PARTIcle Shape ANalyzer PARTISAN – an open source tool for multi-standard two- dimensional particle morphometry analysis

Volcanic particles are commonly characterized using 2D morphometric analysis. Results of analysis are used to compare particles from different events or phases, and to infer clast-generating mechanisms, eruptive styles and the aerodynamic behavior of particles. Such particle-shape analyses can be made from images of particle silhouettes or cross-sectional slices. A number of different morphometric systems have been used to date, with each using its own nomenclature and mathematical definitions of shape-describing parameters. Some of the parameters can only be obtained using specific commercial software. With the PARTIcle Shape ANalyzer PARTISAN we present a freeware tool which parameterizes 2D shapes and provides a suite of shape parameters, following the different standards of the five most commonly used 2D morphometric systems. PARTISAN enables the user to study and archive the results of particle-shape analysis in a format compatible with various published routines, thus increasing the potential for linking new work with results of work previously published by other groups. It will also allow cross-comparison of results obtained by different morphological routines. We see PARTISAN as a “Rosetta Stone” for volcanological particle morphometry, and it opens the way for development of widely agreed treatment of particle shapes in 2D.


Introduction
The only record of many volcanological processes and events is held in their erupted products. Among the features of volcanic particles (e.g. geochemistry, glass-volatile content, vesicularity, crystal morphology), it is the shapes of particles, including their fine-scale surface features, that most directly reflect the fragmentation processes that formed them [Heiken 1972[Heiken , 1974Heiken and Wohletz 1985;Cioni et al. 1992;Büttner et al. 1999]. Virtually all studies of pyroclastic deposits include some description of particle shapes, but there has been limited progress toward a consistent and interpreter-independent method of characterizing particle shapes. Some tools have been developed that normalize for size effects and characterize the projected shapes of ash particles in two dimensions in a procedure is commonly known as 2D morphometry. One of the most commonly used morphometric systems was introduced to volcanology by Dellino and La Volpe [1996], who suggested a classification scheme using four shape parameters acquired from 2D binarized particle images (silhouettes) produced by projection of 3D shapes. The "Image Particle shape Analysis" (IPA) parameters were measured by Dellino and La Volpe [1996] from highresolution scanning electron microscope (SEM) images, and the IPA parameterization has been used in multiple studies to either compare tephra grains from different eruptions, or to compare products of different eruptive phases [Heiken 1974;Dellino et al. 2001;Taddeucci and Palladino 2002;Cioni et al. 2008;Murtagh and White 2013;Iverson et al. 2014;Alvarado et al. 2016]. Other studies have used characteristics of particles generated by known processes in fragmentation experiments to infer the processes that generated natural tephra particles during eruptions [Büttner et al. 2002;Dürig et al. 2012;Schipper et al. 2013;Jordan et al. 2014]. Others have studied fallout ash during ongoing eruptions using semi-automated routines [Lautze et al. 2012[Lautze et al. , 2013, and have derived aerodynamic properties of ash grains relevant to their dispersal and sedimentation [Mele et al. 2011].
In addition to the method introduced by Dellino and La Volpe [1996], a multitude of other shape parameterization approaches have been presented and applied. Some focus on analyzing transport processes in volcanic plumes [Riley et al. 2003;Durant et al. 2009;Klawonn et al. 2014], others seek to determine magma discharge rates and eruption dynamics [Yamanoi et al. 2008;Wright et al. 2012;Miwa et al. 2013Miwa et al. , 2015Suzuki et al. 2013;Eychenne et al. 2015] or reconstruct eruptive mechanisms [Cioni et al. 2008[Cioni et al. , 2014Liu et al. 2015b;Schmith et al. 2017]. Descriptive parameters have also been introduced which can be provided by automated procedures, suitable for real-time, surveillance of eruptions [Leibrandt and Le Pennec 2015].

