PuSH - Publikationsserver des Helmholtz Zentrums München

Export: TXT Text RIS Endnote (RIS) BIB BibTeX
Adamer, M.F.* ; de Brouwer, E.* ; O’Bray, L.* ; Rieck, B.

The magnitude vector of images.

J. Appl. Comput. Topol., DOI: 10.1007/s41468-024-00182-9 (2024)
Verlagsversion DOI
Open Access Hybrid
Creative Commons Lizenzvertrag
The magnitude of a finite metric space has recently emerged as a novel invariant quantity, allowing to measure the effective size of a metric space. Despite encouraging first results demonstrating the descriptive abilities of the magnitude, such as being able to detect the boundary of a metric space, the potential use cases of magnitude remain under-explored. In this work, we investigate the properties of the magnitude on images, an important data modality in many machine learning applications. By endowing each individual image with its own metric space, we are able to define the concept of magnitude on images and analyse the individual contribution of each pixel with the magnitude vector. In particular, we theoretically show that the previously known properties of boundary detection translate to edge detection abilities in images. Furthermore, we demonstrate practical use cases of magnitude for machine learning applications and propose a novel magnitude model that consists of a computationally efficient magnitude computation and a learnable metric. By doing so, we address one computational hurdle that used to make magnitude impractical for many applications and open the way for the adoption of magnitude in machine learning research.
Impact Factor
Scopus SNIP
Altmetric
0.000
1.846
Tags
Anmerkungen
Besondere Publikation
Auf Hompepage verbergern

Zusatzinfos bearbeiten
Eigene Tags bearbeiten
Privat
Eigene Anmerkung bearbeiten
Privat
Auf Publikationslisten für
Homepage nicht anzeigen
Als besondere Publikation
markieren
Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Computer Vision ; Edge Detection ; Metric Learning ; Metric Space Magnitude
Sprache englisch
Veröffentlichungsjahr 2024
HGF-Berichtsjahr 2024
ISSN (print) / ISBN 2367-1726
e-ISSN 2367-1734
Zeitschrift Journal of Applied and Computational Topology
Verlag Springer
Begutachtungsstatus Peer reviewed
Institut(e) Institute of AI for Health (AIH)
POF Topic(s) 30205 - Bioengineering and Digital Health
Forschungsfeld(er) Enabling and Novel Technologies
PSP-Element(e) G-540003-001
DOI 10.1007/s41468-024-00182-9
Scopus ID 85197411343
Erfassungsdatum 2024-07-18
[➜Korrektur melden]