These authors contributed equally to this work.

The grain-scale morphology and size distribution of sediments are important factors controlling the erosion efficiency, sediment transport and the aquatic ecosystem quality. In turn, characterizing the spatial evolution of grain size and shape can help understand the dynamics of erosion and sediment transport in coastal, hillslope and fluvial environments. However, the size distribution of sediments is generally assessed using insufficiently representative field measurements, and determining the grain-scale shape of sediments remains a real challenge in geomorphology. Here we determine the size distribution and grain-scale shape of sediments located in coastal and river environments with a new methodology based on the segmentation and geometric fitting of 3D point clouds. Point cloud segmentation of individual grains is performed using a watershed algorithm applied here to 3D point clouds. Once the grains are segmented into several sub-clouds, each grain-scale morphology is determined by fitting a 3D geometrical model applied to each sub-cloud. If different geometrical models can be tested, this study focuses mostly on ellipsoids to describe the geometry of grains. G3Point is a semi-automatic approach that requires a trial-and-error approach to determine the best combination of parameter values. Validation of the results is performed either by comparing the obtained size distribution to independent measurements (e.g., hand measurements) or by visually inspecting the quality of the segmented grains. The main benefits of this semi-automatic and non-destructive method are that it provides access to (1) an un-biased estimate of surface grain-size distribution on a large range of scales, from centimeters to meters; (2) a very large number of data, mostly limited by the number of grains in the point cloud data set; (3) the 3D morphology of grains, in turn allowing the development of new metrics that characterize the size and shape of grains; and (4) the in situ orientation and organization of grains. The main limit of this method is that it is only able to detect grains with a characteristic size significantly greater than the resolution of the point cloud.

Rock particles or grains are characterized by a large range of size, from clays to large boulders, and a diverse variety of shape and angularity, from spherical or ellipsoidal to cubic or polyhedral (e.g., Blott and Pye, 2008; Domokos et al., 2014; 2020). Grains form initially by fragmentation or chemical weathering, transforming a cohesive rock mass into a granular material. The initial size or shape distributions are controlled by fragmentation, weathering processes and structure of the rock mass (e.g., fracture density and orientation, mineral size) (e.g., Molnar et al., 2007; Garzanti et al., 2008; Sklar et al., 2017; DiBiase et al., 2018; Neely and DiBiase, 2020; Verdian et al., 2021). These initial distributions then evolve due to the action of geomorphological processes, including attrition, chipping, abrasion, fragmentation, chemical weathering and transport of grains by wind, river flow, avalanches along hillslopes, and sea waves and currents (e.g., Attal and Lavé, 2006; 2009; Domokos et al., 2014; Miller et al., 2014; Várkonyi et al., 2016; Novák-Szabó et al., 2018; Marc et al., 2021). Grains are also found at the surface of other planetary bodies or asteroids (Burke et al., 2021) and offer unique constraints on their surface conditions. A striking example is the use of the shape of grains to reconstruct the transport history of pebbles on Mars (Szabo et al., 2015). Moreover, the in situ orientation of grains found in deposits can also provide information on the paleo-flow conditions during sediment deposition (e.g., Johansson, 1963; Rust, 1972).

The distributions of grain size, shape and orientation impact the dynamics of fluvial and sedimentary environments. At the scale of rivers, the size of the sediments strongly controls the mobility of alluvial grains and their incipient threshold of motion (e.g., Shields, 1936), the timescale required to mobilize landslide-driven sediments (e.g., Croissant et al., 2017), the rate of river bedrock incision through the tool-and-cover effect (Sklar and Dietrich, 2004), the width of river channels (e.g., Finnegan et al., 2007; Baynes et al., 2020), and the rate of knickpoint propagation (Cook et al., 2013). At the scale of a sedimentary basin, the size of grains influences the stratigraphy of the basin together with the chemical and mechanical properties of the sediment (e.g., Armitage et al., 2011). Grain size, shape and orientation in riverbeds are also key factors for aquatic habitats (e.g., Kondolf and Wolman, 1993; Riebe et al., 2014), for water and nutrient exchange through the hyporheic zone (e.g., Tonina and Buffington, 2009), and even for river hydraulics by impacting basal friction (e.g., Hodge et al., 2009).

