Geometric Tools for Exploring Manifolds of Light Transport Paths (ACM Research Highlight)

In Communications of the ACM (November 2015)

Visu­al il­lus­tra­tion of the dif­fi­culties of se­quen­tial path sampling meth­ods when ren­der­ing caustic pat­terns at the bot­tom of a swim­ming pool. (a, b): Uni­direc­tion­al tech­niques sample light paths by ex­ecut­ing a ran­dom walk con­sist­ing of al­tern­at­ing trans­port and scat­ter­ing steps. The only way to suc­cess­fully com­plete a path in this man­ner is to ran­domly “hit” the light source or cam­era, which hap­pens with ex­ceed­ingly low prob­ab­il­ity. (c): Bi­d­irec­tion­al tech­niques trace paths from both sides, but in this case they can­not cre­ate a com­mon ver­tex at the bot­tom of the pool to join the par­tial light paths.


Photoreal­ist­ic im­ages cre­ated us­ing phys­ic­al sim­u­la­tions of light have be­come a ubi­quit­ous ele­ment of our every­day lives. The most suc­cess­ful tech­niques for pro­du­cing such im­ages rep­lic­ate the key phys­ic­al phe­nom­ena in a de­tailed soft­ware sim­u­la­tion, in­clud­ing the emis­sion of light by sources, trans­port through space, and scat­ter­ing in the at­mo­sphere and at the sur­faces of ob­jects. Math­em­at­ic­ally, this com­pu­ta­tion in­volves the ap­prox­im­a­tion of many high-di­men­sion­al in­teg­rals, one for each pixel of the im­age, usu­ally us­ing Monte Carlo meth­ods. Al­though a great deal of pro­gress has been made on ren­der­ing al­gorithms, so that phys­ic­ally based ren­der­ing is now routinely used in many ap­plic­a­tions, com­monly oc­cur­ring situ­ations can still cause these al­gorithms to be­come im­prac­tic­ally slow, for­cing users to make un­real­ist­ic scene modi­fic­a­tions to ob­tain sat­is­fact­ory res­ults.

Light trans­port is com­plex be­cause light can flow along a great vari­ety of dif­fer­ent paths through a scene, though only a sub­set of these makes rel­ev­ant con­trib­utes to the fi­nal im­age. The sim­u­la­tion be­comes in­ef­fect­ive when it is dif­fi­cult to find the im­port­ant paths. Com­monly oc­cur­ring ma­ter­i­als like smooth met­al or glass sur­faces can eas­ily lead to such situ­ations, where only very few light­ing paths par­ti­cip­ate, lead­ing to spiky in­teg­rands and poor con­ver­gence. How to ef­fi­ciently handle such cases in gen­er­al has been a long-stand­ing prob­lem.

In this pa­per, we provide a geo­met­ric solu­tion to this prob­lem by rep­res­ent­ing light paths as points in an ab­stract high-di­men­sion­al con­fig­ur­a­tion space that is defined by a sys­tem of con­straint equa­tions. This con­fig­ur­a­tion space is a dif­fer­en­ti­able man­i­fold, which can be loc­ally para­met­er­ized in the neigh­bor­hood of an ex­ist­ing path. Build­ing on this frame­work, we pro­pose Man­i­fold Ex­plor­a­tion, a ren­der­ing tech­nique that ef­fi­ciently ex­plores the in­teg­ra­tion do­main by tak­ing geo­met­ric­ally in­formed steps on the man­i­fold of light paths.

Text citation

Wenzel Jakob and Steve Marschner. 2015. Geometric Tools for Exploring Manifolds of Light Transport Paths (ACM Research Highlight). In Communications of the ACM (November) 58(11). 103–111.

    author = {Wenzel Jakob},
    title = {Geometric Tools for Exploring Manifolds of Light Transport Paths (ACM Research Highlight)},
    journal = {Communications of the ACM},
    volume = {58},
    number = {11},
    pages = {103--111},
    year = {2015},
    month = nov,
    doi = {10.1145/2823402}