a computational framework for assembling pottery vessels presented by: stuart andrews the study of...
Post on 21-Dec-2015
215 Views
Preview:
TRANSCRIPT
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
2
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
A Computational Framework for Assembling Pottery Vessels
5
Goal
• A computational framework for sherd feature analysis
• An assembly strategy
To assemble pottery vessels automatically
A Computational Framework for Assembling Pottery Vessels
6
Challenges
• Integration of evidence
• Efficient search
• Modular and extensible system design
A Computational Framework for Assembling Pottery Vessels
7
Virtual Sherd Data
1. Scan physical sherds
2. Extract iso-surface
3. Segment break curves
4. Identify corners
5. Specify axis
A Computational Framework for Assembling Pottery Vessels
8
A Greedy Bottom-Up Assembly Strategy
Single sherds
A Computational Framework for Assembling Pottery Vessels
9
A Greedy Bottom-Up Assembly Strategy
PairsSingle sherds
A Computational Framework for Assembling Pottery Vessels
10
A Greedy Bottom-Up Assembly Strategy
Single sherds Pairs
A Computational Framework for Assembling Pottery Vessels
11
A Greedy Bottom-Up Assembly Strategy
TriplesSingle sherds Pairs
A Computational Framework for Assembling Pottery Vessels
12
A Greedy Bottom-Up Assembly Strategy
Single sherds Pairs Triples
A Computational Framework for Assembling Pottery Vessels
13
A Greedy Bottom-Up Assembly Strategy
Etc.
Single sherds Pairs Triples
A Computational Framework for Assembling Pottery Vessels
14
Overview
Generate Likely Pair-wise Matches
Generate Likely 3-Way Matches
… etc.
A Computational Framework for Assembling Pottery Vessels
15
Likely Pairs
• Match Proposals
• Match Likelihood Evaluations
Generate Likely Pair-wise Matches
A Computational Framework for Assembling Pottery Vessels
16
A Match
• A pair of sherds
• A relative placement of the sherds
A Computational Framework for Assembling Pottery Vessels
19
Match Likelihood Evaluations
• An evaluation returns the likelihood of a feature alignment
• Based on the notion of a residual
A Computational Framework for Assembling Pottery Vessels
20
Match Likelihood Evaluations
Axis Divergence
Feature: Axis of rotationResidual: Angle between axes
A Computational Framework for Assembling Pottery Vessels
21
Match Likelihood Evaluations
Axis Separation
Feature: Axis of rotationResidual: Distance between axes
A Computational Framework for Assembling Pottery Vessels
22
Match Likelihood Evaluations
Break-Curve Separation
Feature: Break-curveResiduals: Distance between
closest point pairs
A Computational Framework for Assembling Pottery Vessels
23
Match Likelihood Evaluations
Break-Curve Divergence
Feature: Break-curveResiduals: Angle between
tangents at closest point pairs
A Computational Framework for Assembling Pottery Vessels
24
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?
A Computational Framework for Assembling Pottery Vessels
25
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?
A Computational Framework for Assembling Pottery Vessels
26
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
A Computational Framework for Assembling Pottery Vessels
27
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
A Computational Framework for Assembling Pottery Vessels
28
Local Improvement of Match Likelihood
before after
A Computational Framework for Assembling Pottery Vessels
30
Pair-wise Match Results SummaryCorrect Matches Incorrect Matches
A Computational Framework for Assembling Pottery Vessels
31
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!!
A Computational Framework for Assembling Pottery Vessels
32
Overview
Generate Likely Pair-wise Matches
Generate Likely 3-Way Matches
… etc.
A Computational Framework for Assembling Pottery Vessels
33
Likely Triples
• 3-Way Match Proposals
• 3-Way Match Likelihood Evaluations
Generate Likely 3-Way Matches
A Computational Framework for Assembling Pottery Vessels
34
3-Way Match Proposals
• Merge pairs with common sherd
+ =
A Computational Framework for Assembling Pottery Vessels
35
3-Way Match Likelihood Evaluation
• Feature alignments are measured 3-way
A Computational Framework for Assembling Pottery Vessels
37
3-Way Match Results Summary
# of 3-way matches with correct match identified:
Top 1 3
Top 5 11
Top 10 17
Total 31
A Computational Framework for Assembling Pottery Vessels
38
Overview
Generate Likely Pair-wise Matches
Generate Likely 3-Way Matches
… etc.
A Computational Framework for Assembling Pottery Vessels
39
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
A Computational Framework for Assembling Pottery Vessels
41
Multiple Instance Learning
{True Pair / False Pair}
G(S)
S
A Computational Framework for Assembling Pottery Vessels
42
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.]
A Computational Framework for Assembling Pottery Vessels
43
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
A Computational Framework for Assembling Pottery Vessels
44
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
A Computational Framework for Assembling Pottery Vessels
45
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.
top related