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Research Article

Visualizing Variability in Ceramic Micro-Curvature though Novel 3D Morphometric Mapping and Sliced Segmental Extraction

Authors:

James Frances Loftus III ,

Kyushu University, Graduate School of Integrated Sciences for Global Society, JP
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Noriko Seguchi

Kyushu University, Faculty of Social and Cultural Studies; University of Montana – Missoula, Department of Anthropology, JP
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Abstract

In recent years, two-dimensional (2D) outline-based morphometric analysis has begun to be the standard means of shape analysis in the study of ceramics. Despite the ever-increasing repertoire of three-dimensional (3D) ceramic data available to researchers, due to challenges in utilizing landmark-based geometric morphometrics on ceramics, many contemporary studies are forced to rely on 2D outlines, which account for only a small degree of shape variance. Consequently, notions of intra-vessel variance cannot be thoroughly extrapolated, and as such, important themes such as morphogenesis during the production process have not been thoroughly examined. By contrast, the present project utilizes a method derived from high-resolution 3D scans combining “morphometric mapping” and “sliced segmental extraction” to visualize previously unrecognized variability in the micro-curvature of full vessels. This method does not require homologous landmarks, but rather, employs a multistage approach that allows for several stages of analysis that can be adjusted to each given research project, and thus has the potential to elucidate idiosyncratic variability during the morphogenesis process.

 

概要

近年、土器研究において、2次元の輪郭を用いた形状(形態)解析が主流となりつつある。土器の3次元データのレパートリーは増え続けているが、ランドマークを用い た幾何学的形態計測法を土器に適用することは困難であるため、多くの研究は形態のばらつきが小さい2次元外形図に頼らざるを得ない。そのため、製品内のばらつきの概念を十分に定義できず、製作過程における形態形成などの重要なテーマについては十分に検討されていない。これに対し、本研究では、高解像度3Dスキャンから得られる「形態計測マッピング法」と「セグメント抽出法」を組み合わせ、これまで認識されていなかった土器全体の表面の微小曲線のばらつきを可視化することに成功した。この手法は、相同ランドマークを必要とせず、研究プロジェクトごとに分析の様々な段階において調整可能な分析手法を採用しているため、形態形成過程における特異様式を明らかにできる可能性がある。

 

キーワード: 三次元分析; 土器; 日本考古 学; 形態計測マッピング法; セグメント抽出法

How to Cite: Loftus III, J.F. and Seguchi, N., 2022. Visualizing Variability in Ceramic Micro-Curvature though Novel 3D Morphometric Mapping and Sliced Segmental Extraction. Journal of Computer Applications in Archaeology, 5(1), pp.57–77. DOI: http://doi.org/10.5334/jcaa.89
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  Published on 03 Aug 2022
 Accepted on 20 Jun 2022            Submitted on 27 Jan 2022

1. Introduction

The way in which humans transmit knowledge and accumulate production skills is a fundamental question in any study of the production of material cultural products (Herbich 1987; Roux 2019). When considering such fundamental questions, researchers often attempt to compare material cultural/tool production in humans and nonhuman primates as a means of clarifying the uniqueness of human producers through various means. One of the delineating points between these two groups is that of “cumulative knowledge”, as well as the robustness of human cultural traditions to continue over vast stretches of time (Dean et al. 2012). One widely accepted explanation as to how material cultural traditions can continue so strongly is through “high-fidelity copying” (Whiten 2011). While humans are capable of both emulation and imitation, the “highly developed capacity for imitation among humans may be key to the phenomenon of cumulative culture” (Jordan 2015:9). In this way, the high fidelity of imitation/copying during the learning process is crucial to the replication and transmission of material cultural knowledge (Lewis & Laland 2012). Degrees of high-fidelity copying in archaeology and ethnoarchaeology have been noted through studies of the standardization of object forms, with standardized samples being understood as having been produced in a learning environment that was not conducive to individual experimentation and enjoying high degrees of action reproduction when new learners are incorporated into production (Kvamme et al. 1996; Roux 2003).

However, recent studies on reexamining notions of high-fidelity copying have shown that such intensive copying techniques are not the sole cause of cumulative culture (Saldana et al. 2019). In a study on standardized pottery-producing groups in India, Gandon et al. (2020) note that within these “standardized” groups lie a plethora of idiosyncratic “pathways” to creating vessels of similar form (referred to by the authors as “morphogenesis”). Not only the time taken at each stage of the production process, but also the number of hand movements and cognitive ways each individual uses to complete a familiar task, clearly indicates that despite the end product being highly standardized, idiosyncratic actions taken during the formation process of ceramics are rife during the production process (Gandon et al. 2020).

Unfortunately, while contemporary ethnoarchaeological studies may elude to a higher number of idiosyncratic agent actions during the production process, their analytical methods are still difficult to apply directly to prehistoric archaeological samples. In line with recent archaeological studies of ceramic shapes, many ethnoarchaeological studies of ceramics utilize two-dimensional (2D) outline-based geometric morphometrics in tandem with individual potter information such as familial ties, social class, sex, gender, etc… However, as this information may not be readily available for archaeological samples, “standardized” vessels can only remain tangentially connected to notions of agency or idiosyncratic style through ethnographic examples. Although simplified 2D outlined-based morphometrics may not accurately capture the potential idiosyncratic complexities during morphogenesis in standardized samples, recently developed three-dimensional (3D) technologies now allow researchers to visualize any region of intra-vessel variance in form at a much higher degree of detail than previously afforded (as pointed out by Roux & Karasik 2018). How then, can 3D technology be utilized to visualize full-vessel variability during the morphogenesis process?