Despite the ubiquitous role of grain geometry on landscape properties and dynamics, and its potential to constrain paleo-conditions on Earth and other planetary bodies, robustly documenting the 3D geometry of grains and their statistical distributions in natural environments remains a challenge. Sampling the grain-size distribution of the sediments lying at the surface of a riverbed is often done by the grid-by-number method (Wolman, 1954). This method measures the diameter of a pre-defined number of grains, generally greater than 100. The grid-by-number method is simple to implement and is regarded as directly similar to a volumetric sampling (see Bunte and Abt, 2001; and references therein). It is therefore widely used in the field (e.g., D'Arcy et al., 2017; Guerit et al., 2014; 2018; Chen et al., 2018; Roda-Bodula et al., 2018; Watkins et al., 2020; Baynes et al., 2020). However, samples are often taken over a few square meters and thus lead to inherent representativeness and statistical biases associated with the operator, the grain sampling strategy, the measurements themselves and with the choice of the diameter to be measured. Collecting a data set can be extremely time-consuming, especially when many grains have to be measured to be statistically significant (Rice and Church, 1996; Green, 2003; Eaton et al., 2019; Purinton and Bookhagen, 2021). Measurements are also partly destructive (i.e., grains are moved), which generally leads to information being lost on grain orientation and exact location.

These issues have led to the development of alternative methods based on image analysis to characterize large areas in a manageable amount of time. Object-based and statistically based approaches have been developed to characterize grain-size distributions from pictures or 3D data. The first approach (the so-called “photo sieving”) measures each grain or a number of selected grains on a picture (e.g., Bunte and Abt, 2001). Several algorithms now exist to perform these measurements manually on an image (Roduit, 2008). Because this manual procedure can be time-consuming, (semi-)automatic procedures have been implemented to recognize grains from pictures (Butler et al., 2001; Graham et al., 2005a, b; Detert and Weitbrecht, 2012; Buscombe et al., 2013; Langhammer et al., 2017; Carbonneau et al., 2018; Purinton and Bookhagen, 2019) Machine learning approaches are being developed to support grain segmentation for images (Soloy et al., 2020). However, these methods are still time-consuming as they require the manual labeling of a large number of grains. The second approach is based on image-texture analyses and aims to correlate some statistical properties of images with grain sizes of the study site (Buscombe and Masselink, 2009; Buscombe et al., 2010; Rubin, 2004; Carbonneau et al., 2004). Similarly, 3D approaches empirically relating bed roughness measured on high-resolution topographic data can be implemented to infer the grain-size distribution from locally calibrated relationships (e.g., Rychkov et al., 2012; Westoby et al., 2015; Woodget and Austrums, 2017; Vazquez-Tarrio et al., 2017; Pearson et al., 2017; Groom et al., 2018; Detert et al., 2018). These approaches considerably reduce the time spent in the field, efficiently increase the sampling density and coverage, and are non-destructive. Yet, post-processing remains time-consuming, and these methods are inherently limited to the 2D measurement of the apparent axis of individual grains (Graham et al., 2010) or to empirical local correlations with little generalization capability and limited potential to fully explore the 3D geometry of individual grains.

The last decade has seen a steep growth in the use of high-resolution 3D topographic data in Earth Sciences and geomorphology, obtained by lidar measurements and photogrammetry (e.g., Schneider et al., 2015; Westoby et al., 2012; Leduc et al., 2019). The resulting 3D point clouds offer unprecedented access to landscape heterogeneities and to landscape temporal evolution (e.g., Hodge et al., 2009; Leyland et al., 2017; Beer et al., 2017; Bernard et al., 2021). The accessibility of 3D point clouds, obtained from terrestrial, drone and airborne data, and their ability to capture object geometries robustly and accurately in 3D at various scales represent a timely opportunity to develop point-cloud-based methods for the issue of grain-size measurement. Building on this opportunity, Chen et al. (2020) recently developed a deep-learning workflow to segment grains based on structure-from-motion (SfM) data. Walicka and Pfeifer (2022) also successfully applied a DBSCAN (density-based spatial clustering of applications with noise, see Ester et al., 1996) algorithm to segment grains.