Challenges for comparing shape parameters from different morphological systems
A key objective in particle shape analysis is to identify specific characteristics of grain shapes that record specific volcanic processes (e.g. the fragmentation mechanism). The scientific impact of a study is greatly increased if the morphometric results can be directly compared with those already published from other samples.
Such comparisons are currently difficult for several reasons. First, it is important to note that image resolution will strongly affect the outcome of any morphometric analysis -especially the perimeter of the analyzed object, and all derived shape parameters based on that metric [Dellino and La Volpe 1996;Liu et al. 2015a;Schmith et al. 2017]. Care has therefore to be taken that the compared morphometric results are based on images with comparable resolution and magnification (requiring the user to study similar grain sizes). For the same reason, shape parameters derived from pictures obtained by different techniques, such as by optical microscopy or by SEM, cannot be directly compared.
Further complications arise from the fact that morphometric studies have applied two fundamentally different methods of particle preparation. One is the silhouette-based 2D analysis, for which particles are mounted on e.g. a carbon-tape. The other uses polished thin sections or polished grain mounts. This has the significant advantages of being also applicable to lithified samples, and in providing information about internal features of the particles (e.g. vesicle abundance and size distribution; microlites and phenocrysts) [Cioni et al. 2014], but the 2D grain shape from a cut section is not the same as the 2D projection (silhouette) from a whole grain. The biggest shortcoming in this respect is that a cut section need not intersect any of the defining particle diametersa cut that catches only one tip of a particle both underrepresents even the minimum diameter, and may misrepresent particle shape.
Results based on these two different approaches (silhouette vs slices) are incompatible, and no conversion from one to the other is possible. A silhouette's area will always be at least that of the largest area possible for any slice taken normal to the silhouette viewing axis, and may be many times larger. No other general statement can be made about the relationship of one slice to a silhouette along the same axis, and there is an infinite number of possible orientations for either slices or silhouettes for any particle.
Another major problem for comparability is that many of the shape parameters reported in literature have their own nomenclature and mathematical definitions, which overlap with previously defined ones in ways that can be misleading. For example, "circularity" is defined by Dellino and La Volpe [1996] as one of the four IPA parameters. Presumably to adjust the parameter so that the most-circular objects have the highest circularity value, Leibrandt and Le Pennec [2015] inverted the equation but use the same name. For a parameter with the same name of "circularity", entirely different equations are used by Cioni et al. [2014], and Schmith et al. [2017]. Similarly problematic, the parameter "convexity" used by Schmith et al. [2017] is identical to the parameter called "solidity" by Liu et al. [2015aLiu et al. [ , 2015b, whereas "rectangularity" as defined by Schmith et al. [2017] is identical to "compactness" in the notation of Dellino and La Volpe [1996]. In a different kind of inconsistency, "convexity", introduced by Liu et al. [2015a], uses the perimeter of the convex hull, whereas in the definition of Cioni et al. [2014], it is defined by the perimeter of the fitting ellipse. These are just a few examples of inconsistencies that make it challenging to compare results obtained from different studies. Applying the notation listed in Table 1, Table 2 gives an overview of the diversity of notations and mathematical definitions for five shape parameter concepts frequently used in volcanology. For a broader overview see Leibrandt and Le Pennec [2015] (their Table 3). One of the reasons for this apparent lack of standardization is the fact that different instruments and/or software have been used by different research groups, and the results impose their own terminology and measurement routines, which may not be reproducible on other machines or, when insufficiently documented, by any means.
In some cases [Leibrandt and Le Pennec 2015;Schmith et al. 2017] software programs linked to the particle imaging system are used to obtain the shape parameters, so the authors used the terminology of the system. Other studies attempting to optimize shape parameters have had a specific focus on particular characteristics of volcanic particles, and have provided different suggestions for which shape parameters are best to use [Liu et al. 2015a;Schmith et al. 2017]. Although the advantages of a standardized morphological parameterization protocol are apparent, it is very likely that an agreed protocol could only be developed through the common agreement of a focused international commission; no such protocol has yet emerged [Gurioli et al. 2015]. But even if a generally accepted standard is accepted by large parts of the volcanology community, we would still face the problem that the morphometric work previously done might be impossible to rigorously compare with the new data. This would be a setback, blocking utilization of data archives painstakingly acquired over more than two decades.
To make a first step towards unifying the morphometric parameterization systems, a platform-independent, multi-standard tool is needed. We have developed such an open-source software tool, which we call PARTicle Shape ANalyzer (PARTISAN). It computes a multitude of shape parameters, and can reproduce most of the various morphometric analyses that have been presented in recent volcanological literature.

