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chiehwangs / 3d-gaussian-theory

A repository on how to understand the theory of 3D Gaussians Splatting
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color formula question #1

Closed yupengchengg147 closed 1 week ago

yupengchengg147 commented 10 months ago

Color should be Cx = T1 alpha_1 C1 + T2 alpha_2 C2 +...., if i'm not wrong.

截屏2023-12-28 10 14 08
chiehwangs commented 10 months ago

Color should be Cx = T1 alpha_1 C1 + T2 alpha_2 C2 +...., if i'm not wrong. 截屏2023-12-28 10 14 08

Thank you for your communication!

Indeed, the colors in each Gaussian region are not entirely consistent. The weight $T$ is used to control the decay of colors from the center of the Gaussian towards its periphery. I believe the formula in the second figure describes this weight: $\alpha{2}=\mathrm{opacity}{ux}*PDF$, and it is calculated based on the distance from a Gaussian region above a certain pixel to the departure point from the Gaussian center, i.e., the Probability Density Function (PDF).

Of course, this is my understanding, and I welcome further discussion.

best, chieh