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 Members of the SHAPE Lab and the Department of Computer Science

2. Stuart Andrews, The SHAPE Lab, Brown University 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. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 3 Statement of Problem

4. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 4 Statement of Problem

5. Stuart Andrews, The SHAPE Lab, Brown University 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. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 6 Challenges Integration of evidence Efficient search Modular and extensible system design

7. Stuart Andrews, The SHAPE Lab, Brown University 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 16 sherds 120 pairs ! 560 triples !!

8. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 8 A Greedy Bottom-Up Assembly Strategy Single sherds

9. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 9 A Greedy Bottom-Up Assembly Strategy PairsSingle sherds

10. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 10 A Greedy Bottom-Up Assembly Strategy Single sherdsPairs

11. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 11 A Greedy Bottom-Up Assembly Strategy TriplesSingle sherdsPairs

12. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 12 A Greedy Bottom-Up Assembly Strategy Single sherdsPairsTriples

13. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 13 A Greedy Bottom-Up Assembly Strategy Etc. Single sherdsPairsTriples

14. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 14 Overview Generate Likely Pair-wise Matches Generate Likely 3-Way Matches … etc.

15. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 15 Likely Pairs Proposals Likelihood Evaluations Generate Likely Pair-wise Matches

16. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 16 A Match A pair of sherds A relative placement of the sherds

17. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 17 Match Proposals Corner Alignment

18. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 18 Example Corner Alignments

19. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 19 Likely Pairs Proposals Likelihood Evaluations Generate Likely Pair-wise Matches

20. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 20 Match Likelihood Evaluations An evaluation returns the likelihood of a feature alignment Based on the notion of a residual

21. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 21 Match Likelihood Evaluations Axis Divergence Feature: Axis of rotation Residual: Angle between axes

22. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 22 Match Likelihood Evaluations Axis Separation Feature: Axis of rotation Residual: Distance between axes

23. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 23 Match Likelihood Evaluations Break-Curve Separation Feature: Break-curve Residuals: Distance between closest point pairs

24. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 24 Match Likelihood Evaluations Break-Curve Divergence Feature: Break-curve Residuals: Angle between tangents at closest point pairs

25. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 25 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?

26. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 26 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?

27. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 27 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

28. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 28 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

29. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 29 Local Improvement of Match Likelihood beforeafter

30. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 30 Pair-wise Match Results Summary ??

31. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 31 Pair-wise Match Results Summary Correct Matches Incorrect Matches

32. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 32 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!!

33. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 33 Overview Generate Likely Pair-wise Matches Generate Likely 3-Way Matches … etc.

34. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 34 Likely Triples 3-Way Proposals 3-Way Likelihood Evaluations Generate Likely 3-Way Matches

35. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 35 3-Way Match Proposals Merge pairs with common sherd +=

36. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 36 3-Way Match Likelihood Evaluation Feature alignments are measured 3-way

37. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 37 3-Way Match Results Summary

38. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 38 3-Way Match Results Summary # of 3-way matches with correct match identified: Top 13 Top 511 Top 1017 Total31

39. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 39 Overview Generate Likely Pair-wise Matches Generate Likely 3-Way Matches … etc. Future work

40. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 40 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.]

41. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 41 Contributions A computational framework based on match proposal and likelihood evaluation A method for combining multiple features into one match likelihood An example (greedy) assembly strategy

42. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 42 Where to go from here? Improve accuracy of features Add new features and feature comparisons Learn how to classify true and false pairs Design specialized search strategies

43. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 43 Conclusions Encouraging progress on a difficult task We are close to a working system We can get closer by following this approach A uniform statistical analysis of features defines the basis for a complete working system

44. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 44 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.

45. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 45 Results For Discussion Q Q count

46. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 46 Results For Discussion

47. Stuart Andrews, The SHAPE Lab, Brown University A Computational Framework for Assembling Pottery Vessels 47 Results For Discussion