The normal of the intersection plane

[JuewenPeng]

Really nice work.

I have a question about the normal. Is it similar to the concept defined in Eq. 7 of "DN-Splatter: Depth and Normal Priors for Gaussian Splatting and Meshing"?

Looking forward to your reply.

[niujinshuchong]

Hi, our definition of normal is different from DN-Splatter. We use the ray-gaussian intersection plane's normal as the Gaussian's normal. DN-Splatter uses the axis of minimal scale.

[JuewenPeng]

Could you give me more details about the definition of the ray-gaussian intersection plane? Thank you very much.

[niujinshuchong]

Hi, you could refer to our paper and here https://github.com/autonomousvision/gaussian-opacity-fields/issues/38#issuecomment-2129212166

[JuewenPeng]

I noticed that you have written $n_i=-R^T(r_g\odot s^{-1})$ on top of Eq. 12. I don't know whether $s^{-1}$ should be $s$, but if that's the case, this formula will be similar to the inverse operation of Eq. 3, which means $n_i$ is parallel to the original ray direction $r$.

[niujinshuchong]

Hi, it is not the inversion. The compound operation is n_i = R^T @ S^-1 @ S^-1 @ R @ r_ray where r_ray is the ray direction.

[JuewenPeng]

Sorry, but I am still a little confused. How is the formula $n_i=-R^T(r_g\odot s^{-1})$ derived?

[niujinshuchong]

I think you can refer to the above comment to do the transformation step by step.