Instructions for users of the module 'Capacity' Avshalom Karasik, Noam Peled and Uzy Smilansky Department of Physics of Complex Systems The Weizmann Institute of Science, Rehovot 76100, Israel.

The module 'Capacity' is intended for archaeologists who wish to compute the capacity (volume) of vessels with complete profile. The vessels are assumed to be axially symmetric so that a single profile (section) provides the entire information needed to compute the volume. The computation is based on profiles drawn according to the standard conventions in Archaeological reports (see figure 1).

Figure 1: A typical drawing of an axially symmetric bowl.

For each vessel, the program computes three values: 1. The net capacity (to the rim). 2. Volume of the body material. 3. Effective volume - up to the neck (when the neck exists). Their exact definitions will be provided in the sequel. To use the ‘Capacity’ module you have to scan your drawings, and reduce them to the ‘Capacity’ input format as explained in sections B-E. Section G gives a concise list of the steps which have to be followed. The algorithm used for the computations as well as a discussion of the main sources of possible inaccuracies and uncertainties are given in section F. The method was first described in: Karasik, A. and U. Smilansky (2006). ‘Computation of the Capacity of Pottery Vessels Based on Drawn Profiles’. In: Mazar, A. (ed.), Excavations at Tel Beth Shean 1989 -1996, vol. I. Appendix 1A to Chapter 12. (Jerusalem). Important note: We released this module after having checked it to our satisfaction. We cannot exclude, however, the possibility that some errors remain. In case you encountered an error, please inform us by sending a detailed description of the problem. We shall be obliged for any feedback, and in particular suggestions, comments, and, if possible, a short description of your particular project. Contact e-address: [email protected] .

A. Download and install the module ‘capacity’ A.1 Download the folder 'capacity.zip' into your computer and extract the files into one folder. You should have the files: 1) volumes.exe

2) volumes.ctf

4) sample1.jpg

5) sample2.jpg

3) scale.txt

A.2 If you have MATLAB 7.1 (or a more advanced issue) on your computer, the installation is finished. Go to A.4. A.3 If you do not have MATLAB 7.1 then you should download and install also the file 'MCRInstaller.exe'. However, we are not legally aloud to distribute this file on the web, only directly to the users. Please inform us that you wish to use the module 'capacity' and we shall send you a username and password. The 'MCRInstaller.exe' will install some necessary files that are used by the main program. A.4 The program is now ready to run. If this is the first time you run this module, double click on the icon 'volumes.exe'. This is a sample run, in which the program will provide the capacities of the vessels whose images are in the files 'sample1.jpg' and 'sample2.jpg'. Obtaining the correct results (see the appendix to the present document) indicates that you are ready to use ‘capacity’ on your vessels. For this purpose you have to replace the files sample1.jpg and sample2.jpg with 'jpg' files in which the drawings of your vessels are prepared as per the instructions in the following sections. Once you are ready, double click 'volumes.exe' and the program will evaluate your files.

Make sure that your images are well prepared and that the scale is accurate (see next sections).

B. Modify the drawings to the ‘capacity’ input format. Before proceeding any further, please study figure 2 which describes the stages that lead from the original drawing (1) to the 'capacity' input format (4). The scanned file can be modified by Photoshop or any similar software.

1. Scan the original drawing 2. Delete irrelevant data

4. Crop the image to the relevant size and delete the vertical line at the bottom 3. Transfer the profile to one pixel width and keep the highest pixel of the rotation axis

Figure 2: The stages from the original drawing to the 'Capacity' format.

First stage ((1) Æ (2)): Change your image into black and white mode and delete all the details which do not pertain to the section and the symmetry axis (vertical line). In some drawings, the horizontal lines (rim line, carination lines, etc.) touch the sections. When deleting them, take care to leave the boundary of the section as smooth as possible. Second stage ((2) Æ (3)): a. Keep only the upper pixel of the symmetry (vertical) line and delete the rest. b. Extract the boundary line of the section. The thickness of the boundary line should be 1 pixel only. If you use 'Photoshop' the extraction of the boundary can be done by: b.1 Choose the black profile using the 'magic wand' tool, first make sure that you have marked the option 'contiguous' at the top. b.2 Go to 'Select' menu —> 'modify' —> 'contract' —> 1 pixels, and then press 'delete'. Third stage ((3) Æ (4)): a. Remove any remaining parts of the drawing (such as handles or spouts). b. Delete the vertical line that remained at the bottom left of the profile.

c. Crop the image leaving the relevant part in it. d. Store the resulting file as a 'jpg' file in the ‘Capacity’ folder. The number of input files is unlimited. Refrain from using the same name for different files. Observe: - Sometimes, due to improper positioning of the original page on the scanner, the scanned image is not exactly aligned with respect to the page. The correct alignment can be restored if the uppermost pixel on the symmetry line is recognized. This is why stage a. above is essential. - The contour of the profile should be one pixel thick. Deviations may introduce errors in the computation or even interrupt the program.

