SIMS: a multi-level approach to surface reconstruction with sparse implicits

3D shape approximation and processing with implicitly defined surface primitives (Radial Basis Functions and more general kernel-based approximations, Partition of Unity approximations,Moving Least Squares, etc.) are currently a subject of intensive research in Geometric Modeling and Computer Graphics. In this paper, we propose an approach that combines two conflicting criteria: achieving a high approximation accuracy and obtaining an economical surface representation. We employ compactlysupported Radial Basis Functions and use Tikhonov Regularization to achieve a near optimal selection of their centers. An iterative approach, which defines a multi-level approximation, is used to cope with arising constrained optimization problems.