A Computational Framework for Assembling Pottery Vessels

1. A Computational Framework for Assembling Pottery Vessels Presented by: Stuart Andrews Advisor: David H. Laidlaw Members of the SHAPE Lab and the Department of Computer Science The study of 3D shape with applications in archaeology NSF/KDI grant #BCS-9980091

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 To assemble pottery vessels automatically • A computational framework for sherd feature analysis • An assembly strategy 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 • Scan physical sherds • Extract iso-surface • Segment break curves • Identify corners • Specify axis 16 sherds 120 pairs ! 560 triples !! 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 Single sherds Pairs 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 Single sherds Pairs Triples 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 Generate Likely Pair-wise Matches • Proposals • Likelihood Evaluations 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. Corner Alignment Match Proposals A Computational Framework for Assembling Pottery Vessels

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

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

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

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

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

24. Break-Curve Divergence Feature: Break-curve Residuals: Angle between tangents at closest point pairs Match Likelihood Evaluations A Computational Framework for Assembling Pottery Vessels

25. 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

26. 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

27. Example Match Likelihood Evaluation (1) A Computational Framework for Assembling Pottery Vessels

28. Example Match Likelihood Evaluation (2) A Computational Framework for Assembling Pottery Vessels

29. Local Improvement of Match Likelihood before after A Computational Framework for Assembling Pottery Vessels

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

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

32. 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

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

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

35. 3-Way Match Proposals • Merge pairs with common sherd + = A Computational Framework for Assembling Pottery Vessels

36. 3-Way Match Likelihood Evaluation • Feature alignments are measured 3-way A Computational Framework for Assembling Pottery Vessels

37. 3-Way Match Results Summary A Computational Framework for Assembling Pottery Vessels

38. 3-Way Match Results Summary # of 3-way matches with correct match identified: A Computational Framework for Assembling Pottery Vessels

39. Overview Generate Likely Pair-wise Matches Generate Likely 3-Way Matches … etc. Future work 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.] 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 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 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 A Computational Framework for Assembling Pottery Vessels

44. 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

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

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

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