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This research aims to automate the assembly of pottery vessels using a computational framework, addressing challenges in evidence integration, search efficiency, and system design. Virtual sherds are scanned, analyzed, and matched to reconstruct vessels efficiently. Match likelihood evaluations are based on features such as corner alignment and break-curve analysis. The study focuses on generating accurate pair-wise and 3-way matches to improve the accuracy of vessel assembly.
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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
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 A Computational Framework for Assembling Pottery Vessels
Statement of Problem A Computational Framework for Assembling Pottery Vessels
Statement of Problem A Computational Framework for Assembling Pottery Vessels
Goal To assemble pottery vessels automatically • A computational framework for sherd feature analysis • An assembly strategy A Computational Framework for Assembling Pottery Vessels
Challenges • Integration of evidence • Efficient search • Modular and extensible system design A Computational Framework for Assembling Pottery Vessels
Virtual Sherd Data • Scan physical sherds • Extract iso-surface • Segment break curves • Identify corners • Specify axis A Computational Framework for Assembling Pottery Vessels
A Greedy Bottom-Up Assembly Strategy Single sherds A Computational Framework for Assembling Pottery Vessels
A Greedy Bottom-Up Assembly Strategy Single sherds Pairs A Computational Framework for Assembling Pottery Vessels
A Greedy Bottom-Up Assembly Strategy Single sherds Pairs A Computational Framework for Assembling Pottery Vessels
A Greedy Bottom-Up Assembly Strategy Single sherds Pairs Triples A Computational Framework for Assembling Pottery Vessels
A Greedy Bottom-Up Assembly Strategy Single sherds Pairs Triples A Computational Framework for Assembling Pottery Vessels
A Greedy Bottom-Up Assembly Strategy Etc. Single sherds Pairs Triples A Computational Framework for Assembling Pottery Vessels
Overview Generate Likely Pair-wise Matches Generate Likely 3-Way Matches … etc. A Computational Framework for Assembling Pottery Vessels
Likely Pairs Generate Likely Pair-wise Matches • Match Proposals • Match Likelihood Evaluations A Computational Framework for Assembling Pottery Vessels
A Match • A pair of sherds • A relative placement of the sherds A Computational Framework for Assembling Pottery Vessels
Corner Alignment Match Proposals A Computational Framework for Assembling Pottery Vessels
Example Corner Alignments A Computational Framework for Assembling Pottery Vessels
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
Axis Divergence Feature: Axis of rotation Residual: Angle between axes Match Likelihood Evaluations A Computational Framework for Assembling Pottery Vessels
Axis Separation Feature: Axis of rotation Residual: Distance between axes Match Likelihood Evaluations A Computational Framework for Assembling Pottery Vessels
Break-Curve Separation Feature: Break-curve Residuals: Distance between closest point pairs Match Likelihood Evaluations A Computational Framework for Assembling Pottery Vessels
Break-Curve Divergence Feature: Break-curve Residuals: Angle between tangents at closest point pairs Match Likelihood Evaluations A Computational Framework for Assembling Pottery Vessels
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. A Computational Framework for Assembling Pottery Vessels
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 > ²observed } = Q • Individual or ensemble of features • Pair-wise, 3-Way or larger matches A Computational Framework for Assembling Pottery Vessels
Example Match Likelihood Evaluation (1) A Computational Framework for Assembling Pottery Vessels
Example Match Likelihood Evaluation (2) A Computational Framework for Assembling Pottery Vessels
Local Improvement of Match Likelihood before after A Computational Framework for Assembling Pottery Vessels
Pair-wise Match Results Summary ?? A Computational Framework for Assembling Pottery Vessels
Pair-wise Match Results Summary Correct Matches Incorrect Matches A Computational Framework for Assembling Pottery Vessels
Pair-wise Match Results Summary # of pairs with correct match identified: Proposed matches Correct match True Pair … Q=1 decreasing likelihood Q=0 There is no correct match for the remaining 94 pairs!! A Computational Framework for Assembling Pottery Vessels
Overview Generate Likely Pair-wise Matches Generate Likely 3-Way Matches … etc. A Computational Framework for Assembling Pottery Vessels
Likely Triples Generate Likely 3-Way Matches • 3-Way Match Proposals • 3-Way Match Likelihood Evaluations A Computational Framework for Assembling Pottery Vessels
3-Way Match Proposals • Merge pairs with common sherd + = A Computational Framework for Assembling Pottery Vessels
3-Way Match Likelihood Evaluation • Feature alignments are measured 3-way A Computational Framework for Assembling Pottery Vessels
3-Way Match Results Summary A Computational Framework for Assembling Pottery Vessels
3-Way Match Results Summary # of 3-way matches with correct match identified: A Computational Framework for Assembling Pottery Vessels
Overview Generate Likely Pair-wise Matches Generate Likely 3-Way Matches … etc. A Computational Framework for Assembling Pottery Vessels
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
S A Computational Framework for Assembling Pottery Vessels
Multiple Instance Learning S G(S) {True Pair / False Pair} A Computational Framework for Assembling Pottery Vessels
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
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
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
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. A Computational Framework for Assembling Pottery Vessels
Results For Discussion count Q count Q A Computational Framework for Assembling Pottery Vessels
Results For Discussion A Computational Framework for Assembling Pottery Vessels
Results For Discussion A Computational Framework for Assembling Pottery Vessels