We present a fast and simple tech­nique to con­vert im­ages in­to a ra­di­ance sur­face-based scene rep­res­ent­a­tion. Build­ing on ex­ist­ing ra­di­ance volume re­con­struc­tion al­gorithms, we in­tro­duce a subtle yet im­pact­ful modi­fic­a­tion of the loss func­tion re­quir­ing changes to only a few lines of code: in­stead of in­teg­rat­ing the ra­di­ance field along rays and su­per­vising the res­ult­ing im­ages, we pro­ject the train­ing im­ages in­to the scene to dir­ectly su­per­vise the spa­tio-dir­ec­tion­al ra­di­ance field.

The primary out­come of this change is the com­plete re­mov­al of al­pha blend­ing and ray march­ing from the im­age form­a­tion mod­el, in­stead mov­ing these steps in­to the loss com­pu­ta­tion. In ad­di­tion to pro­mot­ing con­ver­gence to sur­faces, this for­mu­la­tion as­signs ex­pli­cit se­mant­ic mean­ing to 2D sub­sets of the ra­di­ance field, turn­ing them in­to well-defined ra­di­ance sur­faces. We fi­nally ex­tract a level set from this rep­res­ent­a­tion, which res­ults in a highqual­ity ra­di­ance sur­face mod­el.

Our meth­od re­tains much of the speed and qual­ity of the baseline al­gorithm. For in­stance, a suit­ably mod­i­fied vari­ant of In­stant NGP main­tains com­par­able com­pu­ta­tion­al ef­fi­ciency, while achiev­ing an av­er­age PSNR that is only 0.1 dB lower. Most im­port­antly, our meth­od gen­er­ates ex­pli­cit sur­faces in place of an ex­po­nen­tial volume, do­ing so with a level of sim­pli­city not seen in pri­or work.