Why PARTISAN?
PARTISAN supports the scientific method's requirement that results should be reproducible, and does so without any need for all researchers to employ a single "black-box" proprietary solution related to a device's operation. Table 3 presents a list of studies on particles from more than 30 different sampling sites that have been morphometrically analyzed based on the IPA parameter concept by Dellino and La Volpe [1996]. They involve the investment of many hundreds of working hours. The IPA measurements, however, are made with commercial software, which makes it very difficultif not impossible-for researchers who have no access to the program to obtain comparable parameters [Schmith et al. 2017].
PARTISAN addresses this problem.
1. It is independent from commercial hard-or software other than MATLAB TM . Our open source script computes morphometric parameters using the IPA shape parameter system [Dellino and La Volpe 1996]. Once IPA imaging guidelines are met, the user is guaranteed to obtain shape parameters compatible with those obtained by other groups using the IPA system, and with published results from it (see Table  3). 2. A multitude of shape parameters in addition to those of the original IPA [Dellino and La Volpe, 1996] are also obtained, using the specifications of morphometric analysis published by Cioni et al. [2014], Leibrandt and Le Pennec [2015], Liu et al. [2015aLiu et al. [ , 2015b and Schmith et al. [2017]. 3. The multi-standard output allows a PARTISAN user to compare shape-analysis data broadly, beyond the limitations imposed by any single specific group's standard. This approach also allows the PARTISAN user to find, for a given task, the shape parameter system most suitable for data interpretation. 4. The open source code allows continued peer-review and improvements by the volcanology community.

Morphometric parameters obtained by PARTISAN
In addition to basic metrics (given in Table 1 and illustrated in Figure 1), PARTISAN provides shape parameters grouped into five morphometric systems, described below. All morphometric parameters are mathematically laid out in Table 2.

The IPA parameters, by Dellino and La Volpe [1996]
The image particle analysis ("IPA") parameter scheme of Dellino and La Volpe [1996] is probably the most established one, and most commonly used for morphometric analysis in volcanology; it is predominantly used to quantify the shapes of particle projections in SEM images, but also applied to optically derived silhouettes of particles and to SEM derived thin sections (see Table 3). It is described here in some detail in order to clarify several misunderstandings which have appeared over the years.
The first two IPA parameters (see also Table 2) are circularity CircDL, and rectangularity RecDL, with the latter depending on the minimum rectangle circumscribing the particle. It is important to note that the orientation of the minimum bounding rectangle is not fixed, and hence independent of the particle's orientation; this contrasts with the approach used in some freely available software, e.g. ImageJ [Schneider et al. 2012;Liu et al. 2015a], in which the bounding rectangle is constrained to have horizontal and vertical axes, regardless of how an elongate particle is oriented.
The other two IPA parameters are compactness ComDL and elongation EloDL. The latter IPA parameter is defined as a fraction, with the longest segment in an object parallel to the long side of the minimum rectangle circumscribing it (denoted as "maximum intercept") as numerator, and the mean length of all chords with 1 pixel spacing perpendicular to the maximum intercept as denominator [Dürig et al. 2012]. We note that the definition of the maximum intercept is NOT identical with the maximum Feret diameter, but, probably because of an unclear description in the original paper by Dellino and La Volpe [1996], it is often misleadingly confused with it.
The four IPA parameters as introduced by the developers are provided by the commercial software Optilab Pro 2.6.1 from Graftek. The complicated definition of EloDL makes it, unfortunately, very difficult to adapt the IPA scheme for use without that software. We know of no available open source software available that computes the maximum and mean intercept according to the definition provided above. As a consequence, some studies using the IPA scheme without having access to Optilab, had to sidestep this problem, and did so by introducing other measures as replacement for EloDL (e.g., Schmith et al., 2017). We note that such a deviation from the original IPA scheme can still provide useful insights on how elongated the analyzed particles are. Results based on these "modified" elongation parameters are still comparable to data sets acquired by the same method, but they are not quantitatively comparable to those obtained by applying the "original" IPA scheme. In the future, by means of PARTISAN, researchers need no longer face this problem. All results computed by the open-source program will be comparable to the original IPA parameters provided by Optilab so long as the same protocol is followed for SEM image acquisition (see section 5.3), which is necessary to avoid introducing resolution-dependent differences in the quantitative results.

