Two Measures for the Homology Groups of Binary Volumes

Aldo Gonzalez-Lorenzo 1, 2, 3 Alexandra Bac 2, 3 Jean-Luc Mari 2, 3 Pedro Real 1
1 University of Sevilla
2 GMOD-LSIS - GMOD-LSIS
LSIS - Laboratoire des Sciences de l'Information et des Systèmes
3 AMU - Aix Marseille Université
Abstract : Given a binary object (2D or 3D), its Betti numbers characterize the number of holes in each dimension. They are obtained algebraically, and even though they are perfectly defined, there is no unique way to display these holes. We propose two geometric measures for the holes, which are uniquely defined and try to compensate the loss of geometric information during the homology computation: the thickness and the breadth. They are obtained by filtering the information of the persistent homology computation of a filtration defined through the signed distance transform of the binary object.
Keywords : binary object distance transform persistent homology geometric information holes
Document type :
Conference papers
Complete list of metadatas

Cited literature [11 references]  Display  Hide  Download
https://hal-amu.archives-ouvertes.fr/hal-01341015
Contributor : Jean-Luc Mari <>
Submitted on : Thursday, February 23, 2017 - 11:44:22 AM
Last modification on : Saturday, June 29, 2019 - 9:10:03 PM
Long-term archiving on : Wednesday, May 24, 2017 - 1:25:13 PM

File

DGCI2016.compressed.pdf
Files produced by the author(s)

Identifiers

Collections

UNIV-TLN | LSIS | UNIV-AMU | LSIS-GMOD | LIS-LAB | UNIV-HESAM

Citation

Aldo Gonzalez-Lorenzo, Alexandra Bac, Jean-Luc Mari, Pedro Real. Two Measures for the Homology Groups of Binary Volumes. 19th IAPR International Conference on Discrete Geometry for Computer Imagery (DGCI 2016), Apr 2016, Nantes, France. pp.154-165, ⟨10.1007/978-3-319-32360-2_12⟩. ⟨hal-01341015⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

195

Files downloads

168

Contact

support.ccsd.cnrs.fr
hal.support@ccsd.cnrs.fr
Logo CCSD