Interactive Reconstruction of Archaeological Fragments in a Collaborative Environment

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Interactive Reconstruction of Archaeological
Fragments in a Collaborative Environment

• Yifan Lu
• eScience project course COMP6702,
• Supervised by
• Rhys Hawkins Henry Gardner
• Department of Computer Science
• Faculty of Engineering and Information
  Technology,
• Ian Farrington,
• Archaeology and Anthropology, Faculty of Arts,
• ANU
• June. 2006

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Outline

• Background Introduction
• Data Acquisition and 3D Model Generation
• Matching Estimation
• Collaborative and Interactive Reconstruction
• Testing and Experimental Results
• Conclusion and Future Work

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Background Introduction

• Motivation
• A problem of reassembly of artefacts from a
  collection of fragments appears very important
  for archaeological studies.
• Purposes
• To relieve archaeologists from some tedious work
• To boost reassembling efficiency by cooperative
  work, joining archaeologists expertise.
• To archive archaeological data
• A computer-aided and collaborative approach

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Background Introduction literature review

• Relevant studies.
• Wagner et al.
• M. Maes.
• Horst Bunke et al.
• Andres Marzal et al.
• Kong et al.
• Argonne National Laboratory

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Background Introduction

• Project scope
• Project features
• Image-based 3D modeling
• Interactive reconstruction
• Collaboration via Access Grid
• Matching estimation by 3D curve fitting ,assume
  fragments has zero thickness

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Introduction Project scope

1. Project pipeline

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Data Acquisition

• Image-based modeling
• A commercial software PhotoModeller is used to
  create 3D models
• PhotoModeller supports exporting various types of
  data
• Boundary curves are manually extracted from
  PhotoModeller

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Data Acquisition

• Issues
• Are image-based 3D modeling techniques efficient
  enough to create 3D models in practice?
• This technique relies greatly on manually marking
  pairs of correspondence points and curves.
• Improvement
• Use more advanced techniques (e.g. laser range
  scanner, might be very expensive)

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Matching Estimation

• Curvature and torsion
• ENO computation
• Curvature and Torsion Approximation
• Least Squares
• Cyclic Edit Distance
• Branch and Bound Algorithm (BBA)
• Trivial Solution
• Kth Shortest Path Algorithm

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Matching Estimation

• Curvature and torsion
• From Differential Geometry the local theory of
  curves implies that two curves which have
  identical curvature and torsion are the same
  curve regardless of translation and rotation.
• Allow string registration method to be applied
• Coordinates independent manner

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Matching Estimation

• 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.
• 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

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Matching Estimation ENO computation

• Based on Kong et al analysis, Consider the
  cylindrical spiral,
• where a0.1 b0.2, 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.

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Matching Estimation ENO computation
(a)
(b)

1. Curvature and torsion versus arc-length using
   ordinary difference method
2. Curvature and torsion versus arc-length using ENO
   method

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Matching Estimation

• Curvature and Torsion Approximation
• Computationally inexpensive.
• Actual values are not curvature and torsion any
  more.
• It based on the assumption of the sample points
  are closed enough.

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Matching Estimation

• Least Squares
• A solution for a system of linear equations.
• Extra sample points are involved to construct the
  interpolating polynomial
• Optimized results rather than exact results.

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Matching Estimation

• Edit distance for common strings
• Edit distance was devised by Wagner et al in
  1974, originally it is aimed to correct typing
  error.
• Adapting our curvature and torsion sequence
  vectors to be applicable for edit distance only
  requires customizing edit operation cost
  functions
• It works on a dynamic programming matrix m by n
  called edit graph

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Matching Estimation Edit distance for common
strings

• Recursive formulation is given ,(where D is used
  to store edit distance, f function assigns
  according edit operations cost)
• Finally, the result of edit distance can be found
  in D(m,n).

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Matching Estimation Edit distance for common
strings

• To solve the edit distance on edit graph is
  intuitively equivalent to solve a single-source
  shortest path problem in Directed Acyclic Graph
  (DAG).
• In this case, shortest path from D(0,0) to D(m,n)
• The total computation time is O(mn)

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Matching Estimation

• Edit distance for cyclic strings
• A trivial solution for cyclic strings This takes
  O(m²n)
• M. Maes provides a divide and conquer algorithm
  with a special non-crossing property , totally
  O(mnlog(n)).
• Andres Marzal et al improve the efficiency of M.
  Maes algorithm by introducing a lower bound
  (known as BBA).

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Matching Estimation Edit distance for cyclic
strings

• Horst Bunke et al propose an approximate
  algorithm.
• Andres Marzal et al s study suggests exact edit
  distance can be solved using Kth shortest path
  for DAG with constraints in O(mnK(mn)).

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Matching Estimation Edit distance for cyclic
strings
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Interactive and Collaborative Reconstruction

• Collaborative work trough Access Grid
• Collaborative work form joins the multiple
  archaeologists intelligence together, improve
  the efficiency of reassembly of artifacts.
• The utilization of the Access Grid removes
  physical distance as an obstacle and also
  provides an opportunity for more archaeologists
  to become involved in collaboration

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Interactive and Collaborative Reconstruction

• Access Grid
• Is a large scale group to group collaborative
  communication environment
• Is "designed space" that explicitly contains the
  high-end audio and visual technology needed to
  provide a high-quality compelling user experience
  
• Is ideal interactive and networked application
  base supporting distant visualization with
  multicasting

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Interactive and Collaborative Reconstruction

• Access Grid Shared application
• 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 ideal and
  shortest routine to plug the matching estimation
  into collaborative work.

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Testing and Experimental Results

1. Curvature and Torsion

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Testing and Experimental Results

1. Curvature and Torsion

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Testing and Experimental Results

1. Cyclic Edit Distance

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Testing and Experimental Results

1. Two curves matching result

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Testing and Experimental Results

1. Usability Testing

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Testing and Experimental Results

1. Usability Testing

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Testing and Experimental Results

1. Usability Testing

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Conclusion Future Work

• Conclusion
• We proposed a collaborative 3D virtual workspace
  that enables matching estimation to reduce the
  burden of manually selecting fragments.
• Future Work
• Some aspect of our system is unsatisfactory, need
  to be improved in the future.
• Data acquisition
• Automated Edge detection in 3D space.
• Friendly interactive manipulation

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Demonstration