The magnitude vector of images Article Swipe
Michael F. Adamer
,
Edward De Brouwer
,
Leslie O’Bray
,
Bastian Rieck
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1007/s41468-024-00182-9
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1007/s41468-024-00182-9
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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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1007/s41468-024-00182-9
- OA Status
- hybrid
- References
- 29
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- 10
- OpenAlex ID
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https://openalex.org/W3210809413Canonical identifier for this work in OpenAlex
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https://doi.org/10.1007/s41468-024-00182-9Digital Object Identifier
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The magnitude vector of imagesWork title
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articleOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-07-02Full publication date if available
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Michael F. Adamer, Edward De Brouwer, Leslie O’Bray, Bastian RieckList of authors in order
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https://doi.org/10.1007/s41468-024-00182-9Publisher landing page
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YesWhether a free full text is available
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hybridOpen access status per OpenAlex
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https://doi.org/10.1007/s41468-024-00182-9Direct OA link when available
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Magnitude (astronomy), Computer vision, Geography, Artificial intelligence, Computer science, Geodesy, Physics, AstronomyTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.we | 60, 88, 113, 132, 164 |
| abstract_inverted_index.The | 1 |
| abstract_inverted_index.and | 99, 143, 157, 178 |
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| abstract_inverted_index.for | 139, 175, 182 |
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| abstract_inverted_index.one | 166 |
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| abstract_inverted_index.so, | 163 |
| abstract_inverted_index.the | 19, 31, 35, 43, 49, 62, 65, 93, 101, 108, 117, 180, 183 |
| abstract_inverted_index.use | 51, 135 |
| abstract_inverted_index.way | 181 |
| abstract_inverted_index.able | 40, 90 |
| abstract_inverted_index.data | 71 |
| abstract_inverted_index.each | 80, 105 |
| abstract_inverted_index.edge | 126 |
| abstract_inverted_index.make | 172 |
| abstract_inverted_index.many | 74, 176 |
| abstract_inverted_index.open | 179 |
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| abstract_inverted_index.that | 116, 149, 169 |
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| abstract_inverted_index.cases | 52, 136 |
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| abstract_inverted_index.model | 148 |
| abstract_inverted_index.novel | 13, 146 |
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| abstract_inverted_index.space | 7 |
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| abstract_inverted_index.finite | 5 |
| abstract_inverted_index.hurdle | 168 |
| abstract_inverted_index.images | 98 |
| abstract_inverted_index.metric | 6, 24, 47, 86 |
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| abstract_inverted_index.space, | 48, 87 |
| abstract_inverted_index.space. | 25 |
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| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5043820325 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 4 |
| corresponding_institution_ids | https://openalex.org/I35440088 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/16 |
| sustainable_development_goals[0].score | 0.5899999737739563 |
| sustainable_development_goals[0].display_name | Peace, Justice and strong institutions |
| citation_normalized_percentile.value | 0.00159224 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |