A Computational Framework for Assembling Pottery Vessels

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A Computational Framework for Assembling Pottery
Vessels

• Presented by Stuart Andrews

Advisor David H. Laidlaw
Committee Thomas Hofmann
Pascal Van Hentenryck
The study of 3D shape with applications in
archaeology NSF/KDI grant BCS-9980091
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Why should we try to automate pottery vessel
assembly?

• Reconstructing pots is important
• Tedious and time consuming
• hours ? days per pot, 50 of on-site time
• Virtual artifact database

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Statement of Problem
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Statement of Problem
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Goal
To assemble pottery vessels automatically

• A computational framework for sherd feature
  analysis
• An assembly strategy

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Challenges

• Integration of evidence
• Efficient search
• Modular and extensible system design

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Virtual Sherd Data

• Scan physical sherds
• Extract iso-surface
• Segment break curves
• Identify corners
• Specify axis

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A Greedy Bottom-Up Assembly Strategy
Single sherds
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A Greedy Bottom-Up Assembly Strategy
Pairs
Single sherds
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A Greedy Bottom-Up Assembly Strategy
Single sherds
Pairs
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A Greedy Bottom-Up Assembly Strategy
Triples
Single sherds
Pairs
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A Greedy Bottom-Up Assembly Strategy
Single sherds
Pairs
Triples
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A Greedy Bottom-Up Assembly Strategy
Etc.
Single sherds
Pairs
Triples
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Overview
Generate Likely Pair-wise Matches
Generate Likely 3-Way Matches
etc.
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Likely Pairs
Generate Likely Pair-wise Matches

• Match Proposals
• Match Likelihood Evaluations

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A Match

• A pair of sherds
• A relative placement of the sherds

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Match Proposals

• Corner Alignment

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Example Corner Alignments
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Match Likelihood Evaluations

• An evaluation returns the likelihood of a feature
  alignment
• Based on the notion of a residual

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Match Likelihood Evaluations

• Axis Divergence
• Feature Axis of rotation
• Residual Angle between axes

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Match Likelihood Evaluations

• Axis Separation
• Feature Axis of rotation
• Residual Distance between axes

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Match Likelihood Evaluations

• Break-Curve Separation
• Feature Break-curve
• Residuals Distance between closest
  point pairs

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Match Likelihood Evaluations

• Break-Curve Divergence
• Feature Break-curve
• Residuals Angle between tangents at
  closest point pairs

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Match Likelihood Evaluations
How likely are the measured residuals?

• Fact Assuming the residuals N(0,1) i.i.d.,
  then we can form a Chi-square ?²observed
• Note Typically, residuals are N(0, ?2) i.i.d.

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Match Likelihood Evaluations
How likely are the measured residuals?

• We define the likelihood of the match using the
  probability of observing a larger ?²random
• Pr ?²random gt ?²observed Q
• Individual or ensemble of features
• Pair-wise, 3-Way or larger matches

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Example Match Likelihood Evaluation (1)
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Example Match Likelihood Evaluation (2)
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Local Improvement of Match Likelihood
before
after
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Pair-wise Match Results Summary
??
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Pair-wise Match Results Summary
Correct Matches
Incorrect Matches
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Pair-wise Match Results Summary
of pairs with correct match identified
Proposed matches
Correct match
True Pair

Q1 ? decreasing likelihood ?
Q0
There is no correct match for the remaining 94
pairs!!
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Overview
Generate Likely Pair-wise Matches
Generate Likely 3-Way Matches
etc.
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Likely Triples
Generate Likely 3-Way Matches

• 3-Way Match Proposals
• 3-Way Match Likelihood Evaluations

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3-Way Match Proposals

• Merge pairs with common sherd

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3-Way Match Likelihood Evaluation

• Feature alignments are measured 3-way

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3-Way Match Results Summary
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3-Way Match Results Summary
of 3-way matches with correct match identified
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Overview
Generate Likely Pair-wise Matches
Generate Likely 3-Way Matches
etc.
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Where to go from here?

• Improve quality of features and their comparisons
• Add new features and feature comparisons
• Use novel discriminative methods to classify true
  and false pairs

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S
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Multiple Instance Learning
S
G(S)
True Pair / False Pair
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Related Work

• Assembly systems that rely on single features
• U. Fedral Fluminense / Middle East Technical U.
  / U. of Athens
• Multiple features and parametric shape models
• The SHAPE Lab Brown U.
• Distributed systems for solving AI problems
• Toronto / Michigan State / Duke U.

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Contributions

• A computational framework based on match proposal
  and match likelihood evaluation
• A method for combining multiple features into one
  match likelihood
• A greedy assembly strategy

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Conclusions

• Reconstructing pottery vessels is difficult
• A unified framework for the statistical analysis
  of features is useful for building a complete
  working system
• Success requires better match likelihood
  evaluations and/or novel match discrimination
  methods

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References

• D. Cooper et al. VAST 2001.
• da Gama Leito et al. Universidade Fedral
  Fluminense 1998.
• A.D. Jepson et al. ICCV 1999.
• G.A. Keim et al. AAAI / IAAI, 1999.
• S. Pankanti et al. Michigan State, 1994.
• G. Papaioannou et al. IEEE Computer Graphics and
  Applications, 2001.
• G. Ucoluk et al. Computers Graphics, 1999.

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Results For Discussion
count
Q
count
Q
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Results For Discussion
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Results For Discussion