α-Concave hull, a generalization of convex hull

Bounding hulls such as convex hull, -shape, -hull, concave hull, crust, etc. offer a wide variety of useful applications. In this paper, we explore another bounding hull, namely -concave hull, as a generalization of convex hull. The parameter determines the smoothness level of the constructed hull on a set of points. We show that it is NP-hard to compute -concave hull on a set of points for any 0<<. This leads us to a generalization of Fekete work (when =). We also introduce MACP as an NP-hard problem similar to the problem of computing -concave hull and present an approximation algorithm for MACP. The paper ends by implementing the proposed algorithm and comparing the experimental results against those of convex hull and -shape models.

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