scholarly journals Mathematical Morphology on Hypergraphs Using Vertex-Hyperedge Correspondence

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bino Sebastian ◽  
A. Unnikrishnan ◽  
Kannan Balakrishnan ◽  
P. B. Ramkumar
Keyword(s):  
Mathematical Morphology ◽  
Lattice Structures ◽  
Computationally Efficient ◽  
Morphological Operators ◽  
Classical Notion ◽  
Vertex Set

The focus of this paper is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyperedge set of a hypergraph H, by defining a vertex-hyperedge correspondence. This allows us to recover the classical notion of a dilation/erosion of a subset of vertices and to extend it to subhypergraphs of H. This paper also studies the concept of morphological adjunction on hypergraphs for which both the input and the output are hypergraphs.

scholarly journals Deterministic mathematical morphology for CAD/CAM

2014 ◽  
Vol 31 (7) ◽  
pp. 1221-1241 ◽  
Author(s):  
Rubén Sarabia-Pérez ◽  
Antonio Jimeno-Morenilla ◽  
Rafael Molina-Carmona
Keyword(s):  
Mathematical Morphology ◽  
Geometric Model ◽  
Three Dimensional ◽  
Morphological Operations ◽  
Basic Operation ◽  
Geometric Data Structures ◽  
Content Type ◽  
Morphological Operators ◽  
Cad Cam ◽  
Definition Of

Purpose – The purpose of this paper is to present a new geometric model based on the mathematical morphology paradigm, specialized to provide determinism to the classic morphological operations. The determinism is needed to model dynamic processes that require an order of application, as is the case for designing and manufacturing objects in CAD/CAM environments. Design/methodology/approach – The basic trajectory-based operation is the basis of the proposed morphological specialization. This operation allows the definition of morphological operators that obtain sequentially ordered sets of points from the boundary of the target objects, inexistent determinism in the classical morphological paradigm. From this basic operation, the complete set of morphological operators is redefined, incorporating the concept of boundary and determinism: trajectory-based erosion and dilation, and other morphological filtering operations. Findings – This new morphological framework allows the definition of complex three-dimensional objects, providing arithmetical support to generating machining trajectories, one of the most complex problems currently occurring in CAD/CAM. Originality/value – The model proposes the integration of the processes of design and manufacture, so that it avoids the problems of accuracy and integrity that present other classic geometric models that divide these processes in two phases. Furthermore, the morphological operative is based on points sets, so the geometric data structures and the operations are intrinsically simple and efficient. Another important value that no excessive computational resources are needed, because only the points in the boundary are processed.

scholarly journals STRUCTURALLY ADAPTIVE MATHEMATICAL MORPHOLOGY BASED ON NONLINEAR SCALE-SPACE DECOMPOSITIONS

2011 ◽  
Vol 30 (2) ◽  
pp. 111 ◽  
Author(s):  
Jesús Angulo ◽  
Santiago Velasco-Forero
Keyword(s):  
Mathematical Morphology ◽  
Scale Space ◽  
Local Regularity ◽  
Natural Image ◽  
Translation Invariant ◽  
Morphological Operators ◽  
Multi Scale ◽  
Nonlinear Scale Space ◽  
Local Intensity ◽  
Nonlinear Scale

Standard formulation of morphological operators is translation invariant in the space and in the intensity: the same processing is considered for each point of the image. A current challenging topic in mathematical morphology is the construction of adaptive operators. In previous works, the adaptive operators are based either on spatially variable neighbourhoods according to the local regularity, or on size variable neighbourhoods according to the local intensity. This paper introduces a new framework: the structurally adaptive mathematical morphology. More precisely, the rationale behind the present approach is to work on a nonlinear multi-scale image decomposition, and then to adapt intrinsically the size of the operator to the local scale of the structures. The properties of the derived operators are investigated and their practical performances are compared with respect to standard morphological operators using natural image examples.

scholarly journals GRADUAL TRANSITION DETECTION FOR VIDEO PARTITIONING USING MORPHOLOGICAL OPERATORS

2011 ◽  
Vol 26 (2) ◽  
pp. 51 ◽  
Author(s):  
Valery Naranjo ◽  
Jesús Angulo ◽  
Antonio Albiol ◽  
Jose M Mossi ◽  
Alberto Albiol ◽  
...  
Keyword(s):  
Motion Estimation ◽  
Mathematical Morphology ◽  
Video Indexing ◽  
Video Data ◽  
Gradual Transition ◽  
Temporal Segmentation ◽  
Perceptual Coding ◽  
Morphological Operators ◽  
Temporal Series ◽  
Spatial Operators

Temporal segmentation of video data for partitioning the sequence into shots is a prerequisite in many applications: automatic video indexing and editing, old flm restoration, perceptual coding, etc. The detection of abrupt transitions or cuts has been thoroughly studied in previous works. In this paper we present a scheme to identify the most common gradual transitions, i.e., dissolves and wipes, which relies on mathematical morphology operators. The approach is restricted to fast techniques which require low computation (without motion estimation and adapted to compressed sequences) and are able to cope with random brightness variations (often occurring in old flms). The present study illustrates how the morphological operators can be used to analyze temporal series for detecting particular events, either working directly on the 1D signal or building an intermediate 2D image from the 1D signals to take advantage of the spatial operators.

