Toward Parallel Computation of Dense Homotopy Skeletons for nD Digital Objects

Real, Pedro; Díaz-del-Río, Fernando; Onchiş, Darian M.

doi:10.1007/978-3-319-59108-7_12

Cited by 4 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Algebraic homology information with coefficients in a field could be defined as the set of processed and structured linear algebraic data describing in some sense its (co)homology classes and the relations between them. We talk about homology and cohomology information as a whole due to the fact that homology and cohomology classes are measured using, up to dimension, the same algorithmic strategy of connectivity clustering over the initial topological data and they both provide the same measurable information quantities, up to "duality" [9,11]. A simple example of (co)homology information is provided by the numerical topological invariants called Betti numbers.…”

Section: Theoretical Briefmentioning

confidence: 99%

Refined Deep Learning for Digital Objects Recognition via Betti Invariants

Onchiş

Istin

Real

2019

Computer Analysis of Images and Patterns

Self Cite

View full text Add to dashboard Cite

In this paper, we make use of the topological invariants of 2D images for an accelerated training and an improved recognition ability of a deep learning neural network applied to digital image objects. For our test images, we generate the associated simplicial complexes and from them we compute the Betti numbers which for a 2D object are the number of connected components and the number of holes. These information are used for training the network according to the corresponding Betti number. Experiments on the MNIST databases are presented in support of the proposed method.

show abstract

Section: Theoretical Briefmentioning

confidence: 99%