The fundamentals of fuzzy mathematical morphology .2. Idempotence, convexity and decomposition

被引：38

作者：

DeBaets, B ^{[1
]}

Kerre, E ^{[1
]}

Gupta, M ^{[1
]}

机构：

[1] UNIV SASKATCHEWAN,INTELLIGENT SYST RES LAB,SASKATOON,SK S7N 0W0,CANADA

来源：

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS | 1995年 / 23卷 / 04期

关键词：

fuzzy mathematical morphology; extensivity; anti-extensivity; idempotence; translation invariance; convexity; concavity; (strict) alpha-cuts; decomposition;

D O I：

10.1080/03081079508908045

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Fuzzy mathematical morphology is an alternative extension of binary mathematical morphology to gray-scale images. This paper discusses some of the more advanced properties of the fuzzy morphological operations. The possible extensivity of the fuzzy closing, anti-extensivity of the fuzzy opening and idempotence of the fuzzy closing and fuzzy opening are studied in detail. It is demonstrated that these properties only partially hold. On the other hand, it is shown that the fuzzy morphological operations satisfy the same translation invariance and have the same convexity properties as the binary morphological operations. Finally, the paper investigates the possible decomposition, by taking (strict) alpha-cuts, of the fuzzy morphological operations into binary morphological operations.

引用

页码：307 / 322

页数：16

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