A Promotion of a Color Morphological Filter

2014 ◽  
Vol 548-549 ◽  
pp. 1064-1067
Author(s):  
Shui Ming He
Keyword(s):  
Image Processing ◽  
Mathematical Morphology ◽  
Digital Image Processing ◽  
Digital Image ◽  
Color Image ◽  
Processing Method ◽  
Color Image Processing ◽  
Morphological Filter ◽  
Morphological Operators ◽  
Gray Image

Mathematical morphology can be seen as a special digital image processing method and theory, which has been widely used in various fields. In this paper, the mathematical morphology is applied to the color image processing. In thespace of color image, I have simply expounded the theories and properties of color morphological changs, and defined its morphological operators. According to the application of omni-directional and multi-angle structuring elements composite morphological filter in gray image, I put forward a kind of color morphological filter with omni-directional and multi-angle structuring elements composite. This algorithm has retained its advantages in gray image, however, remaining some drawbacks. Through the optimization of results based on this algorithm, we finally get the relatively ideal denoising effects.

Programmatic generation of computationally efficient lattice structures for additive manufacture

2017 ◽  
Vol 23 (3) ◽  
pp. 486-494 ◽  
Author(s):  
Matthew Leslie McMillan ◽  
Marten Jurg ◽  
Martin Leary ◽  
Milan Brandt
Keyword(s):  
Numerical Analysis ◽  
Computer Aided Design ◽  
Process Integration ◽  
Additive Manufacture ◽  
Beam Model ◽  
Lattice Structures ◽  
Computationally Efficient ◽  
Content Type ◽  
Complex Lattice ◽  
Stl File

Purpose Additive manufacturing (AM) enables the fabrication of complex geometries beyond the capability of traditional manufacturing methods. Complex lattice structures have enabled engineering innovation; however, the use of traditional computer-aided design (CAD) methods for the generation of lattice structures is inefficient, time-consuming and can present challenges to process integration. In an effort to improve the implementation of lattice structures into engineering applications, this paper aims to develop a programmatic lattice generator (PLG). Design/methodology/approach The PLG method is computationally efficient; has direct control over the quality of the stereolithographic (STL) file produced; enables the generation of more complex lattice than traditional methods; is fully programmatic, allowing batch generation and interfacing with process integration and design optimization tools; capable of generating a lattice STL file from a generic input file of node and connectivity data; and can export a beam model for numerical analysis. Findings This method has been successfully implemented in the generation of uniform, radial and space filling lattices. Case studies were developed which showed a reduction in processing time greater than 60 per cent for a 3,375 cell lattice over traditional CAD software. Originality/value The PLG method is a novel design for additive manufacture (DFAM) tool with unique advantages, including full control over the number of facets that represent a lattice strut, allowing optimization of STL data to minimize file size, while maintaining suitable resolution for the implemented AM process; programmatic DFAM capability that overcomes the learning curve of traditional CAD when producing complex lattice structures, therefore is independent of designer proficiency and compatible with process integration; and the capability to output both STL files and associated data for numerical analysis, a unique DFAM capability not previously reported.

A METHOD FOR QUASI-STATIC ANALYSIS OF TOPOLOGICALLY VARIABLE LATTICE STRUCTURES

2006 ◽  
Vol 03 (01) ◽  
pp. 71-81 ◽  
Author(s):  
IGOR YE. TELITCHEV ◽  
OLEG VINOGRADOV
Keyword(s):  
Crack Nucleation ◽  
Mixed Boundary ◽  
Hexagonal Lattice ◽  
Numerical Procedure ◽  
Mixed Boundary Conditions ◽  
Inverse Matrix ◽  
Lattice Structures ◽  
Computationally Efficient ◽  
Nonlinear Potentials ◽  
Minimization Technique

The proposed time-independent quasi-static approach for simulations of lattice structures with imperfections is based on integration of the Inverse Broyden's Method suitable for finding the equilibrium state for a large system of atoms interacting through strongly nonlinear potentials and the Recursive Inverse Matrix Algorithm (RIMA) capable of updating the inverse matrix when topological changes (broken or new bonds between the atoms) take place. In this approach, the crystal structure is treated as a truss system while the forces between the atoms situated at the nodes are defined by the inter-atomic potentials. Since both the Broyden's and the RIMA algorithms deal with the inverse matrices of the structure their coupling makes the procedure computationally efficient. In addition, the method allows analysis of lattices subjected to mixed boundary conditions. The developed code was verified by the comparison with an alternative numerical procedure based on energy minimization technique. The model and the code developed were applied to the case of a 2D hexagonal lattice with the mode I crack embedded into the structure. For the cases considered, it was observed that the crack nucleation and growth were accompanied by the dislocation emission.

scholarly journals Adaptive Mathematical Morphology on Irregularly Sampled Signals in Two Dimensions

