Boulder shape analysis: is a 2D projection reliable for capturing the 3D geometry?

The boulder shape at the surface of small bodies enables the investigation of the geological processes the surface boulders have undergone, and the estimation of certain mechanical properties (e.g. [1]). Studies conducted on surface boulders observed on extraterrestrial planetary bodies are usually performed using 2D images of the projected surface [1, 2, 3, 4]. 2D projections of irregular particle are known to differ from their 3D geometry [5, 6, 7], therefore, careful precautions are required when comparing different surfaces and, in particular, different representations (2D or 3D).To investigate how representative 2D images of boulders are for estimating bulk 3D morphological parameters, three different granular samples (LHS-1 Lunar Highland Simulant, Øysand soil, and glass grit) were scanned by XCT (X-ray Computed Tomography) to reconstruct the 3D geometry of each particle.  The shapes of more than 2500 particles have been analyzed using both the 3D geometry and different 2D projections from the 3D reconstruction. The 2D shape analysis pipeline used in this study was previously applied in Robin et al. (2024) [1] and Kohout et al. (2024) [8]. A 3D shape analysis has been extended using the same methodology as the 2D analysis.The shape can be expressed using three independent descriptors based on the observation scale [9, 10]: the form (large scale), roundness (intermediate scale), and surface texture (small scale). The morphological parameters measured in this study include axes ratios and sphericity (large-scale measurements), and roundness. In addition to the shape analysis, the size of particles is also computed (fig. 1).Figure 1: Definitions of size and shape descriptors measured for 2D (left) and 3D (right) representations. Using the 2D and 3D morphological analysis of the XCT scan dataset, correlation formulas with confidence intervals have been established between both representations to estimate 3D morphological parameters from 2D measurements.Our methodology to estimate 3D parameters from 2D measurements is being tested with boulders observed on asteroid Bennu by the NASA OSIRIS-REx mission (fig. 2). Boulders on Bennu have been observed by different instruments; in 2D by OCAMS (OSIRIS-REx Camera Suite) [11], and in 3D by OLA (OSIRIS-REx Laser Altimeter) [12]. The results of the comparison between the estimated 3D parameters obtained with the 2D images and the 3D analysis from the same boulders observed with OLA will be presented during the conference in addition to the analysis of XCT scan data.Figure 2: An example of boulders observed on asteroid Bennu by different instruments during the NASA OSIRIS-REx mission. OLA measurements (left) provide the surface topography (3D), and the same surface has also been observed in 2D with OCAMS (right). (Credit: NASA/Goddard/University Of Arizona) References[1] Robin, et al. (2024). Mechanical properties of rubble pile asteroids (Dimorphos, Itokawa, Ryugu, and Bennu) through surface boulder morphological analysis. Nature communications, 15: 6203.[2] Yingst, et al. (2007). Quantitative morphology of rocks at the Mars Pathfinder landing site. Journal of Geophysical Research: Planets, 112.[3] Cambianica, et al. (2019). Quantitative analysis of isolated boulder fields on comet 67P/ Churyumov-Gerasimenko. Astronomy & Astrophysics, 630:15.[4] Jawin, et al. (2023). Boulder Diversity in the Nightingale Region of Asteroid (101955) Bennu and Predictions for Physical Properties of the OSIRIS-REx Sample. Journal of Geophysical Research: Planets, 128:12.[5] Jia et al. (2023). Sphericity and roundness for three-dimensional high explosive particles by computational geometry. Computational Particle Mechanics, 10:817-836.[6] Beemer, et al. (2022). Comparison of 2D Optical Imaging and 3D Microtomography Shape Measurements of a Coastal Bioclastic Calcareous Sand. Journal of Imaging, 8:72.[7] Zheng, et al. (2021). Three-dimensional Wadell roundness for particle angularity characterization of granular soils. Acta Geotechnica, 16:133-149.[8] Kohout, et al. (2024). Impact Disruption of Bjurböle Porous Chondritic Projectile. The Planetary Science Journal, 5:128.[9] Barrett (1980). The shape of rock particles, a critical review. Sedimentology, 27:3.[10] Cho, et al. (2006). Particle Shape Effects on Packing Density, Stiffness, and Strength: Natural and Crushed Sands. Journal of Geotechnical and Geoenvironmental Engineering, 132:5.[11] Rizk, et al. (2018). OCAMS: The OSIRIS-REx Camera Suite. Space Science Reviews, 214:26.[12] Daly, et al. (2017). The OSIRIS-REx Laser Altimeter (OLA) Investigation and Instrument. Space Science Reviews, 212:899-924. AcknowledgementsThis project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement N°870377 (project NEO-MAPP), and CNES in the framework of the Hera mission and the MMX rover/wheelcams. A.D. acknowledges PhD funding from Université de Toulouse III. C.R. acknowledges PhD funding from CNES and ISAE SUPAERO. O. S. Barnouin’s and R. L. Ballouz’s efforts were funded by the NASA New Frontier Data Analysis Program under grand number 80NSSC22K1035 P00004.