Closed Curve Reconstruction from Unorganized Sample Points

This paper considers the problem for reconstructing closed curves from unorganized sample points, where the curve to be reconstructed consists of a finite number of pairwise disjoint components of simple closed curves. This paper formulates this problem as a linear integer programming problem, and proposes an algorithm, called ZERO-ONE, based on it. In addition, two other heuristic algorithms called PASTE and SCISSORS are proposed for reducing computational time. Experimental results show that these algorithms yield exact polygonal reconstruction if the density of the sample points is high enough. In addition, it is shown that SCISSORS can be modified for the reconstruction problem of curves with boundaries.