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.) is 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 high approximation accuracy and obtaining an economical surface representation. We employ compactly supported 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