Question about rho3, rho2 and depth computation choice

[fetian-code]

The depth intersection is computed by
float depth = (rho3d <= rho2d) ? (s.x * Tw.x + s.y * Tw.y) + Tw.z : Tw.z;
I understand (s.x * Tw.x + s.y * Tw.y) + Tw.z is the depth according to Eq. (7), but why the depth is Tw.z when the 2D image-space exponential larger than 3D?

Thanks in advance

[hbb1]

Hi, In my latest commit, I have already made the change, which fixes a minor issue reported by others, see #174

[fetian-code]

Hi, In my latest commit, I have already made the change, which fixes a minor issue reported by others, see #174

Thanks for your quick reply! I just thought perhaps when we replace object-space Gaussian with screen-space Gaussian, it makes sense to use Tw.z. Because the screen-space filter seems to be equivalent to constructing a 2D Gaussian perpendicular to the image plane at the center of the object-space Gaussian, then the computed depth should be the depth of the Gaussian center, which is Tw.z.

Does it make sense? Or, would you mind to let me know the reason you used Tw.z here at the first.

[hbb1]

Hi. This is exact what I thought at the beginning and I also aimed to avoid numerical issue (if any). But after a twice think, I believe using the splat depth is more reasonable because the low pass filter is for pre-filtering not a real 3D reconstruction filter. This means, changing the sampling rate (e.g., rendering resolution, FOV) should not affect the underlying 3D scene representation. So that I switch back to the splat depth instead of point depth Tw.z. I also benchmarked on several data and see no significant differences.

[fetian-code]

I see. Thanks very much for your answer.

[fetian-code]

Hi. I just came up with a new question about the depth gradient computation when we use the 2D low pass filter. Since we always use s.x * Tw.x + s.y * Tw.y + Tw.z as the depth, why neglect the gradient propagation of s.x and s.y when rho3d > rho2d in the backward code? Or maybe you have tested and found no difference whether we neglect it.

[hbb1]

No obvious differences. The main reason is that low pass filter is a rare case so backpropagating to the center would be sufficient.