Here, it is hypothesized that variability in the full-vessel symmetry of ceramics as seen through the curvature of the outer wall could be a means from which differential skills or idiosyncratic variability during morphogenesis could be extracted. When considering that differential time dedication to different vessel regions (Gandon et al. 2020) and the overall number of utilized unique motor skills as seen through hand movements (Gandon & Roux 2019) can differ widely between potters during morphogenesis, a small degree of micro-variability in curvature may be leftover within a standardized vessel type, despite the final piece being highly standardized. In particular, the visualization of the variability in curvature between different regions of a whole vessel could build upon previous 2D geometric morphometric investigations of idiosyncratic stylistic representation in ceramics. Roux (2003) notes that the lip regions of vessels created by potters in Andhra Pradesh are likely stylistic features that allow for some degree of idiosyncratic variability. Furthermore, Gandon and Roux (2019) note that “simpler” shapes, such as vessel bases, require less time to create and a lower number of unique motor skills to form. As such, two visualization methodsone that considers the full morphology of pots, and another that can be further sliced into major morphological regions and further complexly visualizedwould be a useful addition to current 3D methods in ceramic analysis, despite the existing difficulties in current quantification methods for the curvature of full-vessel ceramics.

A lack of homologous points on ceramics for use in landmark analysis has turned many researchers away from attempting 3D ceramic visualizations; to address this issue, the present study aims to clarify inter-vessel variance by visualizing ceramic curvature through a combined approach utilizing morphometric mapping (MM) and sliced segmental extraction (SSE). MM and SSE methods seek to visualize whole-vessel variability in the curvature of the outside face of ceramics. MM/SSE uses 3D mesh or point cloud data to visualize variability in micro-curvature by projecting scalar fields (SFs) on the outside surface of “unrolled” vessels. Prior to the introduction of the pottery wheel in the ceramic morphogenesis process, outer wall curvature was theorized to be much more variable among and between different vessel areas (e.g., a comparison of a prehistoric early Yayoi period tsubo vessel and a modern mass-manufactured earthenware model is shown in Supplementary Figure 1) Through MM and SSE, it may be possible to clarify notions of idiosyncratic style in “standardized” ceramic samples through differential curvature patterns that arise through differential control of motor skills or tool use, and in doing so, may help elucidate the role of high-fidelity copying in the production process (Bril 2015). It should be noted that MM and SSE currently enable a visual representation of micro-curvature; the present study does not seek to quantify variability at this stage. While quantification is a necessary next stage of this methodology, the present study seeks only to showcase the workflow of MM/SSE and a small case study to express its potential for future use. This study utilizes a tentative application of the MM/SSE workflow on prehistoric Japanese ceramics to explore its potential usefulness in future large-scale and quantifiable studies.

2. 2D and 3D morphometric analysis of ceramics

Modern statistical analyses of shape and form in both biological and material cultural samples can be generally categorized into three main groups: 1) traditional/conventional, 2) landmark-based geometric morphometrics, and 3) outline-based geometric morphometrics. These three “groups” do not represent concretized workflows that cannot be deviated from, but rather, should be considered as different “toolboxes” filled with any number of tools that can be more useful for analysis depending on the sample or research goal at hand (Cooke & Terhune 2015). As such, a number of ceramic studies have utilized morphometric analysis across each of these different methods to illuminate different goals (Wilczek et al. 2014; Gandon et al. 2018). To clarify the issues of these analyses with regard to elucidating potential intra-vessel curvature variance, a short synopsis of each method is outlined below, along with example studies (both biological and archaeological).

According to Webster, traditional morphometrics summarize “morphology in terms of length measurements, ratios, or angles that can be investigated individually (univariate analyses) or several at a time (bivariate and multivariate analyses)” (Webster 2010: 163). In biological samples, traditional morphometrics have been used for decades to elucidate complex shapes in 2D representations through metric distance and angle measurements between important morphological points (i.e., homologous landmarks) (He et al. 2013). Traditional methods have also been utilized in ceramic studies, but often encounter issues during statistical analysis stemming from the largest variation falling within notions of size variance rather than shape.

Landmark-based geometric morphometrics is the first of the two main groups of geometric morphometric analysis. Landmark-based geometric morphometrics “summarizes shape in terms of a landmark configuration (a constellation of discrete anatomical loci, each described by 2- or 3-dimensional Cartesian coordinates), and is inherently multidimensional” (Webster 2010: 164). In modern studies of biological samples, either 2D- or 3D-based landmark analysis is the preferred method of data extraction and morphometric analysis. For example, 3D technology and geometric morphometric analysis have been utilized to investigate craniofacial variation, sex differences, and ancestry estimation in attempts to gain a better understanding of population history and structure, and functional morphology (Seguchi & Didzik 2019). While material cultural studies on objects such as stone tools or iron blades have the potential to utilize sliding landmark-based analysis because of their numerous homologous points and lack of extreme curvature (Archer & Presnyakova 2019), one main problem arises when attempting to utilize landmark-based geometric morphometrics in ceramics: there is often a lack of usable landmarks, especially in samples not extremely standardized in form. This is due to the fact that forms that consist of mainly curved surfaces are often not conducive to the accurate placement of landmarks in a reproducible way, and are not the preferred method for elucidating variation in curvature (Wang & Marwick 2020).

