Dilation and Erosion on the Triangular Tessellation: An Independent Approach

Abdalla, Mohsen; Nagy, Benedek

doi:10.1109/access.2018.2827566

Cited by 21 publications

(6 citation statements)

References 32 publications

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“…We should also mention translations of images [25] since the triangular grid is not a point lattice. Mathematical morphology operators are also based on local translations [21]. Thus, our coordinate system provides a new tool for the research direction as well.…”

Section: Discussionmentioning

confidence: 99%

“…That coordinate system gives an efficient tool to work with digital cell complexes on the triangular grid. Various image processing algorithms have been defined and implemented for the triangular grid recently such as discrete tomography [18,19], thinning [20], and mathematical morphology [21]. We should also mention that triangulation is a frequently used technique in imaging and computer graphics.…”

Section: Introductionmentioning

confidence: 99%

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A Continuous Coordinate System for the Plane by Triangular Symmetry

Nagy¹,

Abuhmaidan²

2019

Symmetry

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The concept of the grid is broadly used in digital geometry and other fields of computer science. It consists of discrete points with integer coordinates. Coordinate systems are essential for making grids easy to use. Up to now, for the triangular grid, only discrete coordinate systems have been investigated. These have limited capabilities for some image-processing applications, including transformations like rotations or interpolation. In this paper, we introduce the continuous triangular coordinate system as an extension of the discrete triangular and hexagonal coordinate systems.The new system addresses each point of the plane with a coordinate triplet. Conversion between the Cartesian coordinate system and the new system is described. The sum of three coordinate values lies in the closed interval [−1, 1], which gives many other vital properties of this coordinate system. Symmetry 2019, 11, 191 2 of 17 of the grid. In Figure 1a, the first coordinate value is ascending right-upwardly, the second values are ascending into the right-downward direction, and the third one is ascending into the left-upward direction [7,8]. We should mention that this system could be seen as the extension of the oblique coordinate system using two independent integer values [9] by concerning the third value to obtain zero-sum for every triplet. The digital distance based on the neighborhood relation is computed in Reference [9]. Since the vectors describing the grid are not orthogonal, some geometric descriptions based on Cartesian coordinates are not very clear. However, to simplify the expressions of the constrained three-dimensional coordinate system is recommended. We should also mention that 0-sum triplets allowing real numbers were used in Reference [8] to describe rotations (that may not map the hexagonal grid to itself). In this way, a useful digitization operator is found. Her's system was mentioned and used in References [10,11] for various imaging-related disciplines.Symmetry 2019, 11, 191 3 of 17

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Continuous Coordinate System for the Plane by Triangular Symmetry

Nagy¹,

Abuhmaidan²

2019

Symmetry

Self Cite

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“…Multiple morphological image processing methods can be combined on the basis of dilation, erosion, opening operations, and closing operations. (5) Edge detection is fundamental to basic image features and segmentation; moreover, it constitutes a key information source for texture features and is central to shape quality analysis. The classical edge detection algorithms are local-window gradient operators, such as the Roberts, Sobel, Prewitt, Kirsch, and Laplacian operators.…”

Section: Literature Review and Methodologymentioning

confidence: 99%

Camera Handoff for Multicamera Multiobject Tracking

Wang¹,

Sheu²,

Lai³

2022

Sensors and Materials

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In recent years, the unmanned economy has begun to develop rapidly worldwide. Unmanned shops use technology to replace human personnel and increase efficiency. This technology has increased the demand for accurate and efficient camera surveillance systems. Camera handoff is a crucial step in the tasks of continuous target tracking and the maintenance of consistent crosscamera target marking in a multicamera surveillance system. In this study, we proposed a method of indoor multicamera handoff. To ensure continuous target tracking, the minimum number of required frames was maintained and at least one camera tracked each target. We employed the background subtraction approach to detect the target. Next, we used three trackability measures to evaluate the tracking object and trigger camera handoff accordingly, selecting the optimal camera for target tracking. The three measures considered were the resolution, occlusion, and distance to the edge of the camera's field of view. When one of these reached a preset threshold with an increasing trend, the system triggered the camera handoff.

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“…Morphological operations dilation and erosion are considered for the triangular grid in a more general and mathematical approach in [1,2]. Our aim here was to show how cellular automata can be applied in mathematical morphology and other related image processing tasks on the triangular grid.…”

Section: Literature Reviewmentioning

confidence: 99%

Cellular Automata Approach to Mathematical Morphology in the Triangular Grid

Saadat¹,

Nagy²

2018

ACTA POLYTECH HUNG

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Cellular automata are parallel computing devices working on a discrete timescale. In the paper, each cell of the triangular grid has a state from the binary set (i.e., we have a binary pattern, an image, on the grid), and the state in the next time instant depends only on the actual state of the cell itself and the states of its side-neighbor cells. We illustrate their use in image synthesis, e.g., generating snowflakes, and in image analysis: some of our automata are connected to image processing operations, e.g., dilation and erosion. Computation of Hausdorff distance of two binary images on the triangular grid is also presented. In image processing, and especially in mathematical morphology, operations are local operations, and thus, cellular automata are apt to use. On the other side, the triangular grid is not a point lattice, thus the definition of translation based image operations is not always straightforward.

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Dilation and Erosion on the Triangular Tessellation: An Independent Approach

Cited by 21 publications

References 32 publications

A Continuous Coordinate System for the Plane by Triangular Symmetry

A Continuous Coordinate System for the Plane by Triangular Symmetry

Camera Handoff for Multicamera Multiobject Tracking

Cellular Automata Approach to Mathematical Morphology in the Triangular Grid

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