A Unified Projection Operator for Moving Least Squares Surfaces

Moving-Least Squares (MLS) surfaces are a popular way to define a smooth manifold surface from a set of unorganized points without normals. In this paper we present a formulation of MLS surfaces that sheds light on shortcomings of the original technique proposed by Levin, which is based on a two-step minimization procedure. We show that there are cases intrinsic to the geometry of the underlying surface from which the points are sampled where Levins projection fails to find an adequate fit. These shortcomings occur regardless of sampling density or the amount of noise. Our formulation solves this problem by directly fitting a local approximating function to the surface using a unified minimization scheme. We present a modification of Levins original proof that can be directly adapted to our unified approach. Consequently, this suggests our method can be used to create different families of MLS surfaces, depending on the function space used for the fit. This allows specific priors to be used in the approximation, leading to better reconstructions. We present experimental results that show our technique performs adequately in a wide range of conditions. A Unified Projection Operator for Moving Least Squares Surfaces SCI Institute Tech Report UUSCI-2007-006 Tilo Ochotta Carlos Scheidegger John Schreiner Yuri Lima Robert M. Kirby Claudio Silva