Outline-based geometric morphometrics are the other half of the geometric morphometric set. Analyses such as Elliptical Fourier Analysis (EFA) allows for the full contour of vessel forms (either closed or open) to be utilized in a variety of statistical analyses. In the analysis of material cultural goods that consist of high degrees of curvature, such as ceramics, outline-based morphometrics is a much more reliable method of extrapolating shape information (Cardillo 2010). However, outline-based morphometrics in ceramics utilize 2D outlines of the vessel form, and thus, can only account for a small degree of intra-vessel variance. When comparing groups of vessels from different regions or time periods, such as in Wang and Marwick (2020), who clarified the temporal degrees of standardization of vessel forms in Taiwanese iron-age pottery, outline-based analysis may be a beneficial tool. However, in morphologically standardized samples, outline-based morphometrics, especially those of full vessels, cannot accurately visualize the complexities and detailed nature of idiosyncratic actions. In previous applications of the morphometric analysis of ceramic samples, three main methodological shortfalls have been apparent when attempting to elucidate differential ceramic curvatures and potential notions of idiosyncratic action: 1) interference of size factors, 2) lack of homologous points, and 3) 2D outline deficiencies.

Due to these shortfalls, the proliferation of 3D investigations of ceramic variability has greatly expanded in recent years, with numerous journal issues and conference sessions dedicated to 3D technologies in ceramic research. As the 3D analysis of ceramics covers a wide landscape, the full breadth of scholarship cannot be included here, but recent studies can generally be categorized into three groups: 1) reconstruction/identification; 2) 3D to 2D quantification; and 3) full-vessel extraction. Studies that utilize novel 3D software to reconstruct ceramic vessels from single sherds, piece together a collection of sherds into a full vessel (Banterle et al. 2017; Stamatopoulos & Anagnostopoulos 2017), or seek to identify types of pottery through 3D imaging fall into the first group of recent studies, i.e., those that focus primarily on reconstruction or identification. Studies that utilize 3D mesh or cloud data as a base, but then extract 2D outline or other 2D data (such as length measurements) fall into the second group of studies (recent examples include Göttlich et al. 2021 and Harush et al. 2020). These studies often focus on a particular area of vessels from which to extract 2D data, and can be understood as more likely to be representative of potential variability than of data extracted from photos or line drawings, as any number of 2D outlines can be extracted from any number of regions of the 3D mesh. However, these studies often fall short of the minute visualizations of curvature necessary to capture potential whole-vessel idiosyncratic variability. Studies that focus on extracting visual or quantified data from all 3D data and utilize the full 3D model are still sparse, likely because of the complexity and vast amount of data acquired; however, recent studies utilizing point cloud analysis (for example, see Vo-Phamhi and Leidwanger 2020) have reported that full-vessel analysis is a useful and enlightening methodology to pursue. In particular, when considering potential variability in micro-curvature during the morphogenesis process (Gandon et al. 2020), although focusing attention on one region of vessels may help clarify particular questions related to that region, a holistic view of micro-curvature as visualized on the entire 3D mesh or point cloud data has yet to be thoroughly investigated. Such a holistic view of curvature between whole samples would allow scholars to categorize visually vessels of higher/lower variability within particular subsets of ceramic samples easily, such as those found in standardized production contexts, to extrapolate relative inter-agent variability.

To investigate potential workflows for the visualization of full-vessel 3D curvature, the present study developed a workflow involving 3D MM and SSE. Through MM and SSE, the gap between 2D outlines, the full complexity of 3D forms, and agentic action during the production process may slowly be bridged. In this example, the term “ceramics” is used as a collective term for fired clay objects, and “pottery” (as seen in the following case study) as a term to describe soft-fired and unglazed earthenware (Yamamoto 2001). MM/SSE is thus not limited to one category of ceramics, but rather, may be utilized across a variety of molded and fired objects such as porcelain, stoneware, and earthenware vessels. The MM/SSE workflows are introduced in this study through a small case study of prehistoric Japanese ceramics from the Yayoi period excavated from the Fukuoka plain region of western Japan.

3. Materials and Methods

3.1. Early Yayoi period pottery case study

This study utilizes earthenware from the early Yayoi period (弥生前期) of Japan (~800/700 BC – 300 BC) (Hashino 2018; Miyamoto 2016). This period is understood in previous research as a transitional period between the indigenous hunter-gatherer society of the Jomon (縄文) and the wet rice agricultural society of the middle Yayoi period (弥生中期) (Miyamoto 2018; Yane 1984). The agricultural transition in this period was introduced through waves of migration from the Korean peninsula during periods of climatic cooling, which pushed populations south into the northern Kyushu region (北部九州地方) of the southern Japanese archipelago (Miyamoto 2016). Thus, the earliest examples of interaction between migrant and indigenous populations were seen during this period (Nakazono 2004).

According to previous studies, within the northern Kyushu region itself, the Fukuoka plain region (福岡平野) saw high increases in site/population density during this period, accompanied by increases in the standardization of pottery forms (Tanaka 2011). These pottery forms were then introduced into surrounding peripheral regions as a new, hybridized “Yayoi culture” (Miyamoto 2016: 69). However, previous studies on the pottery forms are often based on statistically irreproducible methods such as “attribute analysis” and typo-chronologies (Hashino 2016; Nakazono 2004). As such, 3D analyses of vessel forms have yet to be conducted. Consequently, intra-site variance is not often well understood, and agentic variance in pottery forms during this period and in this region has yet to be fully explored. Therefore, the present case study utilizes pottery from one site within the “standardized” Fukuoka plain region to visualize variations in pottery forms through the MM of vessel curvature (Figure 1).

