1. 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. Laidlaw Committee: Thomas Hofmann Pascal Van Hentenryck

2. 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

3. A Computational Framework for Assembling Pottery Vessels 3 Statement of Problem

4. A Computational Framework for Assembling Pottery Vessels 4 Statement of Problem

5. A Computational Framework for Assembling Pottery Vessels 5 Goal A computational framework for sherd feature analysis An assembly strategy To assemble pottery vessels automatically

6. A Computational Framework for Assembling Pottery Vessels 6 Challenges Integration of evidence Efficient search Modular and extensible system design

7. 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

8. A Computational Framework for Assembling Pottery Vessels 8 A Greedy Bottom-Up Assembly Strategy Single sherds

9. A Computational Framework for Assembling Pottery Vessels 9 A Greedy Bottom-Up Assembly Strategy PairsSingle sherds

10. A Computational Framework for Assembling Pottery Vessels 10 A Greedy Bottom-Up Assembly Strategy Single sherdsPairs

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

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

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

14. A Computational Framework for Assembling Pottery Vessels 14 Overview Generate Likely Pair-wise Matches Generate Likely 3-Way Matches … etc.

15. A Computational Framework for Assembling Pottery Vessels 15 Likely Pairs Match Proposals Match Likelihood Evaluations Generate Likely Pair-wise Matches

16. A Computational Framework for Assembling Pottery Vessels 16 A Match A pair of sherds A relative placement of the sherds

17. A Computational Framework for Assembling Pottery Vessels 17 Match Proposals Corner Alignment

18. A Computational Framework for Assembling Pottery Vessels 18 Example Corner Alignments

19. 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

20. A Computational Framework for Assembling Pottery Vessels 20 Match Likelihood Evaluations Axis Divergence Feature: Axis of rotation Residual: Angle between axes

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

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

23. 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

24. 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?

25. 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?

26. A Computational Framework for Assembling Pottery Vessels 26 Example Match Likelihood Evaluation (1) ²² nQ Axis Direction 0.48110.488 Axis Overlap 0.00510.940 Closest Pt6.964110.802 Tangent18.720110.066 Ensemble 6.42380.599

27. A Computational Framework for Assembling Pottery Vessels 27 Example Match Likelihood Evaluation (2) ²² nQ Axis Direction 26.35212.845e-7 Axis Overlap 1.38410.239 Closest Pt31.313120.002 Tangent11.924120.452 Ensemble 40.16182.990e-6

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

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

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

31. 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!!

32. A Computational Framework for Assembling Pottery Vessels 32 Overview Generate Likely Pair-wise Matches Generate Likely 3-Way Matches … etc.

33. A Computational Framework for Assembling Pottery Vessels 33 Likely Triples 3-Way Match Proposals 3-Way Match Likelihood Evaluations Generate Likely 3-Way Matches

34. A Computational Framework for Assembling Pottery Vessels 34 3-Way Match Proposals Merge pairs with common sherd +=

35. A Computational Framework for Assembling Pottery Vessels 35 3-Way Match Likelihood Evaluation Feature alignments are measured 3-way

36. A Computational Framework for Assembling Pottery Vessels 36 3-Way Match Results Summary

37. 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

38. A Computational Framework for Assembling Pottery Vessels 38 Overview Generate Likely Pair-wise Matches Generate Likely 3-Way Matches … etc.

39. 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

40. A Computational Framework for Assembling Pottery Vessels 40 S

41. A Computational Framework for Assembling Pottery Vessels 41 Multiple Instance Learning {True Pair / False Pair} G(S) S

42. 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.]

43. 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

44. 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

45. 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.

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

47. A Computational Framework for Assembling Pottery Vessels 47 Results For Discussion

48. A Computational Framework for Assembling Pottery Vessels 48 Results For Discussion