In this paper, we develop another efficient and semi-automatic approach, entitled G3Point (standing for “Granulometry from 3D Point clouds”), to measure grain size, shape and orientation using 3D point clouds. G3Point is a purely geometric algorithm, which in turn does not rely on the a priori training of a neural network on thousands or more grains which is required in Chen et al. (2020). Indeed, the associated workflow consists of the 3D segmentation of individual grains using a type of watershed algorithm, the geometrical description of individual grains using 3D ellipsoidal models, and the description of the 3D geometry of the grain population using statistical distributions. G3Point can be characterized as a semi-automatic approach as it is based on several parameters which can be optimized by a trial-and-error approach. Moreover, validation of the obtained results is performed either by comparing the obtained size distribution to independent measurements (e.g., hand measurements) or by visually inspecting the quality of the segmented grains. After describing the new method, we test it against lab and natural controlled experiments (e.g., riverbeds and beaches), considering point clouds obtained from SfM, to check its ability to robustly capture the 3D geometry and size of grains, independently constrained by hand measurements.

Overview of the G3Point algorithm showing the main series of functions (center) and the results (top and bottom figures). Each main function is described in detail in the Method section.

G3Point is a Matlab program which aims at measuring the size, shape and
orientation of a large number of individual grains as detected from 3D point
clouds describing the topography of surfaces covered by sediments. The main
functions of G3Point are described in the following and Fig. 1. Compared
to 2D digital elevation models (DEMs), where elevation

Three-dimensional view of the point cloud, its segmentation into individual
grains and the fit ellipsoids.

To illustrate the method, we apply it to a point cloud of an active alluvial
riverbed, of an area of

The segmentation of the point clouds into sub-point clouds representing
individual grains uses a single flow algorithm based on the steepest slope
criterion (O'Callaghan and Mark, 1984). This algorithm is generally used to
route water and identify watersheds on 2D DEMs. It uses the steepest slope
criterion to route water between neighborhood points until reaching a local
topographic minimum, which corresponds to the outlet of the watershed. Each
watershed is therefore described by a directed acyclic graph which
associates each point of the point cloud with its outlet node through a single
flow path (e.g., Schwanghart and Scherler, 2014). To perform the watershed
segmentation, we use the Fastscape algorithm as it offers a fast solution to
order points along the steepest water flow path (Braun and Willett, 2013). For each node

To identify grains instead of watersheds, the single flow algorithm is
modified by using the criterion of the steepest slope upward instead of the
steepest slope downward to route water. In other words, water is routed from
a point to its steepest upward neighbor, which is associated with the maximum
value of

Correcting over-segmentation is not a trivial task due to the large range of
grain sizes. Mostly because of this issue, classical clustering approaches
such as hierarchical clustering or DBSCAN (e.g., Esther et al., 1996) proved
ineffective to solving this issue. Moreover, approaches that use all the
points in the point cloud can lead to a longer computational time, which
might become prohibitive for large point clouds. Here, we develop an
approach which makes use of the properties of the segmented watersheds,
which associate grains (i.e., watersheds) to their unique summit points
(i.e., outlets) and to their border nodes (i.e., crests). We combine three criteria (Fig. A1b) to decide if a pair of grains

Criterion 1: the distance

Criterion 2: grains

Criterion 3: the 3D angle between the normals of the crest points of grains

A pair of grains

To increase the quality of the segmentation, we offer optional routines to perform several post-segmentation operations (Fig. A1c):

applying Criterion 3 only, which merges a pair of grains if the 3D angle
between their normal, computed on the common border, is lower than a
threshold

cleaning the segmentation by removing grains with less than

removing flattish or over-elongated grains, as they generally do not
correspond to individual grains but to clusters of fine grains with a
characteristic size much lower than the typical point spacing of classical
point clouds or to improperly segmented grains. To detect flattish or
over-elongated grains, we perform a singular value decomposition (SVD) over
the 3D coordinates of each of the sub-point clouds. If a grain has a minimum
or an intermediate singular value divided by its maximum singular value
(i.e., the axis ratio between the intermediate or minimum dimension of the
3D labeled point cloud and its maximum dimension) lower than a threshold,

