Novel Efficient Two-pass Algorithm for Closed Polygonal Approximation Based on LISE and Curvature Constraint Criteria

• Main Authors: Po-Hsuan Liao, 廖伯璇
• Other Authors: Kuo-Liang Chung
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/b8p4q9

碩士 === 國立臺灣科技大學 === 資訊工程系 === 94 === Given a closed polygonal curve C with n points, the closed polygonal approximation (CPA) problem is defined to find a closed polygon P to approximate C under some error tolerance criteria. Based on the local integral square error (LISE) and the curvature constraint criteria, this paper presents a novel two-pass O(Fn+mn^2)-time algorithm for solving the CPA problem where m (<<n) denotes the minimal number of covering feasible segments for one vertex and empirically the value of $m$ is rather small; F (<<n^2) denotes the number of feasible approximate segments. The first pass of our proposed algorithm can be performed in O(Fn+mn^2) time under the given LISE; the second pass of our proposed algorithm can be performed in O(n) time under the given curvature constraint and the longest vertical distance consideration. Note that under the same LISE criterion, the set of polygonal segments determined by the first pass of our proposed CPA algorithm is minimal and is the same as that obtained by the currently published CPA algorithm by {\sl Chung et al.} whose algorithm takes O(n^3) time. Based on two real closed curves for representing French and Italy, experimental results demonstrate that our proposed two-pass CPA algorithm is faster and more robust than the previous algorithm by Chung {\sl et al.} Based on two real closed curves for representing a semicircle and a chromosome, experimental results demonstrate that under the same number of segments used, our proposed two-pass algorithm has a better quality, but has a little execution-time degradation when compared to the currently published CPA algorithm by {\sl Wu}.