A map of the Japanese archipelago and northern Kyushu region
Figure 1 

The northern Kyushu region. A: The Japanese archipelago and northern Kyushu region are outlined in the red square; B: The northern Kyushu region and Fukuoka plain subregion utilized in the present study.

3.2. Materials

There are several types and styles of vessels within the early Yayoi period; however, this example focuses attention on mortuary vessels known as tsubo (壺) (Figure 2). Tsubo globular pots are most often found as the only remaining burial good from this period, and their depositional context is most often within the variety of grave types found in this region during this period. Specifically, tsubo pots found within the Fukuoka plain region from the period of material culture “standardization” were chosen specifically to elucidate “hidden” curvature in vessel forms. The Shimotsukiguma-Tenjinmori site (下月隈・天神森遺跡) is one of many burial sites within this region. However, while many sites span several morphological phases of the tsubo pot, the Shimotsukiguma-Tenjinmori site mainly contains examples from the Itazuke 1a vessel style. Furthermore, the morphology of these vessels is very similar, making the application of MM an indispensable method for elucidating the curvature of vessel forms. Nine excavated vessels from the Shimotsukiguma-Tenjinmori site are utilized in this example and briefly summarized in Table 1 and Figure 3.

Table 1

Samples utilized in this study with corresponding traditional typological “type” and notes on the preservation of the vessel.


VESSEL CODE SURVEY # TYPE NOTES

T1 3 Itazuke Ia (1) Fair preservation

T2 3 Itazuke Ia (2) Slight lip paste reconstruction

T3 6 Itazuke Ia (2) No lip region

T4 6 Itazuke Ia (2) Sherd reconstruction

T5 3 Itazuke Ia (2) Fair preservation

T6 3 Itazuke Ia (2) Base sherd reconstruction

T7 6 Itazuke Ia (1) No lip region

T8 6 Itazuke Ia (2) Slight body paste reconstruction

T9 3 Itazuke Ia (2) Fair preservation

An earthenware pot and pottery line drawing side by side
Figure 2 

A tsubo globular pot. The pronounced outward curvature of the lip and heart-shaped body connected to a slabbed base are characteristic of this style of pot in this region. (example shown here: Shimotsukiguma-Tenjinmori site, No. T5).

A table containing photos of earthenware pots
Figure 3 

Early Yayoi period tsubo pots from the Tenjinmori site. Nine examples are utilized in this case study.

3.2.1. Data collection permissions

The ceramic vessel data utilized in this study, including photographs, 3D mesh, and cloud data, were collected with the express permission of the housing institute for use in this work. All materials in this study were housed at the Fukuoka City Archaeological Center (福岡市埋蔵文化財センター) at the time of writing. 3D scans were taken using an Artec Space Spider (Artec 3D, Luxembourg City, Luxembourg), which captures 3D data at a resolution of up to 0.1 mm and a point accuracy of up to 0.05 mm using blue-light based technology. As samples are relatively similar in overall size, each scan was produced at a standardized detail of 500,000 vertices/1,000,000 polygons. Postprocessing of scans was done through a combination of Artec Studio 15 (Artec 3D), MeshLab (Cignoni et al. 2008) (Visual Computing Lab, Pisa, Italy), and Geomagic Design X software (3D Systems Inc., Rock Hill, SC, USA).

3.3. Methods

3.3.1. Introduction to MM and SSE

MM is a visualization tool that allows notions of thickness and curvature to be expressed through a chromatic color scale (Bondioli et al. 2010). MM is used most frequently in biological samples in which landmarks cannot be reliably utilized, necessitating the use of a surface visualization method, or in tandem with other types of geometric morphometric analysis. On the other hand, SSE is method developed for use in the present study that further extracts extremely minute variability in ceramic curvature through the “slicing” of mesh/cloud data into horizontal bands, and re-extracting MM on each of these bands individually. In biological anthropology, MM has been used to visualize commonalities and differences in the external diaphyseal surfaces of long bones, which reflect the topography of muscular attachment sites between taxon-specific locomotor adaptations. In these examples, after aligning the morphometric maps in Fourier space, the aligned MMs were submitted to 2D Fourier and principal component analyses (Morimoto et al. 2011, 2012). For these studies, 3D data were acquired using computed tomography, and as such, notions of curvature and bone sample thickness could both be extrapolated. In ceramic samples, MM has yet to be holistically utilized for curvature extrapolation. 3D studies utilizing differential vessel thicknesses often focus on vessel reconstruction from sherds, and cannot be accurately applied to full vessels (Di Angelo et al. 2021). The present study utilizes 3D scanning of ceramic outer surfaces, and as such, cannot extract vessel wall thickness without further computational input (such as that developed by Spelitz et al. 2020). Despite this, detailed notions of curvature can be understood through the use of MM on strictly the outer surface. Furthermore, as 3D scans of the outer surface of ceramic vessels are becoming more accessible, the present study can serve as an example of the possibilities of MM/SSE for use in such samples.

3.3.2. MM using CloudCompare

CloudCompare is open-source software for processing 3D point cloud data that can import a variety of 3D mesh data, extract 3D point clouds, and manipulate these point clouds in a variety of complex analyses (CloudCompare 2.12 2021). The following example utilizes several important features in CloudCompare to extrapolate curvature MM, most importantly: 1. unrolling, 2. SF projection, 3. profile drawing, and 4. sliced segmentation (Figure 4). Using these features in tandem enables the extrapolation of 2D and 3D MM visualization. The following section briefly outlines the general process of creating 3D/2D MM outputs using CloudCompare. It should be noted that the specific settings utilized in this example are only for demonstration purposes, and should be adjusted for each given sample if utilized in further studies.

