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A Computational Framework for Assembling Pottery Vessels

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.

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A Computational Framework for Assembling Pottery Vessels

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  1. 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

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

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

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

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

  24. 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

  25. 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

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

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

  28. Local Improvement of Match Likelihood before after 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: 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

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

  33. Likely Triples Generate Likely 3-Way Matches • 3-Way Match Proposals • 3-Way Match Likelihood Evaluations 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: 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 S G(S) {True Pair / False Pair} 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 • 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

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

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

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

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