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Pebbles, graphs and equilibria: Higher order shape descriptors for sedimentary particles.

Authors :
Ludmány, Balázs
Domokos, Gábor
Source :
Central European Geology; 2022, Vol. 65 Issue 2, p158-177, 20p
Publication Year :
2022

Abstract

While three-dimensional measurement technology is spreading fast, its meaningful application to sedimentary geology still lacks content. Classical shape descriptors (such as axis ratios, circularity of projection) were not inherently three-dimensional, because no such technology existed. Recently a new class of three-dimensional descriptors, collectively referred to as mechanical descriptors, has been introduced and applied for a broad range of sedimentary particles. First-order mechanical descriptors (registered for each pebble as a pair {S, U} of integers), refer to the respective numbers of stable and unstable static equilibria and can be reliably detected by hand experiments. However, they have limited ability of distinction, as the majority of coastal pebbles fall into primary class { S , U } = { 2 , 2 } . Higher-order mechanical descriptors offer a more refined distinction. However, for the extraction of these descriptors (registered as graphs for each pebble), hand measurements are not an option and even computer-based extraction from 3D scans offers a formidable challenge. Here we not only describe and implement an algorithm to perform this task, but also apply it to a collection of 271 pebbles with various lithologies, illustrating that the application of higher-order descriptors is a viable option for geologists. We also show that the so-far uncharted connection between the two known secondary descriptors, the so-called Morse–Smale graph and the Reeb-graph, can be established via a third order descriptor which we call the master graph. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
17882281
Volume :
65
Issue :
2
Database :
Complementary Index
Journal :
Central European Geology
Publication Type :
Academic Journal
Accession number :
173469044
Full Text :
https://doi.org/10.1556/24.2023.00135