Interactive Reconstruction of Archaeological Fragments in a Collaborative Environment

Interactive Reconstruction of Archaeological Fragments in a Collaborative Environment

Yifan LueScienceThe Department of Computer ScienceFaculty of Engineering and Information TechnologyAustralian National UniversityOctober 2005

Outline

Background Introduction Data Acquisition Probability Estimation by Curve

Matching Interactive and Collaborative

Reconstruction Conclusion & Project Plan References

Background Introduction

I. Motivation1. 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.

2. Purposesa. To relieve archaeologists from the

tedious workb. To boost reassembling efficiency, join

archaeologists’ intelligence.3. A computer aided and collaborative

approach is required


II. Related works1. reassembling fragments & pattern recognition

a. Various methods are used to solve this problem in computer vision domain.

① Papaioannou et al ② Andrew et al ③ Helena et al. ④ Kong et al. ⑤ Gokturk Ucoluk(G.U.) et al ⑥ Kampel et al

b. No unified method can solve arbitrary shape fragments. Most of methods use the additional information or assumption.

① e.g. Andrew et al assume artifacts are axially symmetric.

② Helena et al and G. U. et al assume fragments have zero thickness.

Background Introduction: Related works:

2. collaborative visualization.a. Benko et al design a visual interaction sy

stem for archaeology to establish an experimental collaborative mixed reality system

b. Argonne National Laboratory introduces a new concept ”ActiveSpace”, and creates its embodiment-- AccessGrid ,A modern collaborative platform


III. Project scope 1. Complicated system (e.g. Bayesian approach)

–not feasible to achieve in one year

2. A sophisticated visual interaction system (e.g. with see-through head-worn displays, 3D tracked gloves, etc)

–equipments are expensive

3. Interactive Reconstruction of Archaeological Fragments via the AccessGrid ,assisted by curve matching estimation.

–OK, for the first step


IV. Project pipeline

Data Acquisition

I. Image-based modeling1. The commercial software PhotoModeller is

used to create 3D models2. Eight major steps to model a 3D object3. Manual work could directly influence the

accuracy of 3D models4. PhotoModeller supports exporting various

types data1. VRML 2.0 is a suitable type for 3D

representation of fragments2. Curves are exported as either line

segments or NURBS, either of them can be used as the source of curve matching.

Probability Estimation by Curve Matching

The method proposed is based on G.U. et al ’s workI. Curvature and torsion

1. 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.

Probability Estimation by Curve Matching: Curvature and torsion

2. In practical case, a discrete series of points is available source, Hence differentials will be replaced by differences by following formulas.


II. ENO computationENO (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.

1. Curvature and Torsion involve high-order derivatives which are very unstable when noise exists or the sample points are not uniformly separated.

a. e.g.

Probability Estimation by Curve Matching: ENO computation

2. 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


3. 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.


(a) Curvature and torsion versus arc-length using ordinary difference method

(b) Curvature and torsion versus arc-length using ENO method


III. Edge curve matching1. Begin with two sequences of vectors (curvature,

torsion)

2. Points matching & Euclidean distance

Probability Estimation by Curve Matching: Edge curve matching

3. Similarity matrixa. Valid Euclidean di

stance ● not greater than ε

b. Invalid Euclidean distance X greater than ε.

c. It enumerates full combinations

Probability Estimation by Curve Matching : Edge curve matching

4. Longest sequence in G.U. et al ’s work

a. Group successive points into segments

b. Define a following operator “<“

c. Relationships between segments

e.g.

Probability Estimation by Curve Matching : Edge curve matching: Longest sequence in G.U. et al ’s work

d. Find all possible segment sequences which are not subsequences of each other.

e. The longest sequence is chosen as best match e.g. 1,4,7


5. A question to the Longest sequence in G. U. et al ’s work 1. Add anther two valid point in segment 7(left diagram)2. The Result is still same, the longest sequence is 1,4,7. 3. But 3rd and 4th vectors in the first sequence and 7th vectors in

the second sequence have matched two times, this is not correct


6. Reform similarity matrixa. 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.

b. Consider each point as a unitc. To reduce the complexity in cyclic curve

situations, ① define new successor operator “<“ and

predecessor operator “>”② Reform similarity matrix with respect to a start

point.③ The longest merged sequence that begins with

the start point never goes around the reformed similarity matrix

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


7. LSIS (Longest Strictly Increasing Subsequence)a. The “best” match interprets the longest valid

points subsequence b. it also means longest strictly increasing

subsequence in terms of successor operator “<“c. A dynamic programming is used to recursively find

solution

Probability Estimation by Curve Matching : Edge curve matching: LSIS

d. The cost of executing the recursive solution (that regards a valid point as the start point) is very expensive.

e. By carefully observing, We conclude

f. The correctness of above statement can be proved by contradiction method.

g. 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:

Probability Estimation by Curve Matching : Edge curve matching: LSIS


III. Probability Estimation

Interactive and Collaborative Reconstruction

I. Collaborative work trough AccessGrid1. Collaborative work form joins the multiple

archaeologists’ intelligence together, improve the efficiency of reassembly of artifacts.

2. The utilization of the AccessGrid removes physical distance as an obstacle and also provides an opportunity for more archaeologists to become involved in collaboration

II. AccessGrid Shared application and experiment1. 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.

2. The shared application mechanism is a best and shortest routine to plug the local probability estimation into collaborative work via AccessGrid.

3. Experiment with shared Application

Interactive and Collaborative Reconstruction: AccessGrid Shared application and experiment

Conclusion & Project Plan

I. Conclusion1. We just scratched the surface of the problem of

reassembling artifacts 2. 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.

3. Several place need to be studied and improved.a. Data acquisitionb. The complexity of curve matching algorithm c. The fragments Euclidean transformation

Conclusion & Project Plan

II. Project Plan

References

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Interactive Reconstruction of Archaeological Fragments in a Collaborative Environment