Shape parameters by Cioni et al. [2014]
Cioni et al. [2014] morphometrically analyzed particles in the 0 φ fraction (1 to 1.4 mm) to characterize particles from different phases of the Eyjafjallajökull 2010 eruption.
They introduced four shape parameters (see Table 2): solidity SolCI, convexity ConvCI, circularity CircCI and ellipse aspect ratio ARCI. These parameters were obtained using the public domain program ImageJ and binarized images from SEM [Schneider et al. 2012] of whole particles (silhouettes). After SEM analysis, the grains were sectioned, from which vesicle population and microlite data were acquired. The clasts analyzed had compositions ranging from benmorite to trachyte. The authors found that different eruptive styles produced different grain shapes, independent of the compositional changes.

Shape parameters by Leibrandt and Le Pennec [2015]
This morphometric system was introduced to allow rapid automated measurements of 2D shapes projected from grains (i.e. silhouettes) by employing diascopic light imaging, and using a specialized optical particle analyzer "morpho-grainsizer" and associated software (Morphologi G3SE™ by Malvern Instruments™). It can be used for near real-time characterization of tephra during eruptive events. The suggested shape parameters include circularity CircLL, aspect ratio ARLL, convexity ConvLL and solidity SolLL (see Table 2). The authors demonstrated their morphometric system on andesitic clasts from Tungurahua volcano, Ecuador, in the 250 -300 μm grain size range, produced by different eruption styles.
Of these parameters, the aspect ratio, as defined by Leibrandt and Le Pennec [2015], cannot be readily calculated without having a detailed description of the method used by the software, or access to the source code.

Shape parameters by Liu et al. [2015a]
This scheme was originally developed to examine the role of bubbles in producing ash by phreatomagmatic ("hydromagmatic" by the authors) fragmentation. Unlike silhouette-based 2D analysis, this method is applied to 2D shapes from polished thin sections or polished grain mounts imaged with an SEM. For this purpose, four parameters were suggested for optimal particle shape description: form factor (which is equal to CircCI), axial ratio ARLI (equal to the inverse of ARCI), convexity ConvLI and solidity SolLI equivalent to ConvLL and solidity SolLL, respectively. These shape parameters have been applied, e.g. to study basaltic grains from Grímsvötn 2011 in four size fractions ranging from < 32 μm to 125 μm [Liu et al. 2015b].

Shape parameters used by Schmith et al. [2017]
This morphometric system was tailored to the particle shape analysis of bulk samples using the commercial Particle Insight™ dynamic shape analyzer (PIdsa), and associated software. This method works through automated optical acquisition of particle silhouettes. The authors applied this system to investigate basaltic tephra fall samples from six different eruptions with selected grain sizes between 63 and 125 μm: five from Iceland (Fimmvörðuháls 2010, Karl 1210-1240, Katla 1755, Grímsvötn 2011, Hverfjall 2500 BP) and one from Norway (Eggoya 1732), covering different eruptive styles (from Hawaiian to subplinian) and fragmentation mechanisms.
In an effort to morphometrically distinguish phreatomagmatic from magmatic ash grains, the authors developed two main shape parameters: Feret aspect ratio AF and regularity parameter Reg. The latter is the product of circularity CircSC multiplied by rectangularity RecSC (equivalent to CompDL) and form factor (equivalent to CircCI), where CircSC is depending on the bounding circle (see Table 2).
To obtain results consistent with those presented by Schmith et al. [2017], PARTISAN computes the Feret aspect ratio presented in their Fig.3, here denoted ARSC, which is defined as the reciprocal value of AF.