C. Insert the metric length scale The metric length scale of an image gives the length (in millimeters) that every pixel represents in the actual vessel. Using this number, ‘Capacity’ converts the computed volumes and expresses them in liters (1 liter = 106 mm3). The scale (in units of mm/pixel) should be written in the file scale.txt in the ‘Capacity’ input folder. This is a simple text file in which you should write only the number without the units.

NOTE: The ‘Capacity’ input folder may consist of several input files as described above. It is assumed that all of them have the same scale. Thus, for each batch of scanned drawings which share the same scale, you have to prepare a ‘Capacity’ input folder. Examples: a. If the original drawings were drawn to scale (1:1 ratio), and you have scanned them with 600 dpi, then the pixel size is:

25.4 = 0.04233 mm. (1 Inch = 25.4 mm) 600

b. If the original drawings were reduced by 2:5 ratio and you have scanned them with 300 dpi, then the pixel size is

25.4 5 ⋅ = 0.2167 mm. 300 2

c. Another way to calculate the size that one pixel represents in the real vessel, is to scan the scale of the drawing and to count how many pixels are in the scanned scale. Notice that you must use the same scanning resolution.

For instance, in figure 2 the scale of 10cm has 473 pixels along its length. Therefore the scale per pixel is

100 = 0.2114 mm. 473

D. Running ‘Capacity’ and the meaning of its output Before you start, make sure that the correct scale is inserted in the file 'scale.txt', and that all the images in a single ‘Capacity’ input folder have the same scale. Start the program by double click on the icon 'volumes.exe'. All the 'jpg' files which are in the folder will be analyzed sequentially. The results will be kept in a new file 'results.htm' and a new folder ‘neck’. The file 'results.htm' consists of a list of three values per vessel (Figure 4). 4. The net capacity. 5. Volume of the body material. 6. Effective volume-up to the neck. Explanations: The net capacity is the volume of the inner part of the vessel from top to bottom. The volume of the body material is the volume of the fabric and it is proportional to the weight of the vessel. By adding it to the net capacity one gets the exterior volume that determines the total space which is occupied by the vessel. The effective volume is useful only for close containers with narrow neck, such as storage jars, and it gives the volume of the vessel up to a level which the program determines as the beginning of the neck. The algorithm which defines the neck may not coincide with your criteria, and deviations may occur especially when the vessels have complex shapes. You are able to observe the neck level in the output folder of images - 'neck' -, in which the neck of every vessel is colored with red. Vessel name a220422 a210133 a22 a220180 a220263 a220329 a220335

Net capacity 207.8663 48.8151 14.0758 77.8421 52.7013 279.0769 33.0918

volume of the body material 90.0566 21.5822 11.6423 39.2516 19.4783 96.3594 16.5082

Effective volume - up to the neck 196.4615 46.0427 12.7878 77.6792 52.0995 247.7048 32.4276

Figure 4. An example of an output file.

E. Checklist 1.

Download the file capacity.zip' and extract the files into one folder.

2.

If you do not have MATLAB 7.1 (or a later issue) on your computer, you should ask us for the 'MCRInstaller.exe' and install it.

3.

Prepare your images so that only the contour of the profile and the highest pixel of the symmetry axis will remain in each image.

4.

Make sure that all the images have the same scale. Compute this scale and write it down in the file 'scale.txt'.

5.

Copy the prepared images into the same folder of the program as jpg files.

6.

Run the program 'volumes.exe'

7.

The computed volumes appear in the file 'results.htm'

8.

Check the definitions of the necks in the folder 'neck'.

F. Details about the algorithm from: Karasik, A. and U. Smilansky (2006). ‘Computation of the Capacity of Pottery Vessels Based on Drawn Profiles’. In: Mazar, A. (ed.), Excavations at Tel Beth Shean 1989 -1996, vol. I. Appendix 1A to Chapter 12. (Jerusalem). The capacity (volume) of pottery vessels is of great significance for understanding the possible uses of the vessels and the emergence of standard systems of units, inter alia. Direct measurement of volume using granular or liquid materials is time-consuming and can only be applied to whole vessels. However, capacity can also be computed from the drawings of the pottery profiles, provided the profiles are complete and the drawings represent vessels with interiors that are surfaces of revolution (see, e.g., Louise and Dunbar 1995). The method is based on the observation that the threedimensional vessel can be reconstructed from its profile by revolving it around the axis of rotation. The interior of the profile can be defined as the part of the profile that starts at the center of the interior bottom (the point marked 0 in Fig. 5) and ends at the rim top (the point marked t in Fig. 5). The volume enclosed by the interior surface is the capacity, which can be computed by means of a well-known formula explained below. In antiquity, vessels might not have been filled up to the rim—some empty space was left to avoid spilling (e.g., bottle necks) or for seals or corks. Consequently,

