Generating (co)homological information using boundary scale

Molina‐Abril, Helena; Real, Pedro; Díaz-del-Río, Fernando

doi:10.1016/j.patrec.2020.02.028

Cited by 4 publications

(2 citation statements)

References 41 publications

(41 reference statements)

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“…Note that e is considered here as a vector. They connect consecutive hypergraph components, preserving homological information [14,15]. Extracting from a BS 2 -model classical and new (local and global) topological indices is the method of TSF for topologically discriminating brain graphs.…”

Section: Boundary-scale Theory For Hypergraphsmentioning

confidence: 99%

“…In this work, an innovative software tool developed in Python language is presented for the analysis of brain graphs, based on the new "Topological Scale Framework" (TSF) [14,15]. More concretely, the set of algorithms proposed here conforms an iterative process that uses as initial value the incidence matrix (Figure 1) of the original brain graph, to gradually generate a sequence of associated hypergraphs parameterized by a scale of topological nature.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Connectome Graphs Based on Boundary Scale

Moron-Fernández,

Amedeo,

Monterroso Muñoz

et al. 2023

Sensors

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The purpose of this work is to advance in the computational study of connectome graphs from a topological point of view. Specifically, starting from a sequence of hypergraphs associated to a brain graph (obtained using the Boundary Scale model, BS2), we analyze the resulting scale-space representation using classical topological features, such as Betti numbers and average node and edge degrees. In this way, the topological information that can be extracted from the original graph is substantially enriched, thus providing an insightful description of the graph from a clinical perspective. To assess the qualitative and quantitative topological information gain of the BS2 model, we carried out an empirical analysis of neuroimaging data using a dataset that contains the connectomes of 96 healthy subjects, 52 women and 44 men, generated from MRI scans in the Human Connectome Project. The results obtained shed light on the differences between these two classes of subjects in terms of neural connectivity.

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Section: Boundary-scale Theory For Hypergraphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of Connectome Graphs Based on Boundary Scale

Moron-Fernández,

Amedeo,

Monterroso Muñoz

et al. 2023

Sensors

Self Cite

View full text Add to dashboard Cite

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Parallel homological calculus for 3D binary digital images

Díaz-del-Río,

Molina-Abril,

Real

et al. 2024

Ann Math Artif Intell

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Topological representations of binary digital images usually take into consideration different adjacency types between colors. Within the cubical-voxel 3D binary image context, we design an algorithm for computing the isotopic model of an image, called (6, 26)-Homological Region Adjacency Tree ((6, 26)-Hom-Tree). This algorithm is based on a flexible graph scaffolding at the inter-voxel level called Homological Spanning Forest model (HSF). Hom-Trees are edge-weighted trees in which each node is a maximally connected set of constant-value voxels, which is interpreted as a subtree of the HSF. This representation integrates and relates the homological information (connected components, tunnels and cavities) of the maximally connected regions of constant color using 6-adjacency and 26-adjacency for black and white voxels, respectively (the criteria most commonly used for 3D images). The Euler-Poincaré numbers (which may as well be computed by counting the number of cells of each dimension on a cubical complex) and the connected component labeling of the foreground and background of a given image can also be straightforwardly computed from its Hom-Trees. Being $$I_D$$ I D a 3D binary well-composed image (where D is the set of black voxels), an almost fully parallel algorithm for constructing the Hom-Tree via HSF computation is implemented and tested here. If $$I_D$$ I D has $$m_1{\times } m_2{\times } m_3$$ m 1 × m 2 × m 3 voxels, the time complexity order of the reproducible algorithm is near $$O(\log (m_1{+}m_2{+}m_3))$$ O ( log ( m 1 + m 2 + m 3 ) ) , under the assumption that a processing element is available for each cubical voxel. Strategies for using the compressed information of the Hom-Tree representation to distinguish two topologically different images having the same homological information (Betti numbers) are discussed here. The topological discriminatory power of the Hom-Tree and the low time complexity order of the proposed implementation guarantee its usability within machine learning methods for the classification and comparison of natural 3D images.

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