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A Simple Approach to Differentiable Rendering of SDFs

In Transactions on Graphics (Proceedings of SIGGRAPH Asia 2024)

The jump dis­con­tinu­it­ies at the vis­ib­il­ity bound­ary B make phys­ic­ally based ren­der­ing non-dif­fer­en­ti­able. To ex­pli­citly sample and ad­dress such dis­con­tinu­it­ies, we pro­pose to re­lax the vis­ib­il­ity bound­ary to a thin band of re­laxed bound­ary A. This cor­res­ponds to re­lax­ing the sur­faces to thin volumes for sampling dis­con­tinu­it­ies but re­tain­ing sur­face rep­res­ent­a­tions for for­ward ren­der­ing. Con­sequently, we are able to com­pute ac­cur­ate gradi­ents of the rendered im­ages with re­spect to the scene para­met­ers and, in turn, achieve high-qual­ity in­verse ren­der­ing res­ults, with less com­plex­ity than pre­vi­ous meth­ods.

Abstract

We present a simple al­gorithm for dif­fer­en­ti­able ren­der­ing of sur­faces rep­res­en­ted by Signed Dis­tance Fields (SDF), which makes it easy to in­teg­rate ren­der­ing in­to gradi­ent-based op­tim­iz­a­tion pipelines. To tackle vis­ib­il­ity-re­lated de­riv­at­ives that make ren­der­ing non-dif­fer­en­ti­able, ex­ist­ing phys­ic­ally based dif­fer­en­ti­able ren­der­ing meth­ods of­ten rely on elab­or­ate guid­ing data struc­tures or re­para­met­er­iz­a­tion with a glob­al im­pact on vari­ance. In this art­icle, we in­vest­ig­ate an al­tern­at­ive that em­braces nonzero bi­as in ex­change for low vari­ance and ar­chi­tec­tur­al sim­pli­city. Our meth­od ex­pands the lower-di­men­sion­al bound­ary in­teg­ral in­to a thin band that is easy to sample when the un­der­ly­ing sur­face is rep­res­en­ted by an SDF. We demon­strate the per­form­ance and ro­bust­ness of our for­mu­la­tion in end-to-end in­verse ren­der­ing tasks, where it ob­tains res­ults that are com­pet­it­ive with or su­per­i­or to ex­ist­ing work.

Video

Text citation

Zichen Wang, Ziyi Zhang, Wenzel Jakob, and Steve Marschner. 2024. A Simple Approach to Differentiable Rendering of SDFs. In Transactions on Graphics (Proceedings of SIGGRAPH Asia) 43(6).

BibTeX
@article{Wang24Simple,
    author = {Zichen Wang and Ziyi Zhang and Wenzel Jakob and Steve Marschner},
    title = {A Simple Approach to Differentiable Rendering of SDFs},
    journal = {Transactions on Graphics (Proceedings of SIGGRAPH Asia)},
    volume = {43},
    number = {6},
    year = {2024},
    month = nov,
    doi = {10.1145/3680528.3687573}
}