Requirements
PARTISAN runs with the standard version of MATLAB TM and requires the MATLAB TM Image Processing toolbox. To install PARTISAN, the file 'PARTISAN.zip' provided in Supplement S1 has simply to be extracted into a folder of the user's choice.
As input, PARTISAN requires black and white (i.e., binary) images, e.g. of a single clast projected to the XY-plane as a silhouette (see Figure 2) or of a particle cross-section. Lossless formats such as TIFF, BMP or PNG are preferred over lossy formats such as JPEG.
A limitation is that the program does not allow automatic segmentation of images with multiple particles. Each image should show a single particle, with all images placed in the same folder. PARTISAN can then batch analyze all images as a single image stack.
Once the working folder has been assigned, the program can be executed. A step by step instruction can be found in the companion text file 'ReadMe.txt', which is provided with the 'PARTISAN.zip' package (Supplement S1).

Workflow and Output
After being initiated PARTISAN will proceed to cycle through all the matching image files in the assigned directory, processing each of them in turn and collecting the results of the analysis into a common comma-separated text file, ready for opening as a spreadsheet.
Either true-binary (0 or 1) or 8-bit (0 or 255) images may be used. If an image is inverted, this is automatically handled. If an 8-bit grey-scale image contains values other than 0 and 255 it will automatically be thresholded up or down from the central value of 127. Similarly, if a 0 or 1 "binary" image contains floating point values these will be thresholded up or down from 0.5. For details on the algorithms used for measuring the basic parameters (such as perimeter), we refer the reader to comments in the source code including links to further documentation.
During testing, analysis took approximately 1 second per image on a standard desktop PC. If figure generation is enabled, the program will take approximately 75% more time to run. Larger images (larger image files) will take proportionally longer to process.
PARTISAN provides the following output: A comma separated .csv ASCII spreadsheet containing all derived parameters, grouped by the name of the authors that first introduced them, is written to a file named 'particle_stats_output.csv' in the current directory. Each row contains the shape parameters for each image, as described in Tables 1 and 2. A summary of the parameters is displayed to the MATLAB console as the program runs. A figure window is generated for each image, consisting of four plots (see Figure 1): (a) the raw image; (b) the particle rotated to the longer axis of the minimum bounding box; (c) the particle rotated to the maximum Feret distance; and (d) the particle rotated to the major axis of the best-fit ellipse. These figures are well suited for quality assurance, but should be disabled when bulk processing many images (see 'ReadMe.txt' file in Supplement S1 for more details).

Strengths and Caveats
Based on comparisons of test data comprising 32 different shapes, PARTISAN is verified to givewith negligible variations in the perimeteridentical output for the IPA parameters as when using the software OptiLab employed by Dellino and La Volpe [1996]. Moreover, all SEM images kept in the archives, named by the authors that first introduced the shape parameters group, have now been reprocessed with PARTISAN, so users of this program can be sure that their results are compatible with those by the groups represented by the authors of the original paper.
As a general rule, due to the reasons mentioned in section 2, we strongly encourage to make sure that identical imaging and sampling protocols (including imaging type, image resolution, sampling methods, studied grain size) are used as applied to the data sets with which the new datasets will be compared. For example, for obtaining IPA parameters comparable to those kept in the archives by the authors, the area of the cross-section or silhouette (A) should have at least 5000 pixels [Dellino and La Volpe 1996;Mele et al. 2011;Dürig et al. 2012]. Importantly, empirical studies by Liu et al. [2015a] indicate that under no circumstance should the cross-sectional (or silhouette) area of a particle be smaller than 750 pixels.
PARTISAN can be applied to any type of particle images so long as minimum pixels-perparticle scaling is kept consistent. It is not appropriate, however, for data from particle shape silhouettes, whether based on SEM images, microtomography, or other light sources, to be directly compared to images of physically sectioned particles.
The program was developed to extract information needed to calculate IPA parameters in the first place, but it also provides a wide range of other data. These can be utilized to calculate parameters used by other authors, allowing comparison of results across methods. Because of differences in image acquisition (resolution, sharpness, pixel thresholds, etc.), comparisons of data from other studies with PARTISAN-extracted equivalents may, however, be imprecise unless original particle images are available to be reprocessed. To ensure best comparability of data in publications we therefore encourage authors to provide not only the values of the resulting shape parameters but also the binary images used as input.
We also want to stress that the measurement even of basic metrics such as perimeter (and partly also other parameters, such as area) depends on the algorithm implemented in the software, as well as image resolution and relative scaling of pixels vs. particle-surface topography. Differences in algorithm may lead to differences in shape parameters provided by PARTISAN versus those provided by commercial software used for the automated morphometric analysis systems. The output for these systems can therefore not be expected to provide directly comparable shape parameter results. We do not have access to these systems, and thus could not test comparability.
To overcome these difficulties we suggest that, whenever possible, binary images from automated image analyzers be stored. This will allow comparisons to be made with results from other image-acquisition and measurement systems now and in the future.

