About Eq.9

[chensiyuan030105]

In Eq.9, it is the square of covariance plus the square of 3D Filter, but in the code, it is the square of exp(scaling) plus the square of 3D Filter squared. Why?

[niujinshuchong]

Hi, we first get the original scale of the Gaussian by self.get_scaling and after applying square it becomes the variances (left term in L105). Then we apply the 3D filter (sum in L105 in your screenshot, eq.9 in the paper). Finally applying sqrt to the variance results in scales after 3D filtering.

[chensiyuan030105]

Thank you for your reply! I have some other questions.

1. In the article, you proposed three drawbacks of 3DGS : high frequency artifacts, dilation, aliasing. And the article proposed 3D Smooth filter and 2D Mip filter to solve it. After reading the article, I think 3D Smooth filter solve high frequency artifacts by limiting the smallest scale of gaussian (zooming in) and 2D Mip filter solve dilation and aliasing (zooming out). However, in games 310's representation, I get the information that 3D Smooth filter solve both high frequency artifacts(zooming in) and dilation(zooming out), and 2D Mip filter solve aliasing(zooming out). It confused me a lot.

[chensiyuan030105]

[chensiyuan030105]

[chensiyuan030105]

From the ablation study, I think it is 2D Mip filter solves dilation, not 3D Smooth filter, which is different from the conclusion from the games 310

[chensiyuan030105]

And how about dilation(zooming out)?

[Yang-Xijie]

I think 3D Smooth filter solve high frequency artifacts by limiting the smallest scale of gaussian (zooming in) and 2D Mip filter solve dilation and aliasing (zooming out).

From my own point of view,

• 3D filter prevents small gaussians in a scene, which mainly solves high frequency artifacts.
• 3D filter and 2D filter both solve aliasing because they lower the frequency of the scene (pre-filtering).
• The fix for coefficient of gaussian filter in EWA splatting solves dilation (check https://github.com/graphdeco-inria/gaussian-splatting/issues/294#issuecomment-1772688093 for detail), which is included in the 2D filter in this paper.

[chensiyuan030105]

I agree with your first and second statement. However, for dilation, I think the reason for the artifacts caused by dilation is too small gaussian(too high frequency) for zooming out.

[chensiyuan030105]

The coefficient of gaussian filter in EWA splatting is a good correction but not contribute for solving dilation.(I think)