In the example shown in Fig. 2, the segmentation was not cleaned. We
provide some guidelines on how to choose suitable values of

Once the grains are segmented and labeled, the following phase consists of the 3D geometrical description of each grain, particularly their size and orientation. A strong constraint results from the fact that only an unknown fraction of the upper surface of the segmented grains (i.e., the visible part of the grain) is topographically described by the point cloud. This prevents us from directly using the point cloud to describe each grain and measure their sizes and orientations. Instead, we rely on geometrical models to represent each grain. The simplest 3D geometrical model to describe a grain is the ellipsoidal model. Two strategies are adopted to describe the geometry of a grain with an ellipsoidal model: fitting an ellipsoid or determining its ellipsoid of inertia.

Size, shape and orientation distribution of 630 ellipsoids
correctly fitted to the labeled grains. Histogram distribution of the
diameters of the ellipsoids along their

Influence of the grain surface covered by 3D data on the modeled
ellipsoidal geometry of a grain.

Fitting an ellipsoid to a set of points in 3D is a complex problem that has
received attention from different applied mathematics communities, including
computer vision, pattern recognition, numerical analysis and statistics.
Ellipsoids belong to the family of quadric surfaces that can be defined as

The second approach considered to characterize the geometry of the grains computes the inertia ellipsoids corresponding to the labeled points of the grains. This is performed first by computing the mean position of the points, second by computing the covariance matrix of the points subtracted from their mean position and third by making an SVD of the covariance matrix normalized by the number of points.

The approach based on the inertia ellipsoid can be considered simpler than the direct least-square fitting method and does not suffer from mathematical constraints of the direct least-square approach. However, as it is not a fitting method, its main drawback is that it is unable to guess the “hidden” geometry of the grains (i.e., by using the curvature of the visible part of the grain), and the obtained inertia ellipsoids will tend to be flatter than the grains. We later compare the two approaches in the Results section. We also compare the obtained ellipsoids to cuboids that are obtained by determining the minimal 3D bounding box for each grain, with at least one side oriented along the horizontal plan. More specifically, the orientation and dimensions (i.e., length, width and height) of the cuboids are compared to the orientation and dimensions of the major, intermediate and short axes of the ellipsoids.

Once the grains are fitted by an ellipsoid, it is straightforward to access
their geometrical information. For each ellipsoid, we measure the radius
(and the diameter, as classically used for grain-size distributions) of the
major

For each grain, we can also compute the distance of each point of the grain,
of coordinates (

The statistical description of grain geometrical properties of a grain
population, such as the classical 1D grain-size distribution (GSD), is then
performed based on the geometrical attributes of each individual grain of
the considered population (Fig. 3). The range of measured diameters,

In addition to its robustness and efficiency, an algorithm dedicated to extract granulometric information from point clouds must be able to manage various sources of data, including SfM and lidar. In the following, we therefore test the newly developed algorithm against “ground truth” data sets of grain size, obtained in the lab or natural environments. For each data set, we compare the distribution obtained with G3Point to the grain-size distribution measured by hand. It is important to highlight that the grain sampling approach of G3Point belongs to the family of areal or area-by-number approaches. We first start by assessing the pros and cons of the different grain fitting approaches by applying them to individual grains of various shapes.

Two strategies are adopted to describe the geometry of a grain with an ellipsoidal model: fitting an ellipsoid by a direct least-square fitting approach (DLSF) or determining its ellipsoid of inertia (IE). We here test the influence of using these two strategies on the quality of the resulting geometrical models, for individual grains, considering a variable surface covered by the point cloud (Fig. 4).