Demonstration: Shape analysis of selected ash grains from the Havre 2012 submarine rhyolite eruption
In order to demonstrate the functionality of PARTISAN we present results for ash grains collected from deposits of the 2012 submarine Havre eruption, and selected to exemplify the different shapes of clasts in the ash.

Geological background
Havre is a seamount volcano located along the Kermadec arc with its base at 1500-2000 meters below sea level [Wright et al. 2006] and a post-2012 peak along the caldera wall at 600 mbsl. The caldera is 3x4 km elongated toward NW-SW, with average caldera-rim depth of 900 m [Wright et al. 2006] and mostly flat caldera floor at 1500 mbsl.
In 2012 Havre volcano erupted, with a satellite image at 10:50 18 th July 2012 UTC showing an atmospheric plume, a 400 km 2 area of pumice raft on the sea and a plume of discoloured, ash-stained, water emanating from a hot spot point source above Havre. After 21 st July 2012 no further activity at Havre was detected. The eruption produced 14 lava flows from 11 vents along the southern caldera rim and the southwest caldera wall ] and three seafloor clastic deposits, all of which were described, sampled and mapped at high resolution during a 2015 cruise using the autonomous underwater vehicle (AUV) Sentry and the remotely operated vehicle (ROV) Jason. The seafloor clastic deposit of interest here includes an ash-dominant unit termed the Ash with Lapilli (AL). It extends across the whole of the caldera floor and shoulders, showing no clear grainsize or thinning trends to the limits of the 2015 investigation area.
Ash from the AL was sampled from locations around the summit and caldera of Havre volcano using ROV Jason [Murch et al. 2018]. Because the Havre ash is very fine-grained (many samples have a modal particle size of 16-32 µm) it is critical to separate different simple shapes. Also, on these very small particles, effects of surface irregularities are subdued compared with such effects for larger volcanic grains. Havre ash particles were thus divided into 4 morphological classes based on their key shape characteristics (see Figure 2): curvi-planar (labelled "C"), angular ("A"), fluidal ("F"), and elongate tube-vesicle ("T") [Murch et al. 2018]. Curvi-planar clasts are defined by planar and curvi-planar surfaces that intersect to form sharp edges and include both platy and sub-equant blocky clasts. Vesicles in curvi-planar clasts are cross-cut by fracture surfaces, which show no deformation around the bubble. Angular clasts have prominent concavities defined by brittle-fractured vesicle walls. Fluidal clasts have exterior features indicating surface-tension or fluid-dynamic reshaping of the grains while molten. Fluidal clasts include both those with a wholly fluidal form, and those that preserve a single fluidal surface. Fluidal particles are commonly crosscut by undeformed curvi-planar fracture surfaces. Elongate tube-vesicle clasts are bounded by either fluidal or brittle fracture surfaces but typically show curvi-planar fractures that run perpendicular to the elongation direction at either end of the grain.

