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Assembling Virtual Pots from 3D Measurements of their Fragments Geometric Learning

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Andrew Willis, Frederic F. Leymarie, Stuart Andrews, Jill Baker, ... IBM Piet Project (1999) Sherd i Geometric Characterization. Break Curve. Axis of Symmetry ... – PowerPoint PPT presentation

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Title: Assembling Virtual Pots from 3D Measurements of their Fragments Geometric Learning


1
Assembling Virtual Pots from 3D Measurements of
their Fragments(Geometric Learning)
  • BROWN UNIVERSITY
  • The SHAPE Lab
  • Andrew Willis, Frederic F. Leymarie, Stuart
    Andrews, Jill Baker, Yan Cao, Dongjin Han,
    Kongbin Kang, Weixin Kong, Xavier Orriols, Senem
    Velipasalar, Eileen L. Vote, David B. Cooper,
    Martha S. Joukowsky, Benjamin B. Kimia, David H.
    Laidlaw, David Mumford

2
Problem
3
Three Sherd Configurationfor a contemporary
(experimental ground-truth) pot
4
Typical Pot Sherds from Petra
5
How Mother Nature Generates Sherd Geometry
a(z)
ß
Ti
6
Literature Review
  • Technical University of Vienna (2000-01)
  • Middle East Technical University of Ankara (1999)
  • Digital Forma Urbis Romae (2001)
  • University of Athens (2001)
  • IBM Pietà Project (1999)

7
Parameter Estimation
Method Assembly using only the geometry of the
sherd outside surface.
  • Sherd i Geometric Characterization
  • Break Curve
  • Axis of Symmetry
  • Profile Curve

Symbol ßi li ai
8
Sherd Break Curve Data Extraction
  • Vertex Extraction (currently done using HCI).
  • Break Curve data points are extracted in the
    vicinity of each vertex.
  • For V vertices there exist 2V break curves. Each
    break curve is a set of 5 3D points.

Transformation Estimation Objective Function
9
Break Curve Matching
2
2
1
T9
4
9
T5
4
3
5
3
10
Good Curve Matches for a Pot
11
Incorrect Curve Matches for a Pot
12
Axis and Profile Curve Estimation
z
ai (z)
13
Petra Sherd Data
14
Reconstructed Surfaces and Data Profiles
15
Probabilistic Framework
  • The estimated parameters for each sherd alone are
    used for reconstruction.
  • The parameters are combined to form a maximum
    likelihood estimate (MLE) of the global pot
    geometry.

16
Pot Assembly Search Algorithm
  • 1. Obtain Break curve data, and Axis, Profile
    Curves estimate for each sherd (computationally
    costly).
  • 2. For each pair of sherds, estimate all possible
    alignments by matching break curve data (fast).
    Each alignment constitutes a configuration. (for
    200 sherds typically 1.5 minutes)
  • 3. For each configuration, improve the alignment
    using joint (break curve , axis profile)
    estimation (computationally costly).
  • 4. Find configurations which may be merged with
    other configurations or single sherds
    (computationally costly).
  • 5. Continue from step 3.
  • Steps 3-5 operate along contours of constant
    probability starting at the maximum.

17
Additional Considerations
  • Within this framework can include other geometric
    features.
  • Bayesian formulation and search is expected to
    handle more than one pot in the data set, missing
    sherds for a pot, and extraneous sherds not
    associated with any of the pots.
  • Thickness curve
  • Patterns on inside surface
  • Sherd Erosion
  • Color / Patterns on surface
  • Commonality with observed methods
  • Prior knowledge of global shape may be
    incorporated to simplify the search
  • Theoretically possible to assemble a virtual pot
    where no sherds share common break curves.

18
Conclusions
  • Extend to similar more complex geometries
  • Refinement of search and estimation algorithms.
  • Applications to large structures
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