Feature Preserving Point Set Surfaces based on Non‐Linear Kernel Regression

TLDR

Moving least squares (MLS) is a popular meshless surface representation technique, but its least‑squares formulation makes it sensitive to outliers and tends to smooth small or sharp features. This work proposes a novel point‑based surface definition that merges the simplicity of implicit MLS with robust statistical techniques to mitigate these shortcomings. The authors reinterpret MLS as local kernel regression and employ robust kernel regression from the literature to achieve the new definition. The representation handles sparse sampling, preserves fine details, naturally handles sharp features with controllable sharpness, and achieves performance comparable to other non‑robust methods while remaining easy to implement.

Abstract

Abstract Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smooth‐out small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicity of implicit MLS surfaces [ SOS04 , Kol05 ] with the strength of robust statistics. To reach this new definition, we review MLS surfaces in terms of local kernel regression, opening the doors to a vast and well established literature from which we utilize robust kernel regression. Our novel representation can handle sparse sampling, generates a continuous surface better preserving fine details, and can naturally handle any kind of sharp features with controllable sharpness. Finally, it combines ease of implementation with performance competing with other non‐robust approaches.