The fundamentals of fuzzy mathematical morphology. II: Idempotence, convexity and decomposition. (English) Zbl 0845.68107
Summary: 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.
MSC:
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
| 68T99 | Artificial intelligence |
Citations:
Zbl 0845.68106References:
| [1] | De Baets B., International Journal of General Systems. (1994) |
| [2] | DOI: 10.1109/TPAMI.1987.4767941 · doi:10.1109/TPAMI.1987.4767941 |
| [3] | Kerre E., Introduction to the Basic Principles of Fuzzy Set Theory and some of its Applications. (1991) |
| [4] | Serra J., Image Analysis and Mathematical Morphology (1982) · Zbl 0565.92001 |
| [5] | DOI: 10.1109/34.23111 · Zbl 0665.68068 · doi:10.1109/34.23111 |
| [6] | DOI: 10.1016/S0019-9958(65)90241-X · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
