An NSF ITR multidisciplinary project devoted to modeling, manipulation, analysis, and inferencing from data of 3-dimensional shape and its application to archaeology and art.

Principal Research Collaborators @ Brown

COOPER, David           Engineering
JOUKOWSKY, Martha
Archaeology
KIMIA, Benjamin
Engineering
MUMFORD, David
Applied Mathematics
FISHMAN, Richard
Art
LEYMARIE, Frederic
Now at Goldsmiths College, U. of London
GALOR, Katharina
Joukowsky Institute

Principal Research Collaborators Under Subawards funded by NSF ITR Grant # 0205477.

Aytul Ercil  
              Computer Engineering, Sabanci University,

Istanbul, Turkey.

http://vpa.sabanciuniv.edu/modules/aytulercil/
Dimitri Terzopoulos Computer Science, Courant Institute, NYU.

www.cs.ucla.edu/~dt/
Andrew Willis 
Electrical and Computer Engineering,

University of North Carolina, Charlotte.

http://www.ece.uncc.edu/~arwillis/

http://www.visionlab.uncc.edu/

Other Collaborating Organizations

Joukowsky Institute for Archaeology and the Ancient World
        http://www.brown.edu/Departments/Joukowsky_Institute/
Dr. Donald Sanders
The Institute for the Visualization of History, Inc http://www.vizin.org
Karl Aspelund
Brower Hatcher
Mid-Ocean Studio http://www.midoceanstudio.com/

International visiting faculty, post doctoral researchers, graduate-student and undergraduate-student researchers are also involved.

PRINCIPAL PROJECTS

  1. 3-dimensional virtual pot, mural, and sculpture estimation from 3D data measurements (Laser scanner) or images of thousands of fragments found at a site.
  2. Archaeology site buildings, monuments, large sculpture, reconstruction in and for virtual environments such as THE CAVE at Brown. Use of Virtual Reality - The CAVE - for exploring and using trench finds.
  3. 3-dimensional surface reconstruction and meaningful geometry estimation of buildings and medium-size artifacts and objects from multiple images and video.
  4. Methodology for modeling 3D objects and shape based on ridges, medial axes (i.e., axes of symmetry), algebraic surfaces, fragments, deformations of templates, Markov Random Fields, and approaches to estimating these from x,y,z data.
  5. Web services for an internet accessible database containing roughly half a million finds at the Great Temple, Petra, Jordan, as well as 13 sets of dense-data aligned laser scans and 3D meshes of these surfaces, and roughly 120 thirty second video clips. Simple geometric measurements can be made on-line of the 3D surface meshes. Databases at different locations are to be accessible with some of the same queries.
  6. 2-dimensional virtual mural or tile estimation from images of their unorganized broken fragments.
  7. Database search of objects or fragments based on images or geometric properties.
  8. Populating the Great Temple at Petra, Jordan, with artificial life having simple perceptual and cognitive capability for the purpose of testing archaeological site-usage hypotheses.

Web Sites Containing Developed Softwares and Databases

  • Internet accessible Petra Great Temple database including roughly 0.5 million finds with archaeological descriptors, and a small number of recent videos, 3D mesh representations of artifact surfaces, and aligned sets of 3D dense-data laser scans.
    • Artifact Database (A complete description of these Petra databases and their fields is available on the CDs which are avaiable on request.)
    • 3D Images (These are VRML files, you need a VRML viewer to open them. The linked website also gives a link to a Java-based viewer.)
    • Photos
    • Digital Video
  • Apollonia-Arsuf: Excavation site for a number of projects of current interest including reconstruction of the Crusader Castle and reassembly of ceramic and glass vessels from large numbers of fragments.
    http://www.stg.brown.edu/projects/apollonia/

  • Images of Apollonia Crusader Castle Architectural Artifacts.
    Images, some containing calibration boards, of in situ Crusader Castle structure and very large castle fragments that have fallen into the moat or have fallen over the cliff and onto the beach below. 3D representations are being made through dense-data laser scans or by multiview images, and 3D reassembly of the castle on the computer will be based on these representations. http://www.visionlab.uncc.edu/component/option,com_gallery2/Itemid,52/?g2_itemId=1350

  • Simulation of artificial people, having primitive perception and cognition, in the Great Temple.
    The intent of this project was to use simulations with artificial life to test hypotheses concerning the original use of the Great Temple – “what combination of religious, administrative or entertainment purposes was it used for?”. The simulation software was completed, but usage tests have yet to be run. By Wei Shao and Demetri Terzopoulos.


