Title: Assembling Virtual Pots from 3D Measurements of their Fragments Geometric Learning
1Assembling 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
2Problem
3Three Sherd Configurationfor a contemporary
(experimental ground-truth) pot
4Typical Pot Sherds from Petra
5How Mother Nature Generates Sherd Geometry
a(z)
ß
Ti
6Literature 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)
7Parameter 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
8Sherd 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
9Break Curve Matching
2
2
1
T9
4
9
T5
4
3
5
3
10Good Curve Matches for a Pot
11Incorrect Curve Matches for a Pot
12Axis and Profile Curve Estimation
z
ai (z)
13Petra Sherd Data
14Reconstructed Surfaces and Data Profiles
15Probabilistic 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.
16Pot 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.
17Additional 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.
18Conclusions
- Extend to similar more complex geometries
- Refinement of search and estimation algorithms.
- Applications to large structures