Concepts of Binary Morphological Operations Dilation and Erosion on the Triangular Grid

被引：3

作者：

Abdalla, Mohsen ^{[1
]}

Nagy, Benedek ^{[1
]}

机构：

[1] Eastern Mediterranean Univ, Dept Math, Fac Arts & Sci, Mersin 10, Famagusta, North Cyprus, Turkey

来源：

COMPUTATIONAL MODELING OF OBJECTS PRESENTED IN IMAGES: FUNDAMENTALS, METHODS, AND APPLICATIONS, COMPIMAGE 2016 | 2017年 / 10149卷

关键词：

Digital image processing; Mathematical morphology; Binary morphology; Dilation; Erosion; Triangular grid; Non-traditional grids; TRANSFORMATIONS;

D O I：

10.1007/978-3-319-54609-4_7

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, basic concepts of digital binary morphological operations, i.e., dilation and erosion are investigated on a triangular grid. Every triangle pixel is addressed by a unique coordinate triplet with sum zero (even pixels) or one (odd pixels). Even and odd pixels have different orientations. The triangular grid is not a lattice, that is, not every translation with a grid vector maps the grid to itself. Therefore, to extend the morphological operations to the triangular grid is not straightforward. We introduce three types of definition for both of dilation and erosion. Various examples and properties of the considered dilation and erosion are analyzed on the triangular grid.

引用

页码：89 / 104

页数：16

共 22 条

[11]

Matheron G., 1975, RANDOM SETS INTEGRAL

[12] Capacity and surface [J].

Minkowski, H .

MATHEMATISCHE ANNALEN, 1903, 57 :447-495

[13]

Nagy B, 2003, ISPA 2003: PROCEEDINGS OF THE 3RD INTERNATIONAL SYMPOSIUM ON IMAGE AND SIGNAL PROCESSING AND ANALYSIS, PTS 1 AND 2, P101

[14]

Nagy Benedek, 2009, 2009 Proceedings of 6th International Symposium on Image and Signal Processing and Analysis, P432

[15] Finding shortest path with neighbourhood sequences in triangular grids [J].

Nagy, B .

ISPA 2001: PROCEEDINGS OF THE 2ND INTERNATIONAL SYMPOSIUM ON IMAGE AND SIGNAL PROCESSING AND ANALYSIS, 2001, :55-60

[16]

Nagy B., 2004, ACTA MATH ACAD PAEDA, V20, P63

[17] Dense Projection Tomography on the Triangular Tiling [J].

Nagy, Benedek ;

Lukic, Tibor .

FUNDAMENTA INFORMATICAE, 2016, 145 (02) :125-141

[18] Cellular topology and topological coordinate systems on the hexagonal and on the triangular grids [J].

Nagy, Benedek .

ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE, 2015, 75 (1-2) :117-134

[19]

Nagy B, 2014, LECT NOTES COMPUT SC, V8466, P37, DOI 10.1007/978-3-319-07148-0_5

[20]

Serra J., 1983, IMAGE ANAL MATH MORP

← 1 2 3 →