    [higher resolution version download, 32 MB]

  • Wall Drawer: a simple solution to traditional drawing and phtographic recording of archaelogical features.
    http://www.lems.brown.edu/~bazin/Research/WallDrawer.html.

  • HINDSITE: The reconstruction of 2D and 3D artifacts from fragments.
    http://www.lems.brown.edu/vision/hindsite/

  • ShaRP - A Java Based 3D Geometric Processing Environment. Program allows user to perform numerous operations including : (1) fitting 3D algebraic surfaces to 3D data, (2) virtual sculpting of 3D surfaces, and (3) automatic reconstruction of pot profile curves from a collection of axis/profile-curves for pot fragments.
    http://www.visionlab.uncc.edu/component/option,com_wrapper/Itemid,43/.

  • While simple operations such as surface fitting and visualization are easily accomplished, more sophisticated functions such as (1) and (2) requires some review of the software documentation available online. The documentation is a dynamic "wiki" and is constantly being updated both by developers and users to maximize it's clarity and utility to make the provided program understandable and as easy-to-use as possible.
    http://www.visionlab.uncc.edu/component/option,com_jd-wiki/Itemid,46/ .

  • Fitting 2D Algebraic Curves to user-sketched data in a variety of forms.
    http://www.visionlab.uncc.edu/content/view/164/162/.
    (To get good results, fit the lowest degree algebraic curve that provides good representation for the data.)

  • Open VXL Libraries, under development with contributions by the Brown Engineering computer-vision/pattern-recognition group, and use of which is made by this NSF project in addition to use by a number of other projects.
    VXL is an extensive set of C++ libraries for carrying out computer vision research and building practical systems for such applications as: object recognition; structure from motion and change detection. The libraries are maintained and extended by a team of developers from industry and academia. Among the collaborators are General Electric, Rensselaer Polytechnic Institute, Brown University and Kitware Inc. The VXL website can be found at http://vxl.sourceforge.net/, which provides more details and documentation.

Summary of Accomplishments under NSF ITR Grant #0205477 (2002-present)