2020 ◽  
Vol 4 (1) ◽  
pp. 108-126
Author(s):  
Teo Asplund ◽  
Cris L. Luengo Hendriks ◽  
Matthew J. Thurley ◽  
Robin Strand
Keyword(s):  
Mathematical Morphology ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Morphological Operators ◽  
Input And Output ◽  
Adaptive Morphology ◽  
Discrete Domain

AbstractThis paper proposes a way of better approximating continuous, two-dimensional morphology in the discrete domain, by allowing for irregularly sampled input and output signals. We generalize previous work to allow for a greater variety of structuring elements, both flat and non-flat. Experimentally we show improved results over regular, discrete morphology with respect to the approximation of continuous morphology. It is also worth noting that the number of output samples can often be reduced without sacrificing the quality of the approximation, since the morphological operators usually generate output signals with many plateaus, which, intuitively do not need a large number of samples to be correctly represented. Finally, the paper presents some results showing adaptive morphology on irregularly sampled signals.

scholarly journals PERFORMANCE ANALYSIS OF FUZZY MATHEMATICAL MORPHOLOGY OPERATORS ON NOISY MRI

2014 ◽  
Vol 44 (3) ◽  
pp. 231-236
Author(s):  
A. BOUCHET ◽  
F. BENALCÁZAR PALACIOS ◽  
M. BRUN ◽  
V. L. BALLARIN
Keyword(s):  
Magnetic Resonance ◽  
Performance Analysis ◽  
Mathematical Morphology ◽  
Intrinsic Noise ◽  
Magnetic Resonance Images ◽  
Systematic Evaluation ◽  
Artificial Noise ◽  
Morphological Operators ◽  
The Brain ◽  
Fuzzy Mathematical Morphology

 Despite a large amount of publications on Fuzzy Mathematical Morphology, little effort was done on systematic evaluation of the performance of this technique. The goal of this work is to compare the robustness against noise of Fuzzy and non Fuzzy Morphological operators when applied to noisy images. Magnetic Resonance Images (MRI) of the brain are a kind of images containing some characteristics that make fuzzy operators an interesting choice, because of their intrinsic noise and imprecision. The robustness was evaluated as the degree in which the results of the operators are not affected by artificial noise in the images. In the analysis we compared different implementation of Fuzzy Mathematical Morphology, and observed that in most of the cases they show higher robustness against noise than the classical morphological operators.

scholarly journals MATHEMATICAL MORPHOLOGY IN THE CIELAB SPACE

2011 ◽  
Vol 21 (3) ◽  
pp. 201 ◽  
Author(s):  
Allan Hanbury ◽  
Jean Serra
Keyword(s):  
Mathematical Morphology ◽  
Electrostatic Potential ◽  
Weighting Function ◽  
Lexicographical Order ◽  
Colour Space ◽  
Morphological Operators ◽  
Lower Weight ◽  
Higher Weights ◽  
Colour Saturation ◽  
Colour Distance

The use of mathematical morphology in the CIE L*a*b* colour space is discussed. It is possible to impose a total order on the colour vectors in this space by using a weighting function and lexicographical order. An order analogous to one by colour saturation is suggested by making use of a weighting function based on an electrostatic potential. This weighting function assigns a lower weight to colour vectors near the colours with maximum chroma, and higher weights to colour vectors near the lightness axis. The use of morphological operators with the colour vector order imposed by this function is demonstrated. Finally, a top-hat operator making use of the Euclidean colour distance in the L*a*b* space is introduced.

Application of Fuzzy Mathematical Morphology with Adaptive Structuring Elements to Seal Defect Testing

2002 ◽  
Vol 6 (1) ◽  
pp. 62-69
Author(s):  
Takuo Kikuchi ◽  
◽  
Shuta Murakami ◽  
Keyword(s):  
Mathematical Morphology ◽  
Input Image ◽  
Performance Evaluations ◽  
Automatic Inspection ◽  
Morphological Operators ◽  
Fuzzy Morphology ◽  
Structuring Element ◽  
Extraction Performance ◽  
Selection Of ◽  
Fuzzy Mathematical Morphology

Fuzzy mathematical morphology has been proposed as a new method of image processing, especially in the analysis of features from an ambiguous image. Fuzzy morphological operators work with 2 images: an original image to be processed and a structuring element. Generally, we must decide on the shape and value of the structuring element before applying fuzzy morphology. A problem arises when the applied image changes largely by the selection of the structuring element, so it is difficult to apply fuzzy morphological operators to inspection for defect testing. In this paper, we propose a new structuring element for fuzzy morphology, called an adaptive structuring element. The adaptive structuring element determines shapes and values of structuring elements dynamically from an input image by searching for the local features in the image. Consequently, the adaptive structuring element is sensitive to ambiguous images, useful for automatic inspection using fuzzy morphology, and effective for extraction. Performance evaluations via simulations show that the adaptive structuring element efficiently extracts features from an ambiguous image. The adaptive structuring element also shows a higher performance in package defect testing than other filters. We attained experimental results (more than 95.5%) by applying the adaptive structuring element to seal defect testing.

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