Implicit Surface Representation Using Epanechnikov Mixture Regression

We propose a regression-based implicit surface representation using mixture-of-experts based on the Epanechnikov kernel (EK), a mathematical framework that does not depend on neural networks. The modeling method is implemented using signed distance fields (SDF), modeled using the expectation-maximization algorithm to iterate an optimal set of parameters of Epanechnikov mixture regression. The proposed pipeline achieves better reconstruction than the SDF itself and can be upsampled through mixture-of-experts-based interpolation without extra parameters and processing. Furthermore, the proposed method can efficiently realize data compression compared to meshes and SDF. As for the kernel theory, EK demonstrates a more accurate surface recovery than the Gaussian ones, which expands the applications for Epanechnikov-related theories and also shows potential for theoretical substitution for Gaussian-based modeling and representation.