Confused about setting rotations as 4D

fudan-zvg / 4d-gaussian-splatting

[ICLR 2024] Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting

MIT License

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Confused about setting rotations as 4D #17

Open darthandvader opened 9 months ago

darthandvader commented 9 months ago

Hi, very impressive work by you guys! One thing I'm a bit confused about is it mentions we can set the mean and scaling matrix in to 4 dimensional, which is very intuitive, but why you guys set the rotations into a pair of isotropic rotations? I'm just wondering why this process can relate different timestamps with the rotations from the original 3D gaussians. Thank you!

KunruiHuang commented 8 months ago

a rotation in 4D Euclidean space can be decomposed into a pair of isotropic rotations, each of which can be represented by a quaternion