Some Morphological Operators on Simplicial Complex Spaces

Dias, Fabio; Cousty, Jean; Najman, Laurent

doi:10.1007/978-3-642-19867-0_37

Cited by 20 publications

(36 citation statements)

References 11 publications

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“…These topological structures extend graphs to higher dimensions in the sense that a graph is a 1-D structure made of points and edges considered as 0D and 1D elements. As shown in [10], the framework presented in this paper can be extended to complexes by considering additional generators. In 2D, for instance, a third generator for the elementary triangles (or squares) is required.…”

Section: Resultsmentioning

confidence: 99%

“…On the other hand, there is a growing interest for considering digital objects not only composed of points but also composed of elements lying between them and carrying structural information about how the points are glued together (see [6,4,18,31,10,2] for recent examples). The simplest of these representations are the graphs.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, it contains the proof of all properties presented in [10]. For the convenience of the mathematically oriented reader, these proofs are given below the statement of the properties.…”

Section: Introductionmentioning

confidence: 99%

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Morphological filtering on graphs

Cousty

Najman

Dias

et al. 2013

Computer Vision and Image Understanding

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106

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We study some basic morphological operators acting on the lattice of all subgraphs of an arbitrary (unweighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (i) to recover the classical notion of a dilation/erosion of a subset of the vertices of G and (ii) to extend it to subgraphs of G. Afterward, we propose several new openings, closings, granulometries and alternate filters acting (i) on the subsets of the edge and vertex set of G and (ii) on the subgraphs of G. The proposed framework is then extended to functions that weight the vertices and edges of a graph. We illustrate with applications to binary and grayscale image denoising, for which, on the provided images, the proposed approach outperforms the usual one based on structuring elements.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Morphological filtering on graphs

Cousty

Najman

Dias

et al. 2013

Computer Vision and Image Understanding

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106

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“…Let be an edge of ( ), i.e., ∈ ( ). That is, ∈ Equation (3) is implied from (7) and (8). The edge is a priority edge present in .…”

Section: Proposition 2 Let Be the Intuitionistic Fuzzy Hypergraph; Letmentioning

confidence: 99%

“…The purpose of this paper is to define adjunction, opening, closing, and ASF on IFHG. morphological operators for analyzing and filtering objects defined on simplicial complex spaces [8] where a simplex is any finite nonempty set. This finds application in mesh and image filtering.…”

Section: Introductionmentioning

confidence: 99%

Metric Induced Morphological Operators on Intuitionistic Fuzzy Hypergraphs

Dhanya

Sreekumar

Jathavedan

et al. 2018

International Journal of Mathematics and Mathematical Sciences

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A hypergraph consisting of hyperedges and nodes can be made intuitionistic fuzzy hypergraph (IFHG) by assigning membership and nonmembership degrees for both nodes and edges. Just as a hypergraph, an IFHG is also having hyperedges consisting of many nodes. Many flavours of a given IFHG can be created by applying morphological operators like dilation, erosion, adjunction, etc. The focus of this paper is to define morphological adjunction, opening, closing, and Alternative Sequential Filter (ASF) on IFHG. The system modeled in this way finds application in text processing, image processing, network analysis, and many other areas.

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A Comparison of Some Morphological Filters for Improving OCR Performance

Mennillo

Cousty

Najman

2015

Lecture Notes in Computer Science

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International audienceStudying discrete space representations has recently lead to the development of novel morphological operators. To date, there has been no study evaluating the performances of those novel operators with respect to a specific application. This article compares the capability of several morphological operators, both old and new, to improve OCR performance when used as preprocessing filters. We design an experiment using the Tesseract OCR engine on binary images degraded with a realistic document-dedicated noise model. We assess the performances of some morphological filters acting in complex, graph and vertex spaces, including the area filters. This experiment reveals the good overall performance of complex and graph filters. MSE measures have also been performed to evaluate the denoising capability of these filters, which again confirms the performances of both complex and graph filtering on this aspect

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Some Morphological Operators on Simplicial Complex Spaces

Cited by 20 publications

References 11 publications

Morphological filtering on graphs

Morphological filtering on graphs

Metric Induced Morphological Operators on Intuitionistic Fuzzy Hypergraphs

A Comparison of Some Morphological Filters for Improving OCR Performance

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