Publications

1
D. Barrett, A. Brian, Ch. Cloke, E. Egan, A. Joukowsky, M Joukowsky, and S. Karz-Reid.
Petra Rocks! Tales from the Ancient Rock City.
Dig Magazine, 5(5), 2002.
2
P.L. Bazin and M. Boutin.
Structure from motion using invariants.
In Actas del Encuentro de Algebra Computacional y Aplicaciones (EACA 2002), sep 2002.
3
P.L. Bazin and M. Boutin.
Structure from motion: a new look from the point of view of invariant theory.
SIAM Journal on Applied Mathematics, 64(4), 2004.
4
P.L. Bazin and A. Henry.
Walldrawer: a simple solution to traditional drawing and photographic recording of archaeological features.
Shape laboratory report, Brown University, 2003.
5
M. Brand, K. Kang, and D.B. Cooper.
Algebraic solution for the visual hull.
In IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 30-35, Washington, DC, USA, 2004.
6
S.M. Chan.
Semi-automatic assembly of broken fragments, B.S. Honors thesis, Division of Engineering, Brown University, May 2006.
7
Ming-Ching Chang, Frederic Fol Leymarie, and Benjamin B. Kimia.
3D shape registration using regularized medial scaffolds.
In Proceedings of the Symposium on 3D Data Processing Visualization and Transmission, pages 987-994, Thessaloniki, Greece, September 2004.
8
A. Erçil.
Solving the 2d puzzle problem for automated reconstruction of archeological findings.
In Proceedings of SIU, pages 164-167, 2003.
(in Turkish).
9
Ricardo Fabbri and Benjamin B. Kimia.
High-order differential geometry of curves for multiview reconstruction and matching.
In Proceedings of the IEEE Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, pages 645-660. Springer Verlag, November 2005.
10
Peter J. Giblin and Benjamin B. Kimia.
On the intrinsic reconstruction of shape from its symmetries.
PAMI, 25(7):895-911, July 2003.
11
Peter. J. Giblin and Benjamin. B. Kimia.
On the local form and transitions of symmetry sets, medial axes, and shocks.
IJCV, 54(Issue 1-3):143-157, August 2003.
12
Peter J. Giblin and Benjamin B. Kimia.
A formal classification of 3D medial axis points and their local geometry.
PAMI, 26(2):238-251, February 2004.
13
Peter J. Giblin and Benjamin B. Kimia.
Transitions of the 3D medial axis under a one-parameter family of deformations.
PAMI, Submitted, 2006.
14
D. Han, M. Leotta, D.B. Cooper, and J. Munday.
Vehicle class recognition based on 3d curve probes.
In Proceedings 2nd Joint IEEE Intl. Workshop on Visual Surveillance and Performance Evaluation of Tracking and Surveillance (VS-PETS), pages 285-292, Beijing, October 2005.
15
C.D. Jackson, D. Acevedo, D.H. Laidlaw, F. Drury, E. Vote, and D. Keefe.
Designer-critiqued comparison of 2d vector visualization methods: a pilot study.
In Siggraph 2003 Sketches and Applications, 2003.
16
M. Joukowsky.
Technologies in Use at the Brown University Excavations of the Petra Great Temple.
In International Conference on Science and Technology in Archaeology and Conservation, Abstracts of the Hashemite University (Zarqa, Jordan), Zarqa, Hashemite University, 2002. UNESCO.
17
M. Joukowsky.
Excavations at the Petra Great Temple: The Eleventh Campaign, 2003.
ACOR Newsletter, 15(2), 6 2003.
18
D.F. Keefe, D.B. Karelitz, E. Vote, and D.H. Laidlaw.
Artistic collaboration in designing vr visualizations.
IEEE Computer Graphics and Applications, 25(2):18-23, 2005.
19
Frederic Fol Leymarie.
3D Shape Representation via Shock Flows.
PhD thesis, Division of Engineering, Brown University, Providence, RI, 02912, May 2003.
20
Frederic Fol Leymarie, Peter J. Giblin, and Benjamin B. Kimia.
Towards surface regularization via medial axis transitions.
In Proceedings of International Conference on Pattern Recognition, volume 3, pages 123-126, Cambridge, England, August 2004. Computer Society Press.
21
Frederic Fol Leymarie and Benjamin B. Kimia.
Computation of the shock scaffold for unorganized point clouds in 3D.
In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, volume 1, pages 821-827, Madison, Wisconsin, June 16-22 2003. IEEE Computer Society Press.
22
Frederic Fol Leymarie and Benjamin B. Kimia.
Shock scaffold segregation and surface recovery.
DIMACS Workshop on Surface Reconstruction, Apri 30 - May 2 2003.
23
Frederic Fol Leymarie and Benjamin B. Kimia.
The medial scaffold of 3D unorganized point clouds.
PAMI, page In Press, 2006.
