Optimal bandwidth selection for MLS surfaces

We address the problem of bandwidth selection in MLS surfaces. While the problem has received relatively little attention in the literature, we show that appropriate selection plays a critical role in the quality of reconstructed surfaces. We formulate the MLS polynomial fitting step as a kernel regression problem for both noiseless and noisy data. Based on this framework, we develop fast algorithms to find optimal bandwidths for a large class of weight functions. We show experimental comparisons of our method, which outperforms heuristically chosen functions and weights previously proposed. We conclude with a discussion of the implications of the Levin's two-step MLS projection for bandwidth selection.