Robust Shape Fitting via Peeling and Grating Coresets

Let P be a set of n points in Rd . A subset S of P is called a (k, )-kernel if for every direction, the direction width of S -approximates that of P, when k "outliers" can be ignored in that direction. We show that a (k, )-kernel of P of size O(k/(d-1)/2 ) can be computed in time O(n + k2 /d-1 ). The new algorithm works by repeatedly "peeling" away (0, )-kernels from the point set. We also present a simple -approximation algorithm for fitting various shapes through a set of points with at most k outliers. The algorithm is incremental and works by repeatedly "grating" critical points into a working set, till the working set provides the required approximation. We prove that the size of the working set is independent of n, and thus results in a simple and practical, near-linear -approximation algorithm for shape fitting with outliers in low dimensions. We demonstrate the practicality of our algorithms by showing their empirical performance on various inputs...

• Type: Journal
• Year: 2008
• Where: DCG
• Authors: Pankaj K. Agarwal, Sariel Har-Peled, Hai Yu
• Keywords: -approximation Algorithm, Algorithms, DCG 2008, Outliers