How are the

**3D Gaussians parameterized**in*3D Gaussian Splatting*?The

From this the scaling matrix \(S\) and rotatation matrix \(R\) can be constructed.

The typical parameterization of a guassian through a covariance matrix can then be obtained as:

\[\Sigma = RSS^TR^T\]

*anisotropic*3D gaussians are modeled using a**scale vector \(s \in \mathbb{R}^3\) and quaternions \(q\)**.From this the scaling matrix \(S\) and rotatation matrix \(R\) can be constructed.

The typical parameterization of a guassian through a covariance matrix can then be obtained as:

\[\Sigma = RSS^TR^T\]

To avoid overhead they also explicitly derive the gradients of these parameters.

Give a

**schematic****overview**of the**3D Gaussian Splatting**method.How is

**color**parameterized in**3D Gaussian Splatting**?Using

**spherical harmonics**, this allows the color of a gaussian to be different based on the viewing direction.How are the initial 3D gaussians obtained in 3D gaussian splatting?

They are taken from

**SfM**(Structure-from-motion) that is ran prior to 3D Gaussian Splatting.**SfM**also provides the camera parameters for each image.The authors show that using randomly initialized gaussians perform much worse.

Which

**parameters**of the 3D gaussian are**optimized**in**3D Gaussian Splatting**?The

**3D position**of the guassian, the**properties of the anisotropic gaussian**(through scale and rotation), the \(\alpha\) for the \(\alpha\)-blending and the**spherical harmonics**coefficients.