Question about the orientation of each Gaussian

[sunshineatnoon]

Hi, I have maybe a naive question about the orientations of the Gaussians. If my understanding is correct, the _rotation matrix is represented as quaternion, is it possible to get the actually orientation of each Gaussian from this quaternion? I assume there's an oracle orientation?

[Snosixtyboo]

Hi,

I am not sure I understand. Both a quaternion and a matrix are representations of a rotation, just expressed differently. If you need e.g. the rotation matrix, the Python code base includes a function to turn it into a matrix!

[grgkopanas]

https://github.com/graphdeco-inria/gaussian-splatting/blob/414b553ef1d3032ea634b7b7a1d121173f36592c/utils/general_utils.py#L78

and here it is

On Sat, Oct 21, 2023 at 4:35 PM Snosixtyboo @.***> wrote:

Hi,

I am not sure I understand. Both a quaternion and a matrix are representations of a rotation, just expressed differently. If you need e.g. the rotation matrix, the Python code base includes a function to turn it into a matrix!

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[yuedajiong]

@sunshineatnoon

1. Q includs R and t, this is for camera pose. #CAMERA-POSE
2. maybe, the orientation you said is normal? need not in this algorithm, paper said. #POINT-ATTRIBUTE

these infomation used in the GaussSplat render: render1: xyz & opacity #shape render-2: get_covariance | scaling, rotation #pose get_features/shs | colors_precomp(feature, xyz, now_sh_degree) #color

[sunshineatnoon]

Hi, @grgkopanas and @Snosixtyboo Thanks for the quick response. Right, I understand the quaternion represents a rotation matrix. I'm looking for the absolute orientation here. My goal is to extract the normals from the gaussians. So in point cloud, you would compute normal using nearby points, but the Gaussians they already have orientation, so I'm wondering why not just use that as the normals?

[jaco001]

If you look closely at effect of work from datatset all surfaces look like this

3D chaotic cloud ;) You probably will get normals from every splat but what algorithm you will use to 'average' normals from this? It can be less chaotic when you get splats from existing 3D objects, but still.

[kwea123]

The rotation is not relevant to the normal, is it? Imagine a very thin gaussian, you would image the "orientation" is pointing along the long axis, but that is obviously not the normal

[cs-mshah]

You might want to look into https://slothfulxtx.github.io/TexGS/. They have estimated the normal. It is basically one of the eigenvectors of the covariance matrix.

[nnop]

The rotation is independent of the normal, but the eigenvector corresponding to the smallest scaling can serve as the normal direction. @kwea123