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Reversible Jump Metropolis Light Transport using Inverse Mappings

In ACM Transactions on Graphics (Issue ?, 2017)

Fun­da­ment­al is­sues of path sampling us­ing primary sample space: (a) Per­turb­a­tions in PSSMLT cause a ripple change that propag­ates to later ver­tices: here, a per­turb­a­tion of the out­go­ing dir­ec­tion at the cam­era causes a large-scale change of the ver­tex on the light source x3. In such cases, it can be ad­vant­age­ous to switch to a dif­fer­ent sampling strategy, for in­stance one that ex­pli­citly samples a po­s­i­tion on a light source rather than in­ter­sect­ing it by chance. (b) Such strategy changes are pos­sible us­ing a mul­ti­plexed primary sample space such as that of MMLT. However, chan­ging strategies gen­er­ally leads to a large-scale change to the path geo­metry that causes the pro­posed path to be re­jec­ted with high prob­ab­il­ity. The RJMLT tech­nique pro­posed in this pa­per in­tro­duces ef­fi­cient strategy per­turb­a­tions that leave the path geo­metry in­tact.

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.

Text citation

Benedikt Bitterli, Wenzel Jakob, Wojciech Jarosz, and Jan Novák. 2017. Reversible Jump Metropolis Light Transport using Inverse Mappings. arXiv:1704.06835.

BibTeX
@misc{Bitterli2017Reversible,
    author = {Benedikt Bitterli and Wenzel Jakob and Jan Nov\'{a}k and Wojciech Jarosz},
    title = {Reversible Jump Metropolis Light Transport using Inverse Mappings},
    year = {2017},
    Eprint = {1704.06835},
    archivePrefix = {arXiv}
}