Efficient algorithms for 3-D polygonal approximation based on LISE criterion

Given a polygonal curve P in three-dimensional (3-D) space, the polygonal approximation (PA) problem in this research is to 7nd a polygon P′ to approximate P either with the minimal polygonal segments under a given error or, conversely, with the minimal error under a speci7ed number of segments allowable. The former PA problem is called the PA-# problem; the latter PA problem is called the PAproblem. Given a 3-D P with n nodes, under the local integral square error criterion, this paper 7rst presents an O(n)-time algorithm for solving the PA-# problem using O(n) space. Then we present an O(n log n)-time algorithm for solving the PAusingO(n) space. Finally, a sampling technique is employed to reduce the memory requirement from O(n) to O(n). Some experiments are carried out to con7rm the theoretical analysis.? 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.