A flowchart with arrows showing the order of workflow
Figure 4 

Morphometric mapping (MM) and sliced segmental extraction (SSE) workflow; from mesh manipulation, cloud manipulation, scalar field projection, and MM/SSE extraction.

3.3.3. Startup and vessel orientation

The CloudCompare operating environment has a very simple layout, with all important features laid out in the operations bar above the 3D environment (Figure 5). Multiple 3D mesh files can be imported at the same time, allowing for a seamless workflow when handling several samples, as well as easy comparison among several vessels.

A screenshot of the CloudCompare operating environment
Figure 5 

The CloudCompare operating environment.

When the 3D mesh is imported into CloudCompare, if not already oriented to the desired angle, orientation can be completed easily using the “level” tool. The level tool allows three points on the vessel to be selected, after which, the mesh or cloud is oriented to the “top” XY plane (Figure 6). In this example, while the lip region of the vessel is often uneven and may have varying degrees of curvature, the base region is often very flat and easily aligned. The minor differences between lip and base orientation are outlined in the following sections; however, which orientation method to choose should be carefully considered based on the shape, degree of preservation, and desired outcome of the sample at hand.

An 3D pot mesh being orientated to the pot base
Figure 6 

Orientation process using the “level” tool. A: An un-orientated vessel; B: Choosing three points for orientating the mesh; C: A vessel correctly base-orientated.

3.3.4. Cloud extraction and unrolling

While CloudCompare is extremely useful for the visualization and analysis of point cloud data specifically, point clouds are not a necessity for conducting MM and SSE. However, utilizing mesh data “as is” (in file formats such as OBJ and PLY) has certain drawbacks when using this method. First, mesh with texture data (such as OBJ files) should have the texture removed beforehand, as the SF (visualized in color) is projected onto the texture, making it difficult to decipher the curvature. Furthermore, the large size of finely detailed mesh models needed for the extraction of MM/SSE makes it difficult for some machines to import multiple files. Instead, following the orientation of mesh models, sampling cloud data from mesh models and projecting SF visualizations onto this cloud are much more streamlined and user-friendly in terms of overcoming certain challenges in the use of 3D mesh data, as removing texture is not necessary. Alternatively, utilizing the original point cloud data from which the mesh data were acquired is also possible, and removes one step in this process. As such, for those utilizing machines that may struggle with the processing of larger file sizes, or those utilizing large amounts of data that contain texture, sampling or using original point clouds is recommended, and thus introduced in the present study. The choice is left completely to the discretion of each scholar. However, it should be noted that while many online 3D data repositories include detailed mesh data, few contain original point clouds from which the mesh is constructed; as such, for scholars utilizing secondary 3D data with the aim of utilizing the point cloud-based approach detailed in this study, sampling of the point cloud data from the mesh model is necessary.

If the utilization of cloud data has been chosen, sampling point clouds can be done within CloudCompare through the “Mesh → Sample points” tool. Point cloud sampling can be done through either the total number of points in the cloud or the density of said points (Figure 7A utilizes the latter). In the provided example, 1,000,000 points per cloud are sampled to reduce the possibility of holes or gaps, which may affect the outcome of MM analysis. While sampling point clouds from an already converted mesh may introduce certain minute amounts of potential errors depending on the density of the points sampled, the size of the scans and number of sampled points utilized in this study seem to provide an accurate depiction of the same morphological patterns as that of the original mesh data (Supplementary Figure 2). Furthermore, while the number/density of sampled points in a cloud may increase/decrease the visibility of minute curvature patterns, the overall patterns are visible at almost any level, with sparsely populated clouds (100 K points and under in this case) that do not contain enough morphological data to visualize finer details accurately (Supplementary Figure 3). Of course, this depends on the level of detail and the size of the original mesh.

A diagram showing steps of unrolling a 3D pot cloud
Figure 7 

Sampling 3D point cloud from mesh data and the unrolling process. A: A vessel point cloud with 1,000,000 sampled points. B: An unrolled point cloud. C: An unrolled point cloud viewed from the side, with clarified curvature patterns.

As soon as point clouds have been sampled from mesh data, any number of analyses can be conducted using CloudCompare. However, to extrapolate degrees of curvature in the vessel form, it becomes advantageous to “unroll” the point cloud into a “semi-2D” state so that the curvature on various regions of the vessel can be visually inspected. Such unrolling and visual inspection is often applied to objects such as tires or cylindrical objects because in its original form, vessel curvature is difficult to ascertain, and often cannot be understood without close, in-person, physical investigation; even so, variation in curvature can frequently only be explained idiosyncratically. Unrolling is conducted through the “Projection → Unroll” tool, through the center of the vessel, and along the Z axis (Figure 7B, C). This semi-2D cloud can then be oriented in different angles to ascertain regions of outward/inward curvature (Figure 7C). This unrolled point cloud is then ready to be visualized through MM, where varying degrees of curvature are expressed through colored SF projections.

