A Computational Framework for Assembling Pottery Vessels Presented by: Stuart Andrews The study of 3D shape with applications in archaeology NSF/KDI grant #BCS Advisor: David H. Laidlaw Committee: 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 consuming hours  days per pot, 50% of “on-site” time Virtual artifact database

A Computational Framework for Assembling Pottery Vessels 3 Statement of Problem

A Computational Framework for Assembling Pottery Vessels 4 Statement of Problem

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 sherdsPairs

A Computational Framework for Assembling Pottery Vessels 11 A Greedy Bottom-Up Assembly Strategy TriplesSingle sherdsPairs

A Computational Framework for Assembling Pottery Vessels 12 A Greedy Bottom-Up Assembly Strategy Single sherdsPairsTriples

A Computational Framework for Assembling Pottery Vessels 13 A Greedy Bottom-Up Assembly Strategy Etc. Single sherdsPairsTriples

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 17 Match Proposals Corner Alignment

A Computational Framework for Assembling Pottery Vessels 18 Example Corner Alignments

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 rotation Residual: Angle between axes

A Computational Framework for Assembling Pottery Vessels 21 Match Likelihood Evaluations Axis Separation Feature: Axis of rotation Residual: Distance between axes

A Computational Framework for Assembling Pottery Vessels 22 Match Likelihood Evaluations Break-Curve Separation Feature: Break-curve Residuals: Distance between closest point pairs

A Computational Framework for Assembling Pottery Vessels 23 Match Likelihood Evaluations Break-Curve Divergence Feature: Break-curve Residuals: 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:  ² observed 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  ² random Pr{  ² random >  ² observed } = 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² nQ Axis Direction Axis Overlap Closest Pt Tangent Ensemble

A Computational Framework for Assembling Pottery Vessels 27 Example Match Likelihood Evaluation (2) ²² nQ Axis Direction e-7 Axis Overlap Closest Pt Tangent Ensemble e-6

A Computational Framework for Assembling Pottery Vessels 28 Local Improvement of Match Likelihood beforeafter

A Computational Framework for Assembling Pottery Vessels 29 Pair-wise Match Results Summary ??

A Computational Framework for Assembling Pottery Vessels 30 Pair-wise Match Results Summary Correct Matches Incorrect Matches

A Computational Framework for Assembling Pottery Vessels 31 Pair-wise Match Results Summary # of pairs with correct match identified: Top 19 Top 217 Top 320 Total26 Q=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 36 3-Way Match Results Summary

A Computational Framework for Assembling Pottery Vessels 37 3-Way Match Results Summary # of 3-way matches with correct match identified: Top 13 Top 511 Top 1017 Total31

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 40 S

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

A Computational Framework for Assembling Pottery Vessels 46 Results For Discussion Q Q count

A Computational Framework for Assembling Pottery Vessels 47 Results For Discussion

A Computational Framework for Assembling Pottery Vessels 48 Results For Discussion