A new workflow for the automated measurement of shape descriptors of rocks

Abstract

Shape properties of rocks carry important geological information about their origin, and they may also provide a window to study the abrasion processes forming their geometry. The number of mechanical equilibria is a significant property with a profound mathematical background that could reveal the secrets hidden in the artifacts of Nature. Although it is easy to count by hand, the automation of its measurement is not a straightforward task. A new workflow is introduced for the fast and efficient measurement of geometrical properties, including the number and location of stable and unstable equilibrium points 5 of rocks based on a portable 3D scanner combined with computer software that can analyze the resulting point cloud. The technique allows for the fast examination of statistically sufficient sample sizes without the need for transportation or storage of the specimens. A previously hand-measured set of pebbles and fragments was used as a reference for the validation of the method, and its effectiveness is demonstrated through the examination of beach pebbles carried out in Kawakawa Bay, New Zealand. 1 IntroductionMeasuring shape characteristics of sedimentary particles is an effective way to formulate hypotheses about their history based on the mathematical models of abrasion processes. Theoretical results show that analysis of the shape of rocks may answer questions related to their place of origin, travel distance, and it can also reveal details of the abrasive forces that contributed 15 to the final geometry. The most general shape descriptors are the axis ratios (c/a, b/a for a > b > c) (Zingg, 1935) and the roundness or isoperimetric ratio (I) that expresses how close a shape is to a sphere. Traditional measurement techniques often incorporate personal factors or rely on the verbal characterization of the shape (Wentworth, 1923;Boggs, 2001) to approximate these values. The number of stable (S) and unstable (U ) mechanical equilibria of a particle as a shape descriptor gained significant attention recently (Domokos et al., 2009; Miller et al., 2014;Domokos et al., 2015;Novák-Szabó et al., 2018) and it is not only insensitive for small measurement errors, but it also has a rich mathematical literature (Grayson, 1987;Domokos et al., 2015;Domokos and Lángi, 2019).It is beneficial to switch from the traditional hand-measurements to automated shape analysis of the particles to avoid personal bias. Recently, several works appeared aiming to reduce subjectivity by automatically calculating shape properties from 2D digital images of the particles (Roussillon et al., 2009;Durian et al., 2007;Cassel et al., 2018;Cheng et al., 2018), 25 3D laser scanning (Hayakawa and Oguchi, 2005; Anochie-Boateng et al., 2013) or X-ray CT (Deiros Quintanilla et al., 2019). Development in sensors and 3D cameras induced a technological revolution in shape detection in many fields from the poultry industry (Chan et al., 2018) to ballast in railway track structures (Anochie-Boateng et al., 2013). 3D scanning was successfully applied i...

Fully spherical 3D datasets on sedimentary particles: Fast measurement and evaluation

“…We will show in Section "Benchmark" that the size limit of a sample for Structure Sensor Mark I. was 1,000 mm 3 . A video demonstration of the new method is available at Fehér et al, (2020).…”

Downstream rounding rate of pebbles in the Himalaya

“…Tunwal et al (2020) proposed image-based automated particle shape analyses for both consolidated and loose sediments which can measure traditional, mathematically complex and common geometric shape parameters. Fehér et al (2020) demonstrated the effectiveness of 3D laser scanning of beach pebbles by comparing the results with a hand-measured set of pebbles. Thus, advances in technology are making automatic extraction of shape parameters possible.…”