3.3.5. SF projections

SF projections allow for the relative locations of mesh or cloud points to be visualized against a chosen 3D plane. SF projection is conducted through the “Projection → Export coordinates to scalar field” function. The colors represented on the SF correlate to the relative position of each point in the cloud (an invisible plane on a chosen axis). These relative positions allow the minute curvature on the surface of the vessels to be captured visually in ways that cannot be accurately accounted for in 2D photography. However, when projecting SFs on ceramics, it is always recommended to unroll the mesh models beforehand. When projecting SFs onto an unrolled 3D mesh (or unrolled cloud), the issue faced is that because the relative “distance” of each point on the mesh/cloud is visualized from an invisible 2D plane, the opposite side of the ceramic vessel will not be visualized. When studying certain stone tools, a simple solution would be to flip the object on the opposite face and project SFs to visualize both sides. However, as pottery has a continuous curvature face, SFs can be projected onto an endless number of “faces”. As such, an unrolled mesh or cloud in a semi-3D state allows for the variation in curvature to be visualized on the whole vessel (Figure 8).

Diagram of scalar fields on a regular and unrolled pot
Figure 8 

Projection of scalar field on regular vs. unrolled mesh data. Unrolled data allows for the visualization of curvature of the full vessel.

Utilizing an example vessel, through the “high contrast” color scale, regions of white/light blue represent the areas of the vessel closest to the Y axis, and conversely, regions of orange and dark red represent the areas furthest from the Y axis. In Figure 9, the body region shows two areas of outward curvature, demonstrating a clear oblong shape for what should be a distinctly round body. Although the neck region is less visible because of the strong outward protrusion of the body, it also shows interesting curvature patterns, with the midsection of the vessel having a slightly more outward curvature, but does not align with the two areas of curvature of the body. This may be due to the stages of production of these Yayoi vessels, as the lower body, upper body, and lip/neck region are all created at separate stages of coiling. The visualization potentials of this method do not stop at this stage, as certain areas of specific interest can easily be cut and analyzed separately.

An unrolled pot with scalar fields showing variability through color
Figure 9 

Scalar field projection on unrolled point clouds. A: Standard blue > green > yellow > red color scale (blue refers to the region closest to the Y axis, in this case the body); B: “High contrast” color scale revealing different curvature patterns on both the body and lip/neck regions of the example vessel; C: 2D representation of the full unrolled cloud.

3.3.6. Sectional extraction

Sections of specific interest, in this example, the two protruding areas on the body, can be cut away from the rest of the point cloud for analysis as a separate entity using the “Filter points by value” tool. This tool extracts a separate cloud of points falling within a certain range as designated by the user (Figure 10). From the extracted section clouds, any type of SF analysis can be applied to visualize these areas of interest even more clearly. In this example, the two regions of outward curvature become clearly visible, showing that each has a slightly different shape and degree of outward curvature. By extracting areas of particular morphological interest, a plethora of further visualization techniques become available to the user, one of which being the extraction of line contours.

An unrolled pot with the mid section highlighted and removed
Figure 10 

Sectional point cloud extracted using the “Filter points by value” tool. A: Choosing regions of particular interest; B: Extracting point clouds and applying separate scalar field values; C: Rotating and orientating the point cloud to visualize easily the detailed curvature of the vessel form.

3.3.7. Polyline drawing and profile extraction

As previously mentioned, 2D contours of full vessels are sometimes utilized in the automatization of archaeological line drawings; however, few examples have been used to extrapolate and visualize curvature. As shown in Figure 11, a polyline is drawn through the center of the extracted cloud of the body, and at 5-mm orthogonal steps, contour lines are extracted. These contour lines, depending on the settings utilized during the drawing process, return a very precise image of the curvature of not only the whole vessel, but also areas of special importance such as the body shape, as shown previously. It may be possible to export each individual contour line for use in outline-based geometric morphometric analysis (utilizing open outlines) such as EFA and associated statistical tests such as principal component analysis. However, the present study focuses primarily on visualization through MM, and as such, contours are not thoroughly discussed.

A removed pot mid section with contour lines on top
Figure 11 

Contour line extraction through polyline drawing. A: 5-mm steps between each open contour line; B: Contour lines are drawn on the extracted body cloud; C: Extracted contour lines showing the clear curvature of the body of the vessel.

3.3.8. SSE

While MM of the whole vessel results in extremely interesting possibilities for visualizing vessel curvature, depending on the sample being utilized, the body of the vessel may overtake other regions. As seen in Figure 12A, while the body curvature is the most likely to catch attention, other regions of the vessel such as the neck/lip also show varying curvatures. While it is possible to cut the vessel into multiple sections and reapply SF projections, this process is time-consuming and may be prone to error when working with a larger number of samples of varying shapes/sizes. Therefore, a method that utilizes the whole vessel while also accounting for a higher amount of inter-regional curvature is necessary to visualize the vessel curvature holistically. During the process of contour extraction in 5-mm slices, segment extraction at varying widths is also possible. If the section width is aligned to the step width (in this case, 5 mm), the full vessel, sliced into 5-mm sections, can be extrapolated; in the present study, this process is referred to as SSE (Figure 12B/C). These long, horizontal slices account for the full form of the vessel, but SF projection is instead aligned within each of the extracted section clouds. In this way, the regions of the section cloud closest to the Y axis are shown as being the most outwardly curved. This allows for extremely detailed curvatures to be accounted for, which may be very useful for curvature visualization of extremely standardized samples. As shown in Figure 12B, the outward curvature of the neck/lip region, which was previously somewhat obscured, is now extremely clear by using SSE. Furthermore, curvature in the base and lower sections of the example vessel, which were almost completely obscured by the body curvature, has become evident. SSE can also provide insight into differential curvatures arising from the stages of pottery production. For example, early Yayoi pots such as the one shown in Figure 12 are created through clay-band stacking, smoothing, and drying stages. The curvature patterns between, for example, the upper and lower body may hint at these stages of production, which in turn, may be associated with mediating risks of wall collapse (Rice 1984) or differential difficulties in the production of specific shapes (Gandon et al. 2019; Roux 2019).

