Approximating Polygonal Curves in Two and Three Dimensions

Abstract

We discuss theweighted minimum numberpolygonal approximation problem. Eu and Toussaint (1994, CVGIP: Graphical Models Image Process.56, 231–246) considered this problem subject to theparallel-striperror criterion inR²withL_qdistance metrics, and they concluded that it can be solved inO(n²) time by using the Cone intersection method. In this note, we clarify part of their discussion and show that solving their problem correctly requiresO(n²logn) time. Also, we discuss theweighted minimum numberproblem subject to theline segmenterror criterion. When input curves are strictly monotone inR³, we demonstrate that if theL₁orL_∞metric is used, this problem also can be solved inO(n²) time.