Figure 2: Overview of PCAsplat. We regularize Gaussian neighborhoods directly in scene space.
For each Gaussian, we estimate a local neighborhood and compute differentiable PCA statistics
that capture the underlying tangent structure. We then regularize the local eigenspectrum to reduce
neighborhood thickness and promote isotropic tangent-plane coverage. We also align Gaussian
normals with PCA-derived normals, encouraging surface-aligned and well-localized splats. Our
formulation is lightweight, differentiable, and directly compatible with existing splatting pipelines.