24
S. Liu, K. Kang, J.-P. Tarel, and D.B. Cooper.
Free-form object reconstruction from silhouettes, occluding edges and texture edges: A unified and robust operator based on duality.
under review for journal publication.
25
Jonah McBride.
Archaeological fragment reassembly using curve matching.
Master's dissertation, Brown University, Providence, USA, 2003.
26
Jonah C. McBride and Benjamin B. Kimia.
Archaeological fragment re-assembly using curve-matching.
In Proceedings of the IIEEE/CVPR Workshop on Applications of Computer Vision in Archaeology, pages 3-8, Madison, Wisconsin, June 2003. IEEE Computer Society Press.
27
P. Michor and D. Mumford.
Hamiltonian approach to riemannian metrics on spaces of curves.
Applied and Computational Harmonic Analysis, 2007.
(to appear).
28
D. Mumford.
Brain and Systems: New Directions in Statistical Signal Processing, chapter Empirical Statistics and Stochastic Models for Visual Signals.
NIT Press, 2007.
(to appear).
29
D. Mumford and P. Michor.
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms.
Documenta Mathematica, 10, 2005.
30
D. Mumford and P. Michor.
Riemannian geometries on spaces of plane curves.
Journal of the European Mathematical Society, 8:1-48, 2006.
31
http://proteus.brown.edu/PGTdata/1500.
32
Anthony J. Pollitt, Peter J. Giblin, and Benjamin B. Kimia.
Consistency conditions on medial axis.
In Eigth European Conference on Computer Vision, volume 2, pages 530-541, Prague, Czech Republic, May 11-14 2004. Springer Verlag.
33
M. S. Sagiroglu and A. Erçil.
Automated Assembly Problem using an FFT based Matching Approach.
In Proceedings of SIU.
34
M. S. Sagiroglu and A. Erçil.
In Automatic Reconstruction of Archaeological Finds using Inpainting and Texture Synthesis, 2004.
35
M. S. Sagiroglu and A. Erçil.
A Texture based Approach to Assembly Problem.
In Proceedings of SIU, 2005.
36
M. S. Sagiroglu and A. Erçil.
A Texture Based Approach to reconstruction of archaeological finds.
In Proceedings of VAST, pages 137-142, 2005.
37
M. S. Sagiroglu and A. Erçil.
A Texture Based Matching Approach for Automated Assembly of Puzzles.
In Proceedings of ICPR, 2006.
38
M. S. Sagiroglu, A. Erçil, and S. Balcisoy.
Automated Reconstruction of Archaeological Finds.
In Proceedings of CAA, 2006.
39
M. S. Sagiroglu, A. Erçil, C. Özmen, and S. Balcisoy.
A Texture Based Approach to Puzzle Assembly.
In Proceedings of Virtual Retrospect Symposium, pages 38-43, 2005.
40
E. Saykol, Y. Saygin, A. Ercil, A. Willis, M.S. Joukowski, and D.B. Cooper.
A web service platform for web-accessible archaeological databases.
In Lecture Notes in Computer Science (LNCS), (Proc. of 20th International Symposium on Computer and Information Sciences (ISCIS'05)), Vol. 3733,, Istanbull, Turkey, October 2005.
41
E. Saykol, Y. Saygin, and A. Erçil.
MIDAS, A Multimedia Database for Archeological Sites.
In Proceedings of VAST, pages 173-178, 2003.
42
E. Saykol, Y. Saygin, A. Erçil, A. Willis, D. Cooper, and M. S. Joukowski.
A Web Service Platform for Web-Accessible Archaeological Databases.
In LNCS 3733, pages 362-370, 2005.
43
Thomas Sebastian, Philip Klein, and Benjamin Kimia.
On aligning curves.
PAMI, 25(1):116-125, January 2003.
44
W. Shao and D. Terzopoulos.
Video simulation of artificial humans in petra.
http://cs.nyu.edu/~weishao/research/penn/shared_videos/petra_640x480_divx.avi .
(about 72MB).
45
W. Shao and D. Terzopoulos.
Autonomous Pedestrians.
In Proc. SIGGRAPH/EG Symposium on Computer Animation (SCA'05), pages 19-28, Los Angeles, CA, July 2005.
46
W. Shao and D. Terzopoulos.
Environmental Modeling for Autonomous Virtual Pedestrians.
In Proc. SAE Symposium on Digital Human Modeling for Design and Engineering, pages 1-8, Iowa City, IA, June 2005.
SAE Technical Paper 2005-01-2699.
47
W. Shao and D. Terzopoulos.
Environmental Modeling for Autonomous Virtual Pedestrians.
SAE 2005 Transactions Journal of Passenger Cars: Electronic and Electrical Systems, 114(7):735-742, February 2006.
Compilation of the most outstanding SAE technical papers of 2005.
48
W. Shao and D. Terzopoulos.
Populating Reconstructed Archaeological Sites with Autonomous Virtual Humans.
In Proc. 6th International Conference on Intelligent Virtual Agents (IVA 06), Los Angeles, CA, August 2006.
49
W. Shao and D. Terzopoulos.