Indeed, in natural environments, grains have a significant proportion of
their surface that is not topographically described, as it is hidden under
the grain itself, by other grains or features (e.g., vegetation, water), or
due to a lack of visibility with respect to the sensor (e.g., lidar
station). The tested grains consist of a spherical ball (grain 1), a
low-angularity grain (grain 2), an angular grain (grain 3), and an angular,
flattish and elongated grain (grain 4). The point clouds representing the
surface of these four grains were obtained by SfM using Agisoft Metashape.
Each grain was put on a 1 cm radius plastic plate attached to the top of a
tripod and about 50 pictures were acquired all around the grain. For each of
these point clouds, we generated ellipsoidal models considering only a
prescribed percentage of their surface covered by the point cloud, from 10 %
to 100 %. Practically, surface cover is varied by first choosing a random
seed among the points of the point cloud and then sampling a number of
nearest neighbors leading to the sought surface cover of the grain.
Ellipsoidal modeling by DLSF and IE is then applied only to this sampled
part of the total point cloud. The modeled ellipsoidal volume

For the two low angular grains (grains 1 and 2), metrics obtained with DLSF
or IE are consistent with the true geometry of the grain even for relatively
low surface cover, down to 20 %–30 %. DLSF gives significantly better
results than IE, in particular for a surface cover between 20 % and 80 %,
which likely represents a common range for most labeled grains. Thanks to
grain curvature, the DLSF fitting algorithm also converges towards value for

For the angular grain (grain 3), the DLSF and IE approaches give similar
results. The dimensions are well captured for a surface cover greater than
60 %–70 %. The orientation, in particular of the

These results show that the dimensions of spherical or low-angularity grains
are well captured by the IE and DLSF approaches, with this latter giving
good results even for a surface cover lower than 50 %, while their
orientation is poorly captured for a surface cover lower than

Results from the lab experiment considering 39 pebbles on a flat
surface.

Here, we apply G3Point to a lab experiment, consisting of 39 black pebbles,
bought in a hardware store, lying in a horizontal position over a planar
surface of

Despite this, the obtained diameters for the

Despite a good first-order accuracy of the considered ellipsoidal models to represent the 3D dimensions of grains, none of these approaches is deemed systematically suitable by itself. The consistency of the ellipsoidal models with the true geometry of the grains depends on the considered geometrical model, on the surface coverage of the grain by the point cloud and on the shape of the grain itself (Fig. 4). In the following, instead of relying on a single ellipsoidal model, we rather assess the geometry and dimensions of grains by using both the DLSF and IE ellipsoidal models. Indeed, considering the size (or size distribution) obtained with the DLSF and IE ellipsoidal models offers an upper and lower bound on the true size (or size distribution) of the grain (or grain population). We also provide a mean size (or size distribution) obtained with these two ellipsoidal models to offer an approximate solution to the true size of the grain (or grain population).

Field pictures

The second experiment consists of pebbles from three natural field sites in
France: the beach of Pointe du Château Renard (Brittany) with coarse and
angular grains at Site 1 and smaller rounded grains at Site 2 (Fig. 6a–b)
and the Hérault River near Saint-André-de-Majencoules (Cévennes)
with rounded, fluvially transported pebbles (Fig. 6c). At each site, we
sampled the grain-size distribution by the Wolman grid-by-number method (Wolman,
1954). At Site 1 of Pointe du Château Renard, we defined a grid of about

In addition to operator errors, related to the measurement itself and to the
choice of the diameter to measure, the resulting distribution is associated
with uncertainties related to the size of the sample. We used a bootstrap
approach with replacement to evaluate the confidence interval of each
distribution (Rice and Church, 1996; Bunte and Abt, 2001; Green, 2003). For
each sample, we randomly sampled 10 000 replicates of the distribution, and
the scatter defines the confidence interval. The pebbles at Site 1 of the
beach of Pointe du Château Renard have a median

Statistics of the grain-size distributions for the three
sites surveyed by SfM. The six coefficients (

At Château Renard, we used a Nikon D3500 in a

A large number of grains are detected (428, 1077 and 678 for Château Renard
Site 1, Site 2 and the Hérault River, respectively, Table 1). Yet, to
compare the distributions obtained by G3Point to the distributions obtained
by Wolman counts in the field, we must perform virtual Wolman samplings on
the fitted grains. We apply a virtual grid to the 3D point cloud and
automatically extract the three axes of the grains lying under the nodes,
with grid spacing defined as half the maximum

