Pottery Analysis using Mathematical and Computational tools

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Ayelet Gilboa • Avshalom Karasik Ilan Sharon Uzy Smilansky Pottery Analysis using Mathematical and Computational tools

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Pottery Analysis using Mathematical and Computational tools. Ayelet Gilboa Avshalom Karasik Ilan Sharon Uzy Smilansky. Drawbacks of Traditional Typology. The traditional methods used for pottery description, typology and classification, are subjective and qualitative. - PowerPoint PPT Presentation

Transcript of Pottery Analysis using Mathematical and Computational tools

Page 1: Pottery Analysis using Mathematical and Computational tools

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

Pottery Analysis using Mathematical and Computational tools

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Page 2: Pottery Analysis using Mathematical and Computational tools

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.

Page 3: Pottery Analysis using Mathematical and Computational tools

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.

Page 4: Pottery Analysis using Mathematical and Computational tools

Acquisition of the Data

Page 5: Pottery Analysis using Mathematical and Computational tools

Acquisition of the Data

Curvature function computation

Original vesselOriginal vessel

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Curvature Function Computation

ds

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•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 sof the tangent at the point s:

k is positive at convex sections and negative at concave sections.

Page 7: Pottery Analysis using Mathematical and Computational tools

The curvature as a function of the arc-lengthAlternatively, the curvature is the (signed) inverse of the

radius of the osculating circle.

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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.

Page 11: Pottery Analysis using Mathematical and Computational tools

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.

Page 13: Pottery Analysis using Mathematical and Computational tools

A prototype generated as a mean of two rims.

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Rim no. 1 from Tell Dor

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Rim no. 12 from Tell Dor

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The mean of the 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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Dor "smooth type"

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Virtual evolution of the rims, from “complex” to “smooth”.

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Transition from smooth type to complex type

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Iron IaIron IbIron I/IIIron IIa

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Bowls distribution by periods, along the ‘complex-smooth’ axis.

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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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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 .

Hazor – Tyre “torpedo” storage jars

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Hazor / Tyre colored matrix of correlations

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Hazor / Tyre “tree” of correlationscorrelation

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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 Tyre’s 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 1) Every drawing includes interpretation of the artist.

Different drawers emphasize different features.

2) Many inaccuracies derive from the poor quality of the published drawings and from its small scale in the publications.

3) 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.