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The magnitude vector of images.
J. Appl. Comput. Topol., DOI: 10.1007/s41468-024-00182-9 (2024)
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.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Computer Vision ; Edge Detection ; Metric Learning ; Metric Space Magnitude
ISSN (print) / ISBN
2367-1726
e-ISSN
2367-1734
Publisher
Springer
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of AI for Health (AIH)