Animating Autonomous Pedestrians.
Graphical Models, 2007.
(to appear).
50
E. Sharon and D. Mumford.
2d-shape analysis using conformal mapping.
In IEEE Conference on Computer Vision and Pattern Recognition, 2004.
51
E. Sharon and D. Mumford.
2d-shape analysis using conformal mapping.
International Journal of Computer Vision, 70:55-75, 2006.
52
Amir Tamrakar and Benjamin B. Kimia.
Combinatorial grouping of edges using geometric consistency in a lagrangian framework.
In Proceedings of IEEE Workshop on Perceptual Organization in Computer Vision, POCV, 2006.
53
J-P. Tarel, K. Kang, and D.B. Cooper.
A unified linear fitting approach for singular and non-singular 3d quadrics from occluding contours.
In Proceedings First IEEE International Workshop on Higher-Level Knowledge in 3D Modeling and Motion Analysis, page 48, Cannes, France, October 2003.
54
J-P. Tarel, W. Wolovich, and D.B. Cooper.
Covariant-conic decomposition of quartics for shape recognition and alignment.
Journal of Mathematical Imaging and Vision, 19(3):255-273, November 2003.
55
E. Vote, D. Acevedo, C.D. Jackson, J.S. Sobel, and D.H. Laidlaw.
Design-by-example: a schema for designing visualizations using examples from art.
In Siggraph 2003 Sketches and Applications, 2003.
56
E. Vote, D. Acevedo, D. Laidlaw, and M. Joukowsky.
Discovering Petra: Archaeological Analysis in VR.
IEEE Computer Graphics and Applications, pages 38-49, 2002.
57
A. Willis.
Applet for fitting 2d algebraic curves.
http://www.ece.uncc.edu/~arwillis/online/programs/applets/Fit2DApplet/Fit2D.html.
58
A. Willis.
ShaRP - A Java Based 3D Geometric Processing Environment.
http://www.visionlab.uncc.edu/component/option,com_wrapper/Itemid,43/.
59
A. Willis.
ShaRP - Software Documentation.
http://www.visionlab.uncc.edu/component/option,com_jd-wiki/Itemid,46/.
60
A. Willis.
Stochastic 3D Geometric Models for Classification, Deformation, and Estimation.
PhD thesis, Brown University, May 2004.
61
A. Willis, K. Aspelund, B. Hatcher, J. Speicher, and D.B. Cooper.
Computational schemes for biomimetic sculpture.
In Proceedings of the ACM (Association for Computing Machinery),5th Intl. Conference on Creativity and Cognition (C&C), pages 22-31, London, April 2005.
62
A. Willis and D.B. Cooper,
"Estimating a-priori unknown 3d axially symmetric surfaces from noisy measurements of their fragments",
Proceedings of the Symposium on 3D Data Processing, Visualization and Transmission, p. 334, vol. , (2006). Published,
63
A. Willis and D.B. Cooper.
Bayesian pot-assembly from fragments as problems in perceptual-grouping and geometric-learning.
In Proceedings of International Conference on Pattern Recognition, volume III, pages 297-302, 2002.
64
A. Willis and D.B. Cooper.
Alignment of multiple non-overlapping axially symmetric 3d datasets.
In Proceedings of International Conference on Pattern Recognition, volume IV, pages 96-99, 2004.
65
A. Willis and D.B. Cooper.
Bayesian assembly of 3d axially symmetric shapes from fragments.
In Proceedings of Conference on Computer Vision and Pattern Recognition, June 2004.
66
A. Willis, J. Speicher, and D.B. Cooper.
Rapid prototyping 3d objects from scanned measurement data.
Journal of Image and Vision Computing.
to appear Winter 2006-2007.
67
A. Willis, J. Speicher, and D.B. Cooper.
Surface sculpting with stochastic deformable 3d surfaces.
In Proceedings of International Conference on Pattern Recognition, volume II, pages 249-252, 2004.
68
W. Willis, X. Orriols, and D.B Cooper.
Accurately Estimating Sherd 3D Surface Geometry with Applications to Pot Reconstruction.
In IEEE/CVPR Workshop on Applications of Computer Vision in Archaeology (ACVA'03), Madison, Wisconsin, USA, June 2003.
69
H. C. Aras.
Hindsite: A Robust System for Archaeological Fragment Re-Assembly.
Master's thesis, Brown University, Providence, USA, 2007.
70
Willis, A. and Speicher, J. and Cooper D.B.,
"Rapid Prototyping 3D Objects from Scanned Measurement Data",
Journal of Image and Computer Vision, p. 1174, vol. 25, (2007).
71
S. Liu, K. Kang, J.-P. Tarel, and D. B. Cooper,
"Free-form object reconstruction from silhouettes, occluding edges and texture edges: A unified and robust operator based on duality",
IEEE Transactions on Pattern Analysis and Machine Intelligence, p. 131, vol. 20, (2008).
 

