Missing square of gradients?

[atonderski]

Hi,

Thanks for the very interesting work!

I am confused about one thing. In the paper (e.g. equation 11) the hessian is approximated by the square of the gradients, right? However, in the implementation it seems to be approximated using the signed (unsquared) gradient. Am i misunderstanding either the code or the paper? If not, what is the reason behind this? See this code for example (although the same implementation appears in a couple of places)
https://github.com/JiangWenPL/FisherRF/blob/715b76b786010918083604ba9de3c6609606c11b/active/H_reg.py#L69C1-L72C1

Thanks in advance,
Adam

[atonderski]

Separate follow-up question :) G_n in equation 12 is said to be the submatrix of H′′[w^* | D^{train}]. What is the intuition behind this? If i understand correctly that will just give a high uncertainty to gaussians that had a high impact on training views, which is almost the opposite of what we want, right? We are looking for gaussians that have a low impact on training views and a high impact on the novel view (relative to each other).

Shouldn't it rather be the submatrix of the information gain? something like G = local submatrix of H''{new} H''{train}^{-1}

[atonderski]

Aaaand one more thing. When rendering "uncertainty" it is accumulated using the opacity right? But that parameter is uncertain by itself. So we could have an extremely uncertain gauss closest to the camera that just happens to have a low opacity. Am I understanding correctly that this is an issue? Have you thought about potential mitigations? (something like increasing opacity based on uncertainty etc)

[JIANG-CX]

Hi,

Thanks for the very interesting work!

I am confused about one thing. In the paper (e.g. equation 11) the hessian is approximated by the square of the gradients, right? However, in the implementation it seems to be approximated using the signed (unsquared) gradient. Am i misunderstanding either the code or the paper? If not, what is the reason behind this? See this code for example (although the same implementation appears in a couple of places) https://github.com/JiangWenPL/FisherRF/blob/715b76b786010918083604ba9de3c6609606c11b/active/H_reg.py#L69C1-L72C1

Thanks in advance, Adam

I find that the author has replied to this in the issue (#5)

[wangyuanbiubiubiu]

Separate follow-up question :) G_n in equation 12 is said to be the submatrix of H′′[w^* | D^{train}]. What is the intuition behind this? If i understand correctly that will just give a high uncertainty to gaussians that had a high impact on training views, which is almost the opposite of what we want, right? We are looking for gaussians that have a low impact on training views and a high impact on the novel view (relative to each other).

Shouldn't it rather be the submatrix of the information gain? something like G = local submatrix of H''{new} H''{train}^{-1}

Thanks for your attention to this topic! We invite you to explore our work at: FaithFusion. The question you raised is addressed in detail in our paper.