Introduction to mathematical morphology
Computer Vision, Graphics, and Image Processing
Morphological structuring element decomposition
Computer Vision, Graphics, and Image Processing
Image Analysis Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Decomposition of Convex Polygonal Morphological Structuring Elements into Neighborhood Subsets
IEEE Transactions on Pattern Analysis and Machine Intelligence
An algorithmic comparison between square- and hexagonal-based grids
CVGIP: Graphical Models and Image Processing
Resampling on a pseudohexagonal grid
CVGIP: Graphical Models and Image Processing
Discrete Optimization Algorithms with Pascal Programs
Discrete Optimization Algorithms with Pascal Programs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Binary Morphological Algorithms on a Massively Parallel Processor
IPDPS '00 Proceedings of the 14th International Symposium on Parallel and Distributed Processing
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Neighborhood decomposition of 3d convex structuring elements for morphological operations
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation
IEEE Transactions on Image Processing
Geometric transformations on the hexagonal grid
IEEE Transactions on Image Processing
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In this paper, we present a new technique to find the optimal neighborhood decomposition for convex structuring elements used in morphological image processing on hexagonal grid. In neighborhood decomposition, a structuring element is decomposed into a set of neighborhood structuring elements, each of which consists of the combination of the origin pixel and its six neighbor pixels. Generally, neighborhood decomposition reduces the amount of computation required to perform morphological operations such as dilation and erosion. Firstly, we define a convex structuring element on a hexagonal grid and formulate the necessary and sufficient condition to decompose a convex structuring element into the set of basis convex structuring elements. Secondly, decomposability of a convex structuring element into the set of primal bases is also proved. Furthermore, cost function is used to represent the amount of computation or execution time required for performing dilations on different computing environments and by different implementation methods. The decomposition condition and the cost function are applied to find the optimal neighborhood decomposition of a convex structuring element, which guarantees the minimal amount of computation for morphological operations. Example decompositions show that the decomposition results in great reduction in the amount of computation for morphological operations.