DECOMPOSITION OF MAPPINGS BETWEEN COMPLETE LATTICES BY MATHEMATICAL MORPHOLOGY .1. GENERAL LATTICES

被引：65

作者：

BANON, GJF

BARRERA, J

机构：

[1] Instituto Nacional de Pesquisas Espaciais INPE, DPI, 12201-970 Sao Jose dos Campos, SP

[2] Univeridade de São Paulo USP/IME, CP. IME 20570, 01498-970 São Paulo, SP

来源：

SIGNAL PROCESSING | 1993年 / 30卷 / 03期

关键词：

COMPLETE LATTICE; MAPPING DECOMPOSITION; MINIMAL DECOMPOSITION; MATHEMATICAL MORPHOLOGY; EROSION; DILATION; GALOIS CONNECTION; KERNEL; BASIS; IMAGE PROCESSING; BOOLEAN FUNCTIONS SIMPLIFICATION; 4 VALUES LOGIC;

D O I：

10.1016/0165-1684(93)90015-3

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

Two canonical decompositions of mappings between complete lattices are presented, These decompositions are based on the mathematical morphology elementary mappings: erosions, anti-erosions, dilations and anti-dilations. The proposed decompositions are obtained by introducing the concept of morphological connection, that extends the notion of Galois connection. The definitions of sup-generating mapping, kernel and basis within the framework of complete lattices are given. The decompositions are built by analysing the kernel and may be simplified from the basis. The results are specialized to the cases of inf-separable, increasing and decreasing mappings. The presented decompositions are dual. Some examples, including the case of boolean functions simplification, illustrate the key concepts and the decomposition rule.

引用

页码：299 / 327

页数：29

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