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

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.

Survey on 3D Surface Reconstruction

“…Oztireli et al [50] address the noise and losing details issues in surface reconstruction operation using Moving Least Square (MLS) mechanism. Their implicit approximation technique explores MLS focusing on local kernel regression.…”

“…In [50], Oztireli et al address the issues of noisy data and conservation of intrinsic features of surfaces. Their method provides a reconstruction technique to produce surfaces which are resilient to noise and preserve the details like sharp edges.…”

Robust Poisson Surface Reconstruction

“…Moving least squares (MLS) techniques [30,31,32,33] reconstruct surfaces locally by solving an optimization that finds a local reference plane and fit a polynomial to the surface. The least-squares fit of MLS, however, is sensitive to outliers and smooths out small features; for this reason variants robust to outliers [34,35] and sharp features [36,37] appeared. [38] also constructs implicit functions locally but blends them together with partitions of unity.…”

Voronoi-based feature curves extraction for sampled singular surfaces

“…But, this method cannot handle non-manifold structures, and requires careful tuning for noisy data. Later,Ötireli et al [13] combine implicit MLS with a statistical technique, specifically, local kernel regression, to keep features. Their method is robust to outliers and sparse sampling, but requires orientation, which could be unreliable for samples derived from non-manifolds.…”

“…We want to keep those points whose distance to the respective barycenters are small, but no two of them should be mutually close (steps [11][12][13][14][15]. This is achieved by sorting the points in ascending order of d p , and then selecting only those points that are at least d p distance away from the rest of the selected points so far.…”