TY - JOUR
T1 - Algorithms for Morphological Profile Filters and their Comparison
AU - Jiang, Xiangqian
AU - Scott, Paul J.
AU - Lou, Shan
PY - 2012/7
Y1 - 2012/7
N2 - Morphological filters, regarded as the complement of mean-line based filters, are useful in the analysis of surface texture and the prediction of functional performance. The paper first recalls two existing algorithms, the naive algorithm and the motif combination algorithm, originally developed for the traditional envelope filter. With minor extension, they could be used to compute morphological filters. A recent novel approach based on the relationship between the alpha shape and morphological closing and opening operations is presented as well. Afterwards two novel algorithms are developed. By correlating the convex hull and morphological operations, the Graham scan algorithm, original developed for the convex hull is modified to compute the morphological envelopes. The alpha shape method depending on the Delaunay triangulation is costly and redundant for the computation for the alpha shape for a given radius. A recursive algorithm is proposed to solve this problem. A series of observations are presented for searching the contact points. Based on the proposed observations, the algorithm partitions the profile data into small segments and searches the contact points in a recursive manner. The paper proceeds to compare the five distinct algorithms in five aspects: algorithm verification, algorithm analysis, performance evaluation, end effects correction, and areal extension. By looking into these aspects, the merits and shortcomings of these algorithms are evaluated and compared.
AB - Morphological filters, regarded as the complement of mean-line based filters, are useful in the analysis of surface texture and the prediction of functional performance. The paper first recalls two existing algorithms, the naive algorithm and the motif combination algorithm, originally developed for the traditional envelope filter. With minor extension, they could be used to compute morphological filters. A recent novel approach based on the relationship between the alpha shape and morphological closing and opening operations is presented as well. Afterwards two novel algorithms are developed. By correlating the convex hull and morphological operations, the Graham scan algorithm, original developed for the convex hull is modified to compute the morphological envelopes. The alpha shape method depending on the Delaunay triangulation is costly and redundant for the computation for the alpha shape for a given radius. A recursive algorithm is proposed to solve this problem. A series of observations are presented for searching the contact points. Based on the proposed observations, the algorithm partitions the profile data into small segments and searches the contact points in a recursive manner. The paper proceeds to compare the five distinct algorithms in five aspects: algorithm verification, algorithm analysis, performance evaluation, end effects correction, and areal extension. By looking into these aspects, the merits and shortcomings of these algorithms are evaluated and compared.
KW - Alpha Shape
KW - Contact Point
KW - Graham Scan
KW - Morphological Filter
KW - Motif Combination
UR - http://www.scopus.com/inward/record.url?scp=84860238172&partnerID=8YFLogxK
U2 - 10.1016/j.precisioneng.2012.01.003
DO - 10.1016/j.precisioneng.2012.01.003
M3 - Article
AN - SCOPUS:84860238172
VL - 36
SP - 414
EP - 423
JO - Precision Engineering
JF - Precision Engineering
SN - 0141-6359
IS - 3
ER -