A distance-based parameter free algorithm for curve reconstruction

In this paper, a simple, efficient, and parameter free algorithm, DISCUR, is proposed to reconstruct curves from unorganized sample points. The proposed algorithm can reconstruct multiple simple curves that may be open, closed, and/or with sharp corners. The criteria for the curve reconstruction are based on two observations we have made concerning the human visual system: (1) two closest neighbors tend to be connected, and (2) sampling points tend to be connected into a smooth curve. To simulate these two observations, we use the neighborhood feature to connect the nearest neighbors and we present a statistical criterion to determine when two sample points should not be connected even if they are the nearest neighbors. Finally, a necessary and sufficient condition is proposed for the sampling of curves so that they can be reconstructed by using the present algorithm. Numerous examples show that this algorithm is effective.