a computational framework for assembling pottery vessels presented by: stuart andrews the study of...
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A Computational Framework for Assembling Pottery Vessels
Presented by: Stuart Andrews
The study of 3D shape with applications in archaeology
NSF/KDI grant #BCS-9980091
Advisor: David H. LaidlawCommittee: Thomas Hofmann
Pascal Van Hentenryck
A Computational Framework for Assembling Pottery Vessels
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Why should we try to automate pottery vessel assembly?
• Reconstructing pots is important
• Tedious and time consuminghours 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
• A computational framework for sherd feature analysis
• An assembly strategy
To assemble pottery vessels automatically
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Challenges
• Integration of evidence
• Efficient search
• Modular and extensible system design
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Virtual Sherd Data
1. Scan physical sherds
2. Extract iso-surface
3. Segment break curves
4. Identify corners
5. Specify axis
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A Greedy Bottom-Up Assembly Strategy
Single sherds
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A Greedy Bottom-Up Assembly Strategy
PairsSingle sherds
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A Greedy Bottom-Up Assembly Strategy
Single sherds Pairs
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A Greedy Bottom-Up Assembly Strategy
TriplesSingle 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
• Match Proposals
• Match Likelihood Evaluations
Generate Likely Pair-wise Matches
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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 rotationResidual: Angle between axes
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Match Likelihood Evaluations
Axis Separation
Feature: Axis of rotationResidual: Distance between axes
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Match Likelihood Evaluations
Break-Curve Separation
Feature: Break-curveResiduals: Distance between
closest point pairs
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Match Likelihood Evaluations
Break-Curve Divergence
Feature: Break-curveResiduals: Angle between
tangents at closest point pairs
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Match Likelihood Evaluations
• 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.
How likely are the measured residuals?
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Match Likelihood Evaluations
• We define the likelihood of the match using the probability of observing a larger ²random
Pr{ ²random > ²observed } = Q
• Individual or ensemble of features• Pair-wise, 3-Way or larger matches
How likely are the measured residuals?
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Example Match Likelihood Evaluation (1)
² n QAxis Direction
0.481 1 0.488
Axis Overlap
0.005 1 0.940
Closest Pt 6.964 11 0.802
Tangent 18.720 11 0.066
Ensemble 6.423 8 0.599
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Example Match Likelihood Evaluation (2)
² n QAxis Direction
26.352 1 2.845e-7
Axis Overlap
1.384 1 0.239
Closest Pt 31.313 12 0.002
Tangent 11.924 12 0.452
Ensemble 40.161 8 2.990e-6
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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 SummaryCorrect Matches Incorrect Matches
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Pair-wise Match Results Summary
# of pairs with correct match identified:
Top 1 9
Top 2 17
Top 3 20
Total 26Q=1 decreasing likelihood Q=0
True Pair
Proposed matches
…
Correct match
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
• 3-Way Match Proposals
• 3-Way Match Likelihood Evaluations
Generate Likely 3-Way Matches
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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:
Top 1 3
Top 5 11
Top 10 17
Total 31
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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
{True Pair / False Pair}
G(S)
S
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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
1. D. Cooper et al. VAST 2001.
2. da Gama Leito et al. Universidade Fedral Fluminense 1998.
3. A.D. Jepson et al. ICCV 1999.
4. G.A. Keim et al. AAAI / IAAI, 1999.
5. S. Pankanti et al. Michigan State, 1994.
6. G. Papaioannou et al. IEEE Computer Graphics and Applications, 2001.
7. G. Ucoluk et al. Computers & Graphics, 1999.
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Results For Discussion
Q
Q
count
count
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Results For Discussion
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Results For Discussion