A Non-Exponential Transmittance Model for Volumetric Scene Representations

In Transactions on Graphics (Proceedings of SIGGRAPH 2021)

Left: Con­sider the frac­tion of un­oc­cluded rays in two flat­land scen­ari­os in­volving particles gen­er­ated by a Pois­son pro­cess (top) and an opaque sur­face (bot­tom). The former leads to an ex­po­nen­tial de­cay that is the stand­ard mod­el un­der­ly­ing most ex­ist­ing volume ren­der­ing tech­niques. We con­sider a gen­er­al­ized no­tion of trans­mit­tance that also sup­ports the un­usu­al lin­ear de­cay pro­file ex­hib­ited by the sur­face case. Right: We per­form a sim­il­ar ex­per­i­ment in a more com­plex scene by tra­cing rays with­in thick beams (middle) and track­ing their free-flight dis­tance. The dis­tri­bu­tions res­ult­ing from the three beams are plot­ted on the right. Hard sur­faces in­duce lin­ear trans­mit­tance (purple), while un­struc­tured geo­metry like fo­liage re­sembles an un­cor­rel­ated me­di­um that yields ex­po­nen­tial trans­mit­tance (red). A beam that first tra­verses the trees and then a hard sur­face (green) en­coun­ters both lin­ear and ex­po­nen­tial. We also show a para­met­ric fit (dot­ted plots) us­ing either an ex­po­nen­tial or lin­ear mod­el, or piece­wise com­bin­a­tion of the two in case of the  ex­ample.



We in­tro­duce a nov­el trans­mit­tance mod­el to im­prove the volu­met­ric rep­res­ent­a­tion of 3D scenes. The mod­el can rep­res­ent opaque sur­faces in the volu­met­ric light trans­port frame­work. Volu­met­ric rep­res­ent­a­tions are use­ful for com­plex scenes, and be­come in­creas­ingly pop­u­lar for level of de­tail and scene re­con­struc­tion. The tra­di­tion­al ex­po­nen­tial trans­mit­tance mod­el found in volu­met­ric light trans­port can­not cap­ture cor­rel­a­tions in vis­ib­il­ity across volume ele­ments. When rep­res­ent­ing opaque sur­faces as volu­met­ric dens­ity, this leads to both bloat­ing of sil­hou­ettes and light leak­ing ar­ti­facts. By in­tro­du­cing a para­met­ric non-ex­po­nen­tial trans­mit­tance mod­el, we are able to ap­prox­im­ate these cor­rel­a­tion ef­fects and sig­ni­fic­antly im­prove the ac­cur­acy of volu­met­ric ap­pear­ance rep­res­ent­a­tion of opaque scenes. Our para­met­ric trans­mit­tance mod­el can rep­res­ent a con­tinuum between the lin­ear trans­mit­tance that opaque sur­faces ex­hib­it and the tra­di­tion­al ex­po­nen­tial trans­mit­tance en­countered in par­ti­cip­at­ing me­dia and un­struc­tured geo­met­ries. This cov­ers a large part of the spec­trum of geo­met­ric struc­tures en­countered in com­plex scenes. In or­der to handle the spa­tially vary­ing trans­mit­tance cor­rel­a­tion ef­fects, we fur­ther ex­tend the the­ory of non-ex­po­nen­tial par­ti­cip­at­ing me­dia to a het­ero­gen­eous trans­mit­tance mod­el. Our mod­el is com­pact in stor­age and com­pu­ta­tion­ally ef­fi­cient both for eval­u­ation and for re­verse-mode gradi­ent com­pu­ta­tion. Ap­ply­ing our mod­el to op­tim­iz­a­tion al­gorithms yields sig­ni­fic­ant im­prove­ments in volu­met­ric scene ap­pear­ance qual­ity. We fur­ther show im­prove­ments for rel­ev­ant ap­plic­a­tions, such as scene ap­pear­ance pre­fil­ter­ing, im­age-based scene re­con­struc­tion us­ing dif­fer­en­ti­able ren­der­ing, neur­al rep­res­ent­a­tions, and com­pare it to a con­ven­tion­al ex­po­nen­tial mod­el.


Text citation

Delio Vicini, Wenzel Jakob, and Anton Kaplanyan. 2021. A Non-Exponential Transmittance Model for Volumetric Scene Representations. In Transactions on Graphics (Proceedings of SIGGRAPH) 40(4). 136:1–136:16.

    author = {Delio Vicini and Wenzel Jakob and Anton Kaplanyan},
    title = {A Non-Exponential Transmittance Model for Volumetric Scene Representations},
    journal = {Transactions on Graphics (Proceedings of SIGGRAPH)},
    volume = {40},
    number = {4},
    pages = {136:1--136:16},
    year = {2021},
    month = aug,
    doi = {10.1145/3450626.3459815}