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Dec 27, 2019 at 16:46 comment added lightxbulb @0xbadf00d The earlier $L_e$ are simply absorbed by the earlier terms of the Neumann expansion. When you do recursive bounces, and are not actually restarting the path for each path length you are really estimating the first $M$ terms of the Neumann expansion, where $M$ is the number of bounces you do. That is you actually evaluate $M$ estimators. Reusing the throughput you have computed on the path is just an optimization, one could technically regenerate paths from scratch for each path length.
Dec 27, 2019 at 15:47 comment added user8592 I am not sure I still understand what your question is now. Want exactly are you asking?
Dec 27, 2019 at 15:34 comment added 0xbadf00d Yes, I know. I was actually talking about the measurement contribution function as defined on page 223 of Veach's thesis.
Dec 27, 2019 at 15:14 comment added user8592 If you are referring to the path integral formulation as done in Veach's thesis on chapter 8, then a path starting from the eye and ending at a light source is not meant to say that we always stop there. If the light source is a surface reflecting or transmitting light, there will still be other paths along the same vertices as the first path from the eye to the light source but we do not consider the surface a light source then, but keep on going further along more path vertices until we hit another light source. And the final result is the accumulations of all such paths.
Dec 27, 2019 at 13:58 comment added 0xbadf00d Thank you for your answer. Well, I guess what's confusing me is that in the context of the path integral formulation of the light transport equation it seems like that we only consider the emitted radiance from the first vertex. To be precise, if we consider a path $(x_0,\ldots,x_k)$ of length $k$, where $x_k$ is on the camera, there's only the emitted radiance $L_e(x_k\to x_{k-1})$ occurring in the expansion of the recursive area form of the LTE. Or am I missing something?
Dec 27, 2019 at 13:24 vote accept 0xbadf00d
Dec 26, 2019 at 10:15 review First posts
Dec 27, 2019 at 10:27
Dec 26, 2019 at 10:13 history answered user8592 CC BY-SA 4.0