we wished to determine volumes up to a prescribed level of filling. We computed the effective capacity by defining the level of filling as the starting point of the neck (the point marked f in Fig. 5). This was determined as the point of maximum negative curvature in the interior (for the curvature function, see Gilboa et al. 2004; Saragusti et al. 2005). The exterior volume that determines, for example, the number of vessels that can be stored in a given space—such as a storage room or a ship’s hull—is also of interest. This can be computed from the exterior part of the profile (see Figure 5). The difference between the exterior and the interior volumes is the volume of the fabric itself. This volume is proportional to the weight of the vessel, and may be pertinent to the study of the technological aspects of ancient ceramics manufacture. In practice, the drawings that appear in the archaeological report were scanned with a simple scanner at a resolution of 300 dpi. The smoothed contours of the vessels were extracted using the procedure described in Karasik 2003, and four volumes were computed for each vessel: the interior and the exterior volumes up to the rim, the effective capacity up to the neck, and the volume of the fabric. The procedure is efficient and reliable, and the only relatively time-consuming stage of the work is the scanning process. The main sources of inaccuracy and uncertainty in this method of computing capacity result from the following two factors: 1. Inaccurate rendering of the vessel profile, especially when it is hand-drawn. This can be overcome by measuring the profile using a profilograph or a 3-d scanning camera (Sablatnig and Menard 1996; Leymarie et al. 2001; Razdan et al. 2001). 2. Deformation of the original vessel, which invalidates the assumption that a single profile represents the entire shape. Finally, the computer algorithm extracts for each point on the contour its distance r from the axis of symmetry, its height h measured from the horizontal basis plain, and the arc length s traversed from the lowest point on the contour of interest (e.g., 0 for the interior part) to the point of interest. Once the entire contour is traversed, the height and distance from the axis are determined as functions of the arc length, and denoted by h(s) and r(s), respectively. If we denote the arc length to the filling point by f, the volume is expressed as: f

Volume = π ∫ [ r ( s )]2 0

dy ds ds

This slightly more general form of the standard formula (see e.g., Gray 1997) is used because ceramic profiles are often not simple in the sense that r is not a single valued function of y.

t

Axis of rotation Exterior profile Neck profile Interior profile (effective volume)

f

0

Figure 5: Profile of a ceramic vessel showing sections used in the various volume computations

Bibliography

Gilboa, A., et al. 2004. Towards Computerized Typology and Classification of Ceramics. Journal of Archaeological Science 31/6: 681–94. Gray, A. 1997. Surfaces of Revolution. Ch. 20 in Modern Differential Geometry of Curves and Surfaces with Mathematica (2nd ed.). Boca Raton, FL. Karasik, A. 2003. Mathematical Methods and Computer Applications in the Classification and Typology of Pottery. Unpublished M.A. thesis, Hebrew University of Jerusalem (Hebrew).

Leymarie, F., et al. 2001. The SHAPE Lab.—New Technology and Software for Archaeologists. Pp. 79–89 in Stancic, Z. and Veljanovski, T. (eds.), Computing Archaeology for Understanding the Past CAA2000. Computer Applications and Quantitative Methods in Archaeology (BAR Int. Ser. 931). Oxford.. Louise, M. S. and Dunbar, P.B. 1995. Accurately Estimating Vessel Volume from Profile Illustrations. American Antiquity 60/2: 319–34. Razdan, A., et al. 2001. Using Geometric Modeling for Archiving and Searching 3D Archaeological Vessels. Paper presented at the International Conference on Imaging Science, Systems, and Technology, Las Vegas. Sablatnig, R. and Menard, C. 1996. Computer-based Acquisition of Archaeological Finds: The First Step towards Automatic Classification. Paper presented at the the 3rd International Symposium on Computing and Archaeology, Rome. Saragusti, I., et al. 2005. Quantitative Analysis of Shape Attributes Based on Contours and Section Profiles in Archaeological Research. Journal of Archaeological Science 32/6: 841–53.

Appendix 1. The following table describes the expected results for the two sample vessels. If your test run gives the same results, then the module 'capacity' was well installed and it is ready to run on your data. Vessel name Net capacity volume of the body material Effective volume - up to the neck sample1 1.9177 0.64535 1.7923 sample2 14.455 2.3696 14.4092 2. The next two figures shows the definitions of the necks for the two sample files as were defined by the program.