Similarity between Hypergraphs Based on Mathematical Morphology

Bloch, Isabelle; Bretto, Alain; Leborgne, Aurélie

doi:10.1007/978-3-642-38294-9_1

Cited by 10 publications

(9 citation statements)

References 17 publications

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“…While different similarity measures have been proposed for traditional graphs [29], among them graph edit distances (GED) [10], the picture looks different for hypergraphs. There are a few approaches based on mathematical morphology [3] and error-tolerant hypergraph matching, including edit distance [5]. However, common to these approaches is their high computational cost.…”

Section: Neighborhoodsmentioning

confidence: 99%

A Similarity Measure for Weaving Patterns in Textiles

Helmer

Ngo

2015

Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval

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We propose a novel approach for measuring the similarity between weaving patterns that can provide similarity-based search functionality for textile archives. We represent textile structures using hypergraphs and extract multisets of k-neighborhoods from these graphs. The resulting multisets are then compared using Jaccard coefficients, Hamming distances, and cosine measures. We evaluate the different variants of our similarity measure experimentally, showing that it can be implemented efficiently and illustrating its quality using it to cluster and query a data set containing more than a thousand textile samples.

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Section: Neighborhoodsmentioning

confidence: 99%

A Similarity Measure for Weaving Patterns in Textiles

Helmer

Ngo

2015

Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval

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“…After defining a hypergraph representation for textiles, we now need a method to compare these graphs. Many of the approaches found in literature, such as subgraph isomorphisms for hypergraphs (Ha et al 2018), graph editing distances for hypergraphs (Bunke et al 2008), and morphology-based techniques (Bloch et al 2013), have a high complexity, i.e., exponential run time.…”

Section: Comparing Textile Graphsmentioning

confidence: 99%

Structural textile pattern recognition and processing based on hypergraphs

et al. 2021

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The humanities, like many other areas of society, are currently undergoing major changes in the wake of digital transformation. However, in order to make collection of digitised material in this area easily accessible, we often still lack adequate search functionality. For instance, digital archives for textiles offer keyword search, which is fairly well understood, and arrange their content following a certain taxonomy, but search functionality at the level of thread structure is still missing. To facilitate the clustering and search, we introduce an approach for recognising similar weaving patterns based on their structures for textile archives. We first represent textile structures using hypergraphs and extract multisets of k-neighbourhoods describing weaving patterns from these graphs. Then, the resulting multisets are clustered using various distance measures and various clustering algorithms (K-Means for simplicity and hierarchical agglomerative algorithms for precision). We evaluate the different variants of our approach experimentally, showing that this can be implemented efficiently (meaning it has linear complexity), and demonstrate its quality to query and cluster datasets containing large textile samples. As, to the best of our knowledge, this is the first practical approach for explicitly modelling complex and irregular weaving patterns usable for retrieval, we aim at establishing a solid baseline.

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“…In the past, several authors studied morphological operators on graphs [9,24] and simplicial complexes [11,20]. However, very few studies exist about basic morphological operators on hypergraphs [3][4][5]23] and none deal with the filtering problem. The objective of this article is to help bridging this gap.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Morphological filtering on hypergraphs

Vadakkenveettil

Unnikrishnan

Balakrishnan

et al. 2017

Discrete Applied Mathematics

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a b s t r a c tIn this work we study the framework of mathematical morphology on hypergraph spaces. Hypergraphs were introduced in the 60s as a natural generalization of graphs, where edges become hyperedges and can contain more than two vertices. Mathematical morphology is one of the most powerful frameworks for image processing, and is heavily used for many applications. However, morphological operators on hypergraph spaces is not a concept fully developed in the literature. We consider lattice structures on hypergraphs on which we build morphological operators. We propose several new openings, closings, granulometries and alternate sequential filters acting (i) on the subsets of the vertex and hyperedge set of a hypergraph and (ii) on the subhypergraphs of a hypergraph. We illustrate with applications in image processing for filtering objects defined on hypergraph spaces.

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Similarity between Hypergraphs Based on Mathematical Morphology

Cited by 10 publications

References 17 publications

A Similarity Measure for Weaving Patterns in Textiles

A Similarity Measure for Weaving Patterns in Textiles

Structural textile pattern recognition and processing based on hypergraphs

Morphological filtering on hypergraphs

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