A new algorithm for fitting a rectilinear x-monotone curve to a set of points in the plane

Authors:
Der Perng Wang
Affiliations:
Department of International Trade, National Pingtung Institute of Commerce, 51 Min Sheng E. Road, Pingtung, Taiwan, ROC
Venue:
Pattern Recognition Letters
Year:
2002

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Abstract

Let S = {pi = (xi,yi), i = 1,2,..., n}, x1 2 n, be a set of n points in the plane and k be a positive integer. We give an O(n2)-time algorithm for finding a rectilinear x-monotone curve R to fit S such that the number of links of R is not larger than k and the error of R with respect to S is minimized. In this paper, we will deal with the L∞ measure of error [Comput. Graphics Image Process. 19 (1982) 248; Comput. Vision Graphics Image Process. 53 (1991) 132], i.e., the error of R with respect to S is defined to be the maximum vertical distance from the points of S to R. We take a plane sweep strategy with two sweeping lines. The previous best running time of this problem is O(n2 log n) [Eur. J. Oper. Res. 130 (2001) 214].