Understanding to the "SampleNetwork" module

[apchenstu]

Hi there, really nice work!
And I'm trying to understand this line code, it looks different from Eq.3 of the main paper, the "surface_output, surface_sdf_values" seems are the same value and it would be really helpful if you could explain it more. Thank you in advance!

[lioryariv]

Hi, thanks :)
You are right, it is a small issue (can be viewed as some implementation detail) which we did not describe in the paper.

First, note that : surface_sdf_values = surface_output.detach()
Meaning only one variable is in the computational graph.
Plug in : surface_output - surface_sdf_values
Instead of surface_output
Will give us the desired property of the function x(theta, c, v) (described in equation 3) which is:
x(theta0, c0, v0) = x0
Meaning the function is correct with respect to the current state.

This handles the case when surface_output is not exactly zero, meaning that the point x is on some s-levelest, so this correction will lead to the correct derivation.
Differentiate f(x;theta) = s ,as shown in section C in the appendix, will result the same.
Partially, it is not always guaranteed that s=0, but we do know it is very close as a result of our ray-marching algorithm.

In fact, this idea based on a former paper from our lab (https://arxiv.org/abs/1905.11911) where we developed the formula of how to control general s-levelsets of the network f.
It might have seen only as a numeric issue, since really the values surface_output are indeed close to zero, but this kind of correction is a more accurate implementation to eq 3.

Hope it clears your concern!

[apchenstu]

Hi lioryariv, thanks for your timely reply, sounds really interesting, I will take a look at the paper.