physics) , theoretical computer science , computer graphics (images) , artificial intelligence , graph , physics , quantum mechanics , acoustics
We introduce rank‐1 lattices as a quasi‐random sequence to the numerical estimation of the high‐dimensional path integral. Previous attempts at utilizing rank‐1 lattices in computer graphics were very limited to low‐dimensional applications, intentionally avoiding high dimensionality due to that the lattice search is NP‐hard. We propose a novel framework that tackles this challenge, which was inspired by the rippling effect of the sample paths. Contrary to the conventional search approaches, our framework is based on recursively permuting the preliminarily selected components of the generator vector to achieve better pairwise projections and minimize the discrepancy of the path vertex coordinates in scene manifold spaces, resulting in improved rendering quality. It allows for the offline search of arbitrarily high‐dimensional lattices to finish in a reasonable amount of time while removing the need to use all lattice points in the traditional definition, which opens the gate for their use in progressive rendering. Our rank‐1 lattices successfully maintain the pixel variance at a comparable or even lower level compared to Sobol′ sampler, which offers a brand new solution to design efficient samplers for path tracing.