Unrolled pots side by side comparing MM and SSE outputs
Figure 12 

Sliced segmental extraction of the whole-vessel form; white/dark red regions are areas of inward curvature, and green/light blue regions are areas of extreme outward curvature. A: A normal morphometric mapping output; B, C: Sliced 5-mm segments clarify the detailed curvature; D: Each sliced segment can be examined individually and exported as a separate mesh data file.

Therefore, through a workflow consisting of both MM and SSE, a holistic representation of vessel curvature in 3D space can be visualized both quickly and accurately. The level of detailed curvature as seen through these methods is something previously unreproducible in traditional outline-based geometric morphometrics. In the following section, these methods are applied to archaeological samples to express fully how MM may elucidate previously unrecognized patterns of curvature in pottery forms.

4. Results

4.1. Orientation methods

A point of concern when conducting MM analysis is which orientation method is chosen at the beginning of the workflow. Depending on the balance of the vessel on the base or the degree of curvature of the lip, deciding how to orientate the vessel in CloudCompare needs to be decided carefully. In the present study, base orientation is utilized as the main method of orientation, as some samples have only partial lip regions. Furthermore, all samples chosen have clay slab bases, which are well adjusted to the main body in a way that does not result in major balance issues. Vessel T1 from the sample set is outlined below, along with a summary of the minute differences between the orientation of the lip and base in both MM and SSE (Figures 13, 14).

Two MM outputs, oriented from the base and the lip
Figure 13 

Morphometric mapping of sample T1. A: Base orientation; B: Lip orientation.

Two SSE outputs, oriented from the base and the lip
Figure 14 

Sliced segmental extraction of sample T1. A: Base orientation; B: Lip orientation.

As seen in Figures 13 and 14, the morphological differences between the extracted curvature using the base- and lip-orientation methods are minimal at best. Most obvious is the position of each region of morphological interest; this arises from the fact that no morphologically homologous point exists from which to begin the unrolling process. As a result, unrolling cuts the cloud in different positions unless predetermined by the user. Despite this, from which point the unrolling process begins does not affect the outcome of the MM results in any way. It can be concluded that either through base or lip orientation, the results will be almost completely the same. As previously mentioned, all the samples utilized in this study have well-preserved base regions, and as such, are oriented from the base.

4.2. Full MM and SSE

Full MM and SSE outputs for each of the nine samples utilized in this study are shown below. A short description of each output can also be found beneath each figure, and a final summary of the results is compiled at the end of the results section for reference. Output descriptions are categorized based on morphometric positions on the vessel. In this example, six regions of important morphology (i.e., lip, neck, upper body, mid body, lower body, and base) are outlined (Figure 15).

Pot line drawing and SSE output with lines delineating regions
Figure 15 

Six categorical regions of morphological importance on example vessels; descriptions of morphometric mapping are organized based on these six regions. A: Six morphological regions overlaid on a 2D line drawing of an example vessel; B: Six morphological regions overlaid on morphometric mapping.

The lip region of vessels generally showed one region of outward curvature that was, in turn, aligned with outward curvature of the neck region. This alignment with similar patterns on the neck region fits well with the common understanding that the upper half of vessels during this period was attached after the base and the lower half of the pot was created and slightly dried (Koudaigakukyoukai 2014). Within the one region of outward curvature, vessels with a wider area of slight curvature and those with a smaller region of extreme curvature were also present.

The neck region in general aligns with lip curvature and tends to have a strong central point of curvature with bended “tails” that level out to a wide area of slightly bent clay closest to the connecting point between the lip/neck and body regions. The only example of multiple areas of curvature in this study is in sample T6 (Figure 21), where a region of inward curvature bisects two areas of curvature aligned above two similar regions on the mid body. Furthermore, the connecting region between the neck and body also shows clear delineation, further extrapolating the notion that the neck and body regions were created separately, rather than as one smoothed entity.

The upper body begins to show a higher degree of variance in a number of regions of outward curvature, as well as the alignment of these regions to other areas of curvature on the vessel. As shown in Figure 2, the upper/mid body is understood to be formed at the same time as the lower body, but is typically built from a separate clay slab. As a result, the curvature of this region may show slightly disconnected alignment to that of, for example, the widest point of the vessel in the mid body. For example, sample T4 (Figure 19) shows upper body curvature aligned with regions of outward curvature on the midsection of the pot, but sample T1 (Figure 16) shows two regions of upper body curvature, with the stronger region of curvature being unaligned to the strongest region of mid-body curvature. In this way, due to the varying degrees of alignment and unalignment, the shaping process of the upper body cannot be shown clearly using this method.

MM/SSE outputs and summary table by pot region (T1)
Figure 16 

Sample T1 MM and SSE output.

The mid body is the region that has clearly identifiable patterns of vessel curvature. Utilizing SSE, it becomes clear that much of the vessel curvature is aligned to these mid-body curvature patterns, which may hold valuable clues related to the production process, especially the action of vessel wall smoothing. For example, while sample T1 (Figure 16) possesses one main region of outward curvature, other samples such as T5 (Figure 20), T6 (Figure 21), T2 (Figure 17), T2 (Figure 18), and T7 (Figure 22) contain two areas of curvature situated on what would be opposite sides of the 3D vessel (in turn, creating a body shape more akin to an oval rather than the preferred rounded style of this period). On the other hand, sample T9 (Figure 24) has a rather even mid-body curvature, with only several small regions of slight outward curvature along a relatively horizontally aligned plane. Through the patterns of the mid body, the general shape of the body becomes clearly delineated between that of an oblong or oval shape, and that closer to the intended round shape.

