Ayelet Gilboa

1
Pottery Analysis using Mathematical and
Computational tools

• Ayelet Gilboa
• Avshalom Karasik
• Ilan Sharon
• Uzy Smilansky

2
Drawbacks of Traditional Typology

• The traditional methods used for pottery
  description, typology and classification, are
  subjective and qualitative.
• The huge amount of data in published
  archaeological reports renders impossible any
  exhaustive comparison of assemblages.

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Main Goals and Motivations

• To develop new objective and quantitative tools
  for morphological description, classification and
  analysis of archaeological artifacts.
• Considering the overwhelming abundance of data in
  the archaeological reports, we would like to
  implement comparative, typological analysis on a
  computer aided basis.

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Acquisition of the Data
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Acquisition of the Data
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Curvature Function Computation

• The curvature function k(s) provides the
  curvature k as a function of the arc-length s
  along the line.
• The curvature is the rate of change of the
  direction q (s) of the tangent at the point s

k is positive at convex sections and negative at
concave sections.
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The curvature as a function of the arc-length

• Alternatively, the curvature is the (signed)
  inverse of the radius of the osculating circle.

8

• 20

• 15

• 10

• 5

• 0

• -10

• -5

• 0

• 5

• 10

• 15

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A profile of a bowl and its graph of curvature.
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Why Curvature ?

• Efficiency - the most efficient and economic way
  to specify a planar curve is by its curvature,
  one variable describing two dimensional line.
• Invariance - the curvature holds all the
  information about the curve and it does not
  changes under translations or rotations.
• Uniqueness - the original curve and its curvature
  function are in one-to-one relation. Each can be
  uniquely and accurately reconstructed from the
  other.
• Archaeological relevance the curvature
  emphasizes features, which are relevant to the
  archaeological analysis such as rim, base,
  carination etc.

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Comparing Vessels

• The correlation between two curvature functions
  is defined in terms of the scalar product.
• The range of C is

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New Method for Defining Prototypes

• The fact that vessels are represented by
  numerical functions, enables us to calculate the
  mean of a group of vessels.
• One can define this mean as representing a
  prototype which is specified by the group.
• The mean vessel is virtual. However, we can
  plot it and compare it both visually and
  quantitatively to other real or virtual vessels.

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A prototype generated as a mean of two rims.
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Boring Bowls A Test Case

• The assemblage 87 Iron age I-IIa bowls from Tel
  Dor.
• Goal To test the hypothesis that there is a
  morphological development along the period, from
  a complex rim to a smooth one.

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Tel Dor prototypes
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Virtual evolution of the rims, from complex to
smooth.
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Bowls distribution by periods, along the
complex-smooth axis.
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Iron Ia
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Iron Ib
Iron I/II
8
Iron IIa
7
6
5
4
3
2
1
0
complex
smooth
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Hazor Tyre torpedo storage jars

• The assemblage 24 (Tyre) and 53 (Hazor) storage
  jars, which were the subject of several
  scientific articles .
• Goal To shed new light on this problematic
  issue, using our objective tool for ceramic
  comparison and classification.
• See Geva S. BASOR 248 Bikai P. BASOR 258
  Gilboa A. In QEDEM Reports 2.

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Hazor Tyre torpedo storage jars

• The procedure
• Step 1 scanning all the jars published in the
  respective excavation reports, and calculating
  their curvature functions.
• Step 2 computing the correlation matrix for the
  combined assemblage. It represents the
  correlation for every pair of jars
• Step 3 A cluster analysis of the correlation
  matrix reveals the inner structures of the
  assemblages, demonstrated on a cluster tree
  where distinct branches indicate well-segregated
  morphological types .

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Hazor / Tyre colored matrix of correlations
Hazor
Tyre
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Hazor / Tyre Possible Conclusions

• The lack of a significant typological overlap
  raises doubts about the claims that the 'torpedo'
  jars indicate commercial links between Hazor and
  Tyre.
• The higher inner similarities observed in the
  assemblage of Tyres jars supports the
  possibility that they were produced locally, by a
  workshop which follows a well defined tradition,
  as suggested by Bikai.
• In the Tyre assemblage there are three jars,
  which differ from the rest. These may possibly be
  of foreign origin.

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Problems and Inaccuracies

• Every drawing includes interpretation of the
  artist. Different drawers emphasize different
  features.
• Many inaccuracies derive from the poor quality of
  the published drawings and from its small scale
  in the publications.
• The pottery published in the archaeological
  reports is partial and therefore biased.

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Profile drawing from a 3D scanner
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Summary

• We have developed new methodological tool for
  typological analysis and classification.
• This objective and quantitative method has been
  proved to be archaeologically meaningful and even
  more sensitive than the human eye.
• A large digital database of ceramic drawings will
  enables automatic search for parallels.
• Modern devices such as 3D scanners have a great
  potential in the field of pottery analysis.