Comparison of the key percentiles (10th, 16th,
25th, 50th, 75th, 84th, 90th) obtained by manual
counts and by G3Point at the three study sites and for the three diameters.
Distributions from G3Point are derived from the virtual Wolman sampling and
uncertainties correspond to the envelopes defined by the DLSF and IE models.
For manual counts, uncertainties are derived from a bootstrap approach with
replacements. The dash lines indicate a

To better compare the two approaches, we compare the key percentiles
(10th, 16th, 25th, 50th, 75th, 84th,
90th) of the grain-size distributions obtained by manual counts and by
virtual Wolman on the segmented point cloud (Fig. 7). For each diameter at
each study site, points align along a

This second experiment based on natural grains thus confirms that G3Point is efficient at recovering Wolman-like grain-size distributions for pebble and cobble populations in different environments and for various grain angularity, with a limited temporal cost in the field and in the lab.

As already demonstrated, G3Point is designed to perform semi-automatic 3D
granulometric measurements on point clouds over surface area

As demonstrated in this paper, G3Point can be applied to point clouds
obtained with a terrestrial lidar or by SfM. Point clouds obtained with
terrestrial lidar data provide better accuracy than SfM but can be
associated with varying point density, while the ones obtained by SfM provide
uniform point density but can lead to some inaccuracies. In particular,
point clouds obtained with SfM were observed to generate smooth or
inaccurate topographic transitions between grains, as these correspond to
“shadow” areas difficult to capture with pictures. This might be related
to the quality of the photos (lighting, blurring, resolution), as with any
SfM study. These smooth transitions are not too problematic for G3Point, as
it is based on the steepest slope, but they prevent efficiently using
a criterion based on topographic curvature to segment grains or to correct the
segmentation obtained with G3Point. In that case, we recommend removing
points located at local topographic minima to ease segmentation (this is an
option provide by G3point). For lidar data, the issue of spatially varying
point density can lead to a non-optimal set of parameters, in particular

In terms of total working time, using G3Point over a surface area of about
1–100 m

Because G3Point samples virtually all the grains at the surface, it belongs
to the family of areal or area-by-number grain sampling approaches. To
compare this distribution to the Wolman field counts, it must be converted
to a grid-by-number distribution, which is considered equivalent to a
volumetric grain-size distribution. Conversion factors have been proposed to
convert grain-size data acquired with one approach to another one, based on
geometrical arguments (Kellerhals and Bray, 1971; Church et al., 1987;
Diplas and Fripp, 1992). For example, converting an area-by-number (or
areal) distribution to a grid-by-number (or volumetric; e.g., Wolman)
distribution requires multiplying the frequency of all the particle classes
by the factor

Illustration of conversion from a G3Point grain-size distribution to a Wolman-like distribution. Data are from Site 2 of Château Renard. The initial G3point distribution is an area-by-number one (large dashed line) that can be converted to a grid-by-number (e.g., Wolman) one with a conversion factor of 2 (small dashed line). Alternatively, a virtual Wolman count can be performed directly on the segmented and fitted grains (black line). The shaded envelope indicates the variability observed with 50 realizations.

Azimuth and dip angles of the grains fitted to the two
approaches (DLSF and IE) at

With our new approach, we work on 3D point clouds covering large areas, and a
large number of grains can be identified. Therefore, instead of converting
from an area-by-number to a grid-by-number distribution, we can apply a
virtual grid over the point cloud and perform a Wolman count on the fitted
grains. To account for the spatial variability of the grains, we repeat this
operation 25 times to define an uncertainty envelope and use the average
distribution as the grain-size distribution of the sample. For our field
examples, we observe that the geometrical conversion is always coarser than
the virtual Wolman distribution, yet within uncertainties (Figs. 8, S6, S7,
S8). The only exception is for the

Here, we briefly present some results on the orientation of grains that we obtain with G3Point. The idea is not to dedicate a detailed study of this metric but to illustrate the ability of G3Point to automatically measure it with no additional efforts. This represents a real benefit of G3Point as most field or picture measurements of grain orientation are either cumbersome or approximate (e.g., using qualitative classification), with the exception of the azimuth angle that can be accessed with approaches based on 2D pictures (e.g., Purinton and Bookhagen, 2019).