MM/SSE outputs and summary table by pot region (T2)
Figure 17 

Sample T2 MM and SSE output.

MM/SSE outputs and summary table by pot region (T3)
Figure 18 

Sample T3 MM and SSE output.

MM/SSE outputs and summary table by pot region (T4)
Figure 19 

Sample T4 MM and SSE output.

MM/SSE outputs and summary table by pot region (T5)
Figure 20 

Sample T5 MM and SSE output.

MM/SSE outputs and summary table by pot region (T6)
Figure 21 

Sample T6 MM and SSE output.

MM/SSE outputs and summary table by pot region (T7)
Figure 22 

Sample T7 MM and SSE output.

The lower body more often (compared with the upper body) clearly aligns with the curvature of the mid-body regions of the samples. Whereas no samples show extreme misalignment between the lower and mid body, some samples, such as T8 (Figure 23), show alignment to only one area. In general, the lower body seems to possess only one wide region of aligned outward curvature, which reaffirms the notion that the lower and mid body were created at the same time.

MM/SSE outputs and summary table by pot region (T8)
Figure 23 

Sample T8 MM and SSE output.

MM/SSE outputs and summary table by pot region (T9)
Figure 24 

Sample T9 MM and SSE output.

The base in general only has one region of outward curvature, and in most examples, is not clearly aligned to the curvature of the lower body of the vessels.

5. Discussion

This case study has comprehensively outlined the potential benefits of 3D MM (and SSE) for the elucidation of intra-vessel variance of form (curvature), and in doing so, suggests the possibility of 3D data analysis in ceramic studies. While other methods of morphometric study involving vessel shape (such as 2D outline-based geometric morphometrics) may successfully elucidate whether a group of vessels is standardized, these 2D techniques inevitably fall short of visualizing more complex variance in vessel forms that may be connected to notions of differential tool usage or idiosyncrasies during the morphogenesis process (Gandon et al. 2020). The results shown above suggest that MM may be a reliable method for visualizing the stages of production in vessels that are formed and dried at differing intervals. Furthermore, positioning/alignment of outward/inward curvature on the vessel surface may help elucidate the idiosyncratic motor skills acquired during the social learning process.

The curvature details in both normal MM and SSE, which have yet to be clearly understood in other morphometric analyses, could lead to interesting results in the comparison of multiple types of pottery styles. However, even more importantly, they could possess the potential to bridge the gap between archaeology and modern ethnoarchaeological ceramic studies in regard to the elucidation of individual craftsperson styles within standardized pottery production contexts. Through a combination of detailed 3D MM, anthropological craft theory, geometric morphometrics, and ethnoarchaeological studies, clear visualization of the social learning process in craft production may soon be achievable.

6. Conclusion and Future Potential

This study focused solely on the potential of visualizing ceramic curvature using MM; however, notions of quantification in MM remain unclear. In future endeavors, the quantification of the curvature patterns shown above should be systematically applied in two ways: 1) A scoring/attribute system, and 2) GMM analysis of 3D contours.

6.1. Scoring/attribute system

As shown in the above results, several reoccurring curvature patterns in each section of the example vessels became clear through MM. For example, clearly delineated patterns in the mid-body section show the general shape of the body (i.e., two areas of outward curvature on opposite sides of the vessel should result in a more oblong-shaped body, whereas a vessel with relatively similar curvature patterns should result in a more evenly rounded body), and in turn, may suggest the differential skill levels of potters, tool usage, sitting position, etc. After collecting a sufficiently wide range of samples, these visual patterns may be extracted and categorized into a scoring system consisting of different “types” of curvature patterns for each region of the vessel. Figure 25 exemplifies a potential “scoring” method (i.e., creating a typology) for mid-body curvature patterns, with type 1 and type 2 curvature patterns expressed visually and in writing. Creating a scoring system for all regions of ceramic vessels and eventually comparing them in a matrix-type analysis may clarify the general methods of pottery formation in a more quantifiable way.

Photo & line drawings of two types of mid-body curvature
Figure 25 

Example of a potential scoring system for mid-body region curvature patterns.

6.2. Outline-based GMM on contours

As briefly discussed in section 3.3.7, the extraction of contour lines of any region on ceramic vessels is possible through 3D means. As such, regions of particular morphological importance may be expressed through a combination of MM and the use of these contours. As contour lines are a 2D representation of curvature, it is possible to apply open, outline-based geometric morphometrics to quantify these specific regions, in contrast to the traditional method of analyzing only one face of a 3D vessel. While these contours may be taken without the use of MM, as shown in this study, applying MM to clarify regions of curvature and then extracting the contours of these specific regions would certainly lead to a level of quantification of form not yet seen in modern analyses of ceramics.

Additional File

The additional file for this article can be found as follows:

Supplementary Figures

Figure 1 to 3. DOI: https://doi.org/10.5334/jcaa.89.s1

Funding Information

This work was supported under the Japan Society for the Promotion of Science (JSPS) Research Fellowship for Young Scientists Program (Grant No. 19J21494) and the Ministry of Education, Culture, Sports, Science and Technology (MEXT) KAKENHI (Grant No. JP19H05737).

Competing Interests

The authors have no competing interests to declare.

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