A Few Papers Published Under NSF KDI Grant #BCS-9980091

  • D. Acevedo, D. Laidlaw, and M. Joukowsky.
    ARCHAVE: A Virtual Environment for Archaeological Research.
    In Tatjana Z. V. Stancic, editor, CAA 2000 Proceedings: Computing Archaeology for Understanding the Past, British Archaeological Reports, pages 313-316, Oxford, 2001.
  • D. Acevedo, E. Vote, D. Laidlaw, and M. Joukowsky.
    Archaeological Data Visualization in VR: Analysis of Lamp Finds at the Great Temple of Petra, A Case Study.
    In IEEE Visualization, Conference Proceedings, October 2001.
  • F. Leymarie, D. Cooper, M. Joukowsky, B. Kimia, D. Laidlaw, D. Mumford, and E. Vote.
    The SHAPE Lab: New Technology and Software for Archaeologists.
    In Tatjana Z. V. Stancic, editor, CAA 2000 Proceedings: Computing Archaeology for Understanding the Past, British Archaeological Reports, pages 79-90, Oxford, 2001.
  • E. Vote, D. Cooper, D Laidlaw, and M. Joukowsky.
    Archave: A virtual environment for archaeological research.
    In Computer Applications in Archaeology, CAA 2000: 28th Annual International Conference, Ljubljana, Slovenia, April 2000.
  • E. Vote, D. Feliz, D. Laidlaw, and M. Joukowsky.
    Virtual Reality and Scientific Visualization in Archaeological Research.
    In Virtual Archaeology: Between Scientific Research and Territorial Marketing, Arezzo, Italy, November 2000.
  • E. Vote, D. Feliz, D. Laidlaw, and M. Joukowsky.
    ARCHAVE: A Three-Dimensional GIS for a CAVE Environment (As Applied to Petra's Great Temple Project).
    In ASOR Annual Meeting Abstracts, November 2000.

Students Trained or Graduated with Partial Support from Grant #0205477

Post Doctoral Fellows:

  • Pierre-Louis Bazin, Post Doc. Fellow, Engineering, 2001-2003, presently Research Associate, Johns Hopkins Medical School.
  • Mireille Boutin, Post Doc. Fellow, Applied Math and Engineering, 2001-2002, presently Assistant Professor, E.C.E., Purdue.
  • Dr. Eitan Sharon, Post Doc. Fellow, Applied Mathematics, 2003-2004; Post Doc. Fellow, Weizmann Institute of Science, Israel, 2004-2005; currently Assistant Professor, Technion, Israel.

Ph.D.:

  • Kongbin Kang, Ph.D. Computer Engineering, 2004, Post Doc., Brown, 2004, Senior Research Associate, Engineering, Brown.
  • Andrew Willis, Computer engineering, 2004, Post Doc., Brown, 2004-2005, Assistant Prof., Electrical and Computer Engineering, Univ. Of North Carolina, Charlotte.
  • Frederic Leymarie, PhD, Engineering, 2003; Post Doc. 2003-2004; currently a full Professor in the Department of Computing at Goldsmiths College, University of London, leading an interdisciplinary effort at the interface of computer vision and the arts, expanding on the themes of this grant.
  • Yan Cao, PhD, Applied Mathematics, 2003; currently Asistant Profesor, UT Dallas.
  • Kathryn Leonard, PhD, Applied Mathematics, June, 2004; currently at Cal State Univ., Channel Islands.
  • Eileen Vote, Ph,D 2002 Archaeology and Visualization, Post Doc. CS, Brown, 2002-2005.
  • Wei Shao, PhD, NYU CS, 2006; currently at Google.

M.A.:

  • John Speicher, BA Engineering, BA Art, 2002, MA Multimedia, 2004; adjunct instructor teaching technology for art courses at Brown and Rhode island School of Design, and working for Telart, Providence in industrial design.
  • Jonah McBride, MSc; currently research scientist at Charles River Analytics.
  • Huseyin Can Aras, MSc Engineering, Brown, 2007; currently Financial Software Developer in Bloomberg LP.

B.S.:

  • Sye-Min Chan, BS Computer Engineering (The outstanding Computer Engineering Graduating Award) 2005, presently Graduate student in AI, Stanford.

Other Students:

  • At Brown, 5 current students working toward their PhD degrees, two on shape theory in applied mathematics, two in engineering, and one in archeology.
  • At Sabanci University, Istanbul, graduate students have worked on web services for the archaeology database, and on reconstructing tiles from surface-glaze patterns on their broken fragments.


http://www.lems.brown.edu/shape/