Interactive Reconstruction of Archaeological Fragments in a Collaborative Environment

1. Interactive Reconstruction of Archaeological Fragments in a Collaborative Environment Yifan Lu eScience The Department of Computer Science Faculty of Engineering and Information Technology Australian National University October 2005

2. Outline • Background Introduction • Data Acquisition • Probability Estimation by Curve Matching • Interactive and Collaborative Reconstruction • Conclusion & Project Plan • References

3. Background Introduction • Motivation • A problem of reassembly of artifacts from a collection of fragments appears very important for archaeological studies. But it requires a tedious and laborious work. • Purposes • To relieve archaeologists from the tedious work • To boost reassembling efficiency, join archaeologists’ intelligence. • A computer aided and collaborative approach is required

4. Background Introduction • Related works • reassembling fragments & pattern recognition • Various methods are used to solve this problem in computer vision domain. • Papaioannou et al • Andrew et al • Helena et al. • Kong et al. • Gokturk Ucoluk(G.U.) et al • Kampel et al • No unified method can solve arbitrary shape fragments. Most of methods use the additional information or assumption. • e.g. Andrew et al assume artifacts are axially symmetric. • Helena et al and G. U. et al assume fragments have zero thickness.

5. Background Introduction: Related works: • collaborative visualization. • Benko et al design a visual interaction system for archaeology to establish an experimental collaborative mixed reality system • Argonne National Laboratory introduces a new concept ”ActiveSpace”, and creates its embodiment-- AccessGrid ,A modern collaborative platform

6. Background Introduction • Project scope • Complicated system (e.g. Bayesian approach) –not feasible to achieve in one year • A sophisticated visual interaction system (e.g. with see-through head-worn displays, 3D tracked gloves, etc) –equipments are expensive • Interactive Reconstruction of Archaeological Fragments via the AccessGrid ,assisted by curve matching estimation. –OK, for the first step

7. Background Introduction • Project pipeline

8. Data Acquisition • Image-based modeling • The commercial software PhotoModeller is used to create 3D models • Eight major steps to model a 3D object • Manual work could directly influence the accuracy of 3D models • PhotoModeller supports exporting various types data • VRML 2.0 is a suitable type for 3D representation of fragments • Curves are exported as either line segments or NURBS, either of them can be used as the source of curve matching.

9. Probability Estimation by Curve Matching The method proposed is based on G.U. et al ’s work • Curvature and torsion • The Theorem in the local theory of curves implies that two curves which have identical curvature and torsion are the same curve regardless of translation and rotation.

10. Probability Estimation by Curve Matching: Curvature and torsion • In practical case, a discrete series of points is available source, Hence differentials will be replaced by differences by following formulas.

11. Probability Estimation by Curve Matching • ENO computation ENO (Essential Non-Oscillatory Scheme) firstly is introduced by Harten et al, later made more efficient by Shu and Osher, and extended to shock-placing ENO in Siddiqi et al ‘s study. • Curvature and Torsion involve high-order derivatives which are very unstable when noise exists or the sample points are not uniformly separated. • e.g.

12. Probability Estimation by Curve Matching: ENO computation • The general principle for the ENO schemes is neighboring discontinuities, the smoothing is always from the side not containing the discontinuity. The basic idea is to select between two contiguous sets of data points for interpolation the one which gives the lower variation

13. Probability Estimation by Curve Matching: ENO computation • Based on Kong et al analysis, Consider the cylindrical spiral, where a=0.1 b=0.2, we calculate curvatures and torsions on a set of discrete points at cylindrical spiral by ordinary difference method and third order ENO with interpolation polynomial with degree three.

14. Probability Estimation by Curve Matching: ENO computation • Curvature and torsion versus arc-length using ordinary difference method • Curvature and torsion versus arc-length using ENO method

15. Probability Estimation by Curve Matching • Edge curve matching • Begin with two sequences of vectors (curvature, torsion) • Points matching & Euclidean distance

16. Probability Estimation by Curve Matching: Edge curve matching • Similarity matrix • Valid Euclidean distance ● not greater than ε • Invalid Euclidean distance X greater than ε. • It enumerates full combinations

17. Probability Estimation by Curve Matching : Edge curve matching • Longest sequence in G.U. et al ’s work • Group successive points into segments • Define a following operator “<“ • Relationships between segments e.g.

18. Probability Estimation by Curve Matching : Edge curve matching: Longest sequence in G.U. et al ’s work • Find all possible segment sequences which are not subsequences of each other. • The longest sequence is chosen as best match e.g. 1,4,7

19. Probability Estimation by Curve Matching : Edge curve matching • A question to the Longest sequence in G. U. et al ’s work • Add anther two valid point in segment 7(left diagram) • The Result is still same, the longest sequence is 1,4,7. • But 3rd and 4th vectors in the first sequence and 7th vectors in the second sequence have matched two times, this is not correct

20. Probability Estimation by Curve Matching : Edge curve matching • Reform similarity matrix • The reason causes the problem in G. U. et al ’s work is that they regarded the successive points into one unit segment. So they only had two choices, discard or append entire the segment. • Consider each point as a unit • To reduce the complexity in cyclic curve situations, • define new successor operator “<“ and predecessor operator “>” • Reform similarity matrix with respect to a start point. • The longest merged sequence that begins with the start point never goes around the reformed similarity matrix

21. Probability Estimation by Curve Matching : Edge curve matching: Reform similarity matrix

22. Probability Estimation by Curve Matching : Edge curve matching • LSIS (Longest Strictly Increasing Subsequence) • The “best” match interprets the longest valid points subsequence • it also means longest strictly increasing subsequence in terms of successor operator “<“ • A dynamic programming is used to recursively find solution

23. Probability Estimation by Curve Matching : Edge curve matching: LSIS • The cost of executing the recursive solution (that regards a valid point as the start point) is very expensive. • By carefully observing, We conclude • The correctness of above statement can be proved by contradiction method. • Although valid points in the same LSIS don’t need to be calculated, but the complexity of running time is still very high, and it has a bound:

24. Probability Estimation by Curve Matching : Edge curve matching: LSIS

25. Probability Estimation by Curve Matching • Probability Estimation

26. Interactive and Collaborative Reconstruction • Collaborative work trough AccessGrid • Collaborative work form joins the multiple archaeologists’ intelligence together, improve the efficiency of reassembly of artifacts. • The utilization of the AccessGrid removes physical distance as an obstacle and also provides an opportunity for more archaeologists to become involved in collaboration • AccessGrid Shared application and experiment • A shared application is a piece of software that enhances collaboration, where two or more people are allowed to view, modify, and add information simultaneously. • The shared application mechanism is a best and shortest routine to plug the local probability estimation into collaborative work via AccessGrid. • Experiment with shared Application

27. Interactive and Collaborative Reconstruction: AccessGrid Shared application and experiment

28. Conclusion & Project Plan • Conclusion • We just scratched the surface of the problem of reassembling artifacts • We proposed a collaborative virtual workspace which allows several archaeologists to interactively reassemble fragments and enables matching probability estimation to reduce the burden of manually selecting fragments. • Several place need to be studied and improved. • Data acquisition • The complexity of curve matching algorithm • The fragments Euclideantransformation

29. Conclusion & Project Plan • Project Plan

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