Demonstration of results given by PARTISAN
In Figure 2, binarized projections of end-member examples of each morphology class are shown. These images are provided in Supplement S2 and can be used by the reader to practice applying the script. The relevant output results for these particle silhouettes, following the five shape parameterization approaches, are shown in Table 4. The complete output can be found in Supplement S3.
For this demonstration, imagine that these test data represent a large set of imaged grains, which we want to statistically analyze for features indicative of fragmentation style. Particleshape analysis and PARTISAN will help us to explore and find the best morphometric system to discriminate between grains generated by brittle versus ductile fragmentation mechanisms.
If applied to representative sample populations, such a procedure could provide a smart way to automate particle classification for statistical analysis, which otherwise would take tedious hours of manual sorting.
While curvi-planar and angular particles of the classes "A" and "C" can be assigned to brittle generation processes, the second group includes, in addition to thedescriptively namedfluidal grains (class "F"), also the elongate tube-vesicle (class "T") clasts, which were shaped by ductile stretching.
Our aim in this example is to find shape parameters which can be plotted against one another, individually or in combination, to provide the best discrimination between brittle and ductile particles. For this purpose we utilize and compare existing diagrams as proposed by various studies for each morphometric system implemented in PARTISAN (see Figure 3). Figure 3(a) follows the IPA system as defined by Dellino and La Volpe [1996] showing the plot of RecDL x ComDL vs EloDL x CircDL. This type of diagram has also been used for example by Büttner et al. [2002] to define a morphometric boundary (green dashed line) to discriminate shoshonite clasts by shape between brittle and ductile fragmentation mechanisms. For the rhyolitic grains demonstrated here the brittle-ductile (brittle-fluid) boundary appears to be lower on the y-axis (blue dashed line). The IPA plot has correctly placed the elongate tubular-vesicle clasts of class "T" in the ductile field, together with the fluidal grains of class "F", despite their very different overall shapes.
In Figure 3(b) another kind of IPA diagram is displayed, after Murtagh and White [2013]. A line separating "F" and "T" particles from "C" and "A" ones is possible (solid line), but the location is slightly different from their boundary (dashed line), and the F and T grains lie in their 'phreatomagmatic' field (because the other field captures vesicular fragments, hence the C and A grains). We do not recommend the use of this diagram for fine rhyolite ash.
Figure 3(c) shows the Havre results plotted following Cioni et al. [2014], who used their plot to discriminate ash from phreatomagmatic versus magmatic phases of the Eyjafjallajökull 2010 eruption. In our example, this diagram does not discriminate well the two groups of fragmentation mechanisms, since "T" and "F" class data points plot in significantly different sectors of the plot, which makes it difficult to group them together. The "F" and "A" class particles plot close together, whereas C class particles appear to cover a larger range in the diagram, which makes it difficult to achieve the desired discrimination.
In Figure 3(d) the Havre data are plotted in a diagram proposed by Leibrandt and Le Pennec [2015], using their morphometric system to discriminate between eruptive styles in ongoing eruptions. While "C" and "A" class data intersect, the data points for "T" class grains are plotted in a different area. The "F" class data points, however, are separated from the T' class data with "C" class data interfering, which inhibits the definition of a simple discrimination criterion that would separate grains formed in 'brittle' versus 'ductile' regimes. Figure 3(e) displays the data of the Havre samples in a diagram type suggested by Liu et al. [2015a]. Our results are, however, based on particle silhouettes, which are not expected to match with slices as used by [Liu et al. 2015a[Liu et al. , 2015b[Liu et al. , 2017. The 'A' and "C" class data plot with broad scatter, making it difficult to discriminate them from the "T" and "F" grains.
Figures 3 (f) plots the test data into a diagram provided by Schmith et al. [2017], in which the regularity parameter Reg is plotted over the Feret aspect ratio ARSC. This type of diagram can be used to derive a parameter introduced as regularity index (defined as the slope of the linear trendline), which was found to be sensitive to fragmentation style [Schmith et al. 2017]. We note that in contrast to the original diagram by these authors we use a larger range for the ARSC -axis, in order to be able to display all of our data points. In good agreement to Schmith et al. [2017] the "T" class data points all plot to the right of the dashed line, which indicates the threshold between elongated and non-elongated particles as found in their study. The overlap of "C" and "F" class data, however, do not support use of this system for establishing a 'brittle/ductile' discrimination criterion.
For each system, the results followed the expected trends with fluidal particles appearing more circular, angular particles plotting as more irregular, and curvi-planar particles generally falling between these two clusters. The elongate tube-vesicle clasts are characterized by extreme elongation parameters, such as the aspect ratio.
For our objective in this demonstration, the discrimination of brittle-fragmented from ductilefragmented clasts, the IPA system shown in Figure 3(a) is the best of the six compared.
The small number of selected particles with 'extreme' shapes used in this demonstration are not considered to be representative of the overall Havre eruption. The findings also are insufficient to support general advice on which morphometric system is best to use for achieving various volcanological goals. This choice must be made by the users, based on the aims of shape analysis in different projects. Existing data sets and their comparability in terms of sample type, grain size, and particle imaging method should be considered. What PARTISAN provides is a holistic tool for selecting and using the best fitting morphometric systems and diagrams.

