MATHEMATICAL MORPHOLOGY - A MODERN APPROACH IN IMAGE-PROCESSING BASED ON ALGEBRA AND GEOMETRY

被引:89
作者
HEIJMANS, HJAM
机构
[1] Cent for Mathematics and Computer, Science, Amsterdam
关键词
IMAGE ANALYSIS; MATHEMATICAL MORPHOLOGY; HIT-OR-MISS OPERATOR; MINKOWSKI SUM AND DIFFERENCE; DILATION; EROSION; OPENING; CLOSING; BOOLEAN FUNCTION; COMPLETE LATTICE; ADJUNCTION; MORPHOLOGICAL FILTER; ITERATION OF MORPHOLOGICAL OPERATORS; DOWN-ARROW-(RESPECTIVELY; UP-ARROW-) CONTINUOUS OPERATOR; METRIC; GAUGE FUNCTION; CONVEX SET; GEODESIC OPERATOR; GRANULOMETRY; METRIC DILATION; DISTANCE TRANSFORM; COST FUNCTION; GRAY-SCALE MORPHOLOGY; FLAT FUNCTION OPERATOR;
D O I
10.1137/1037001
中图分类号
O29 [应用数学];
学科分类号
070104 [应用数学];
摘要
Mathematical morphology is a theory of image transformations and image functionals which is based on set-theoretical, geometrical, and topological concepts. The methodology is particularly useful for the analysis of the geometrical structure in an image. The main goal of this paper is to give an impression of the underlying philosophy and the mathematical theories which are relevant to this field. The following topics are discussed: introduction to mathematical morphology; generalization to complete lattices; morphological filters and their construction by iteration; geometrical aspects of morphology (e.g., convexity, distance, geodesic operators, granulometries, metric dilations, distance transform, cost functions); and extension of binary operators to grey-scale images.
引用
收藏
页码:1 / 36
页数:36
相关论文
共 50 条
[1]
[Anonymous], 1975, RANDOM SETS INTEGRAL
[2]
MINIMAL REPRESENTATIONS FOR TRANSLATION-INVARIANT SET MAPPINGS BY MATHEMATICAL MORPHOLOGY [J].
BANON, GJF ;
BARRERA, J .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1991, 51 (06) :1782-1798
[3]
BIRKHOFF G, 1967, AM MATH SOC C PUBL, V25
[4]
DISTANCE TRANSFORMATIONS IN DIGITAL IMAGES [J].
BORGEFORS, G .
COMPUTER VISION GRAPHICS AND IMAGE PROCESSING, 1986, 34 (03) :344-371
[5]
DISTANCE TRANSFORMATIONS IN ARBITRARY DIMENSIONS [J].
BORGEFORS, G .
COMPUTER VISION GRAPHICS AND IMAGE PROCESSING, 1984, 27 (03) :321-345
[6]
Busemann H., 1955, GEOMETRY GEODESICS
[7]
DOUGHERTY ER, 1987, IMAGE PROCESSING CON
[8]
GIARDINA C, 1988, MORPHOLOGICAL METHOD
[9]
GOUTSIAS J, IN PRESS COMPUTER VI
[10]
Hadwiger H., 1957, VORLESUNGEN INHALT O