The azimuth and dip angles of a grain may give some information about the
flow that transported and deposited a population of grains. G3Point offers a
very simple way to access the orientation of a large population of grains as
the azimuth and dip angles can easily be determined from the fit ellipsoids
(Fig. 3). On average, the two fitting methods are efficient at recovering
orientation, but they do not lead to the exact same results (Fig. 5g).
Therefore, if grain orientation is a key element of a study, preliminary
tests may be useful to determine the best-fitting approach in terms of
orientation (which may depend for example on the geometry of studied
grains). Here, we show the results of both approaches to illustrate their
similarity and differences. Azimuth is given with respect to the

The G3Point algorithm presented here makes progress on the issue of grain segmentation and shape analysis from 3D point cloud data. G3Point represents a methodological alternative to previous granulometric approaches, including hand measurements or 2D image analysis. Its main advantages are (1) its computational efficiency and speed that rely on the use of a state-of-the-art watershed algorithm (e.g., Braun and Willett, 2013) to segment grains, (2) its scale-free approach which enables the segmentation of grains with a large range of sizes above the neighborhood scale (i.e., typically a few centimeters), (3) its 3D nature which enables the calculation of metrics (e.g., sphericity, orientation) which are seldom obtained in the field, and (4) its ability to perform a large number of measurements, which favors a good representativeness of the results.

The G3Point algorithm was able to properly describe the size and orientation of grains in a lab experiment. It was also qualitatively successful compared to hand measurements (e.g., Wolman count) in segmenting and quantitatively capturing the size distribution of hundreds to thousands of grains in fluvial and coastal environments. The modeling of grain geometry was performed using ellipsoidal models obtained either with a direct least-square fitting approach or by taking the inertia ellipsoid. Both ellipsoid models accurately infer the major and intermediate axes, but the inertia ellipsoids and the direct least-square ellipsoids tend to underestimate or overestimate the minor axis, respectively. This in turn impacts the ability of G3Point to infer the volume and surface area of grains. For the minor axis, the mean value of the inertia and direct least-square ellipsoids provides estimates that are consistent with hand measurements. Other geometrical models were tested, including bounding boxes. We acknowledge that future work could focus on providing better geometrical models or a better fitting approach to describe the geometry of grains. Alternatively, future efforts could investigate the surface geometry of segmented grains by G3Point, without relying on fitted geometrical models (e.g., ellipsoidal model) but by exploring the topology of the segmented point clouds. An inherent limit remains that, in natural environments, only a fraction of the grain surface is visible and can be topographically described using lidar or SfM.

Fascinating and first-order issues remain for understanding the shape and size of grains and interpreting them in terms of abrasion and fragmentation processes (Domokos et al., 2014, 2015, 2020; Novák-Szabó et al., 2018). This is pivotal for better exploiting the unique geological archives contained in the size, shape and orientation of grains found in natural systems on Earth and other planetary bodies (e.g., Szabo et al., 2015). G3Point, by filling a methodological gap, could foster the development of a more systematic characterization of grain shape in natural environments and lead to a better understanding of the physics of geomorphological processes and of their past dynamics.

A MATLAB version of the algorithm can be accessed through a GitHub and/or a
Zenodo repository:

The data that support the findings of this study are available from the corresponding authors, Philippe Steer and Laure Guerit, upon reasonable request.

The supplement related to this article is available online at:

PS and LG wrote the paper. PS initiated this study, developed the numerical algorithm, performed the initial tests and provided funding. LG performed the analysis and tested the algorithm in natural environments. PS, LG, DL, AC and AG acquired field data, motivated the study and contributed to the writing of the paper. All authors checked and revised the text and the figures of the paper and contributed to the ideas developed in this study.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank Thomas Croissant, Edwin Baynes, Benjamin Bruneau, Benjamin Guillaume, Lucas Pelascini and Romy David for their help acquiring data. We thank Edwin Baynes for proofreading the paper. We are grateful to Rebecca Hodge, Benjamin Purinton and an anonymous reviewer for their constructive comments and their work on this paper.

This research has been supported by the H2020 European Research Council (grant agreement no. 803721). We also acknowledge support by Université Rennes 1 and CNRS.

This paper was edited by Rebecca Hodge and reviewed by Benjamin Purinton and one anonymous referee.