Conclusions
PARTISAN is a Free and Open Source software (FOSS) routine that runs in MATLAB to parameterize 2D shapes of particle silhouettes and provide IPA statistics [Dellino and La Volpe 1996]. It also extracts other parameters that can, with some unavoidable caveats, allow cross-comparisons among other 2D morphological routines. The same parameters for external 2D shape can be measured for both silhouettes and sectioned particles, but shapes of particles prepared in these different ways cannot be compared directly. With a test case using ash grains from a submarine rhyolite eruption we demonstrated how PARTISAN can be used to find the most suitable shape analysis method for a specific task.  • • 2• 2 1 : using the notation of Dürig et al. [2012] 2 : List for studies using these IPA parameters: see Table 3 3 : defined as "hydromagmatic" in Liu et al. [2015bLiu et al. [ , 2017 4 : SEM stands for scanning electron microscope 5 : but also used to analyze SEM slices and silhouettes from both photographs and images obtained by optical microscopy. See Table 3 for detailed list.  Table 4: Output results by PARTISAN for the particle shapes displayed in Figure 2. The complete output file labelled "particle_stats_output.csv" can be found in Supplement S3.    Table 1 for the description of annotated parameters. The analyzed particle is displayed in four orientations: (a) original orientation of the raw image; (b) particle rotated to the longer axis of the minimum bounding box; (c) orientated along the maximum Feret distance dF (blue line); lines in green denote the major and minor axis of the best fit ellipse; (d) particle rotated to the major axis of the best-fit ellipse. The Feret lengths lF and wF listed in Table 1 are identical with the width w and breadth b of the minimum area bounding box displayed in (a). Also in (a), the particle perimeter p is highlighted in yellow. The perimeter pcp is that of the smallest convex hull with area Acp, which is illustrated in blue in the background of the grain silhouette. The diameter of the bounding circle denoted BC (in green) is listed in Table 1 as dBC.

Data and sharing resources
The orange colored circle is of perimeter c and Heywood diameter dH.

Figure 3:
Morphometric diagrams as used in morphometric systems underlying PARTISAN. (a) Image particle shape analysis diagram using the system by Dellino and La Volpe [1996]. Green dashed line indicates boundary between brittle and ductile fragmentation regime provided by Büttner et al. [2002] for shoshonite clasts. In contrast, the shape of rhyolitic Havre particles with brittle angular and curvi-planar features suggest a lowered boundary (blue line). (b) Complementary IPA diagram with axes as used by, e.g., Murtagh and White [2013]. In addition, the resulting diagrams according to the presentation methods by Cioni et al. [2014] (c), Leibrandt and Le Pennec [2015] (d), Liu et al.
[2015a] (e) and Schmith et al. [2017] (f) are presented. In the latter plot the dashed line indicates the threshold between elongated and non-elongated particles as found by Schmith et al. [2017]. For the analyzed Havre ash particles, the best choice for an automated discrimination between brittle and ductile particle classes would be the morphometric system and diagram type presented in (a).