Abstract

In this paper we discuss the challenges of processing and converting 3D scanned data to representations suitable for interactive manipulation in the context of virtual restoration applications. We present a constrained parametrization approach that allows us to represent 3D scanned models as parametric surfaces defined over polyhedral domains. A combination of normal- and spatial-based clustering techniques is used to generate a partition of the model into regions suitable for parametrization. Constraints can be optionally imposed to enforce a strict correspondence between input and output features. We consider two types of virtual restoration methods: (a) a paint restoration method that takes advantage of the normal-based coarse partition to identify large regions of reduced metric distortion suitable for texture mapping and (b) a shape restoration approach that relies on a refined partition used to convert the input model to a multiresolution subdivision representation suitable for intuitive interactive manipulation during digital studies of historical artifacts.

References

1.
Boier-Martin
,
I.
,
Rushmeier
,
H.
, and
Jin
,
J.
, 2004, “
Parameterization of Triangle Meshes Over Quadrilateral Domains
,” in
Proc. SGP 04
, July 8-10, Nice, France.
2.
Bernardini
,
F.
, and
Rushmeier
,
H.
, 2002, “
The 3D Model Acquisition Pipeline
,”
Comput. Graph. Forum
0167-7055,
21
(
2
), pp.
149
172
.
3.
Godin
,
G.
,
Beraldin
,
J. A.
,
Taylor
,
J.
,
Cournoyer
,
L.
,
Rioux
,
M.
,
El-Hakim
,
S.
,
Baribeau
,
R.
,
Blais
,
F.
,
Boulanger
,
P.
,
Domey
,
J.
, and
Picard
,
M.
, 2002, “
Active Optical 3d Imaging for Heritage Applications
,”
IEEE Comput. Graphics Appl.
0272-1716,
22
(
5
), pp.
24
36
.
4.
Levoy
,
M.
,
Pulli
,
K.
,
Curless
,
B.
,
Rusinkiewicz
,
S.
,
Koller
,
D.
,
Pereira
,
L.
,
Ginzton
,
M.
,
Anderson
,
S.
,
Davis
,
J.
,
Ginsberg
,
J.
,
Shade
,
J.
, and
Fulk
,
D.
, 2000 “
The Digital Michelangelo Project: 3D Scanning of Large Statues
,” in
SIGGRAPH ’00
, July 23-28, New Orleans, LA, pp.
131
144
.
5.
Ikeuchi
,
K.
,
Nakazawa
,
A.
,
Hasegawa
,
K.
, and
Ohishi
,
T.
, 2003, “
The Great Buddha Project: Modeling Cultural Heritage for VR Systems Through Observation
,” in
IEEE ISMAR03
, October 7-10, Tokyo, Japan.
6.
Khodakovsky
,
A.
,
Litke
,
N.
, and
Schröder
,
P.
, 2003, “
Globally Smooth Parameterizations With Low Distortion
,”
ACM Trans. Graphics
0730-0301,
22
(
3
), pp.
350
357
.
7.
Ray
,
N.
,
Li
,
W. C.
,
Levy
,
B.
,
Sheffer
,
A.
, and
Alliez
,
P.
, 2005, “
Periodic Global Parameterization
,” Technical Report TR, submitted to ACM TOG.
8.
Eck
,
M.
, and
Hoppe
,
H.
, 1996, “
Automatic Reconstruction of B-Spline Surfaces of Arbitrary Topological Type
,” in
Proc. SIGGRAPH 96
, August 4-9, New Orleans, LA, pp.
325
334
.
9.
Kho
,
Y.
, and
Garland
,
M.
, 2003, “
User-guided Simplification
,” in
Proc. ACM I3D Symp
, April 27–30, Monterey, CA, pp.
123
126
.
10.
Velho
,
L.
, 2000, “
Quadrilateral Meshing Using 4–8 Clustering
,” in
Proc. CILANCE’00
, December 6–8, pp.
61
64
.
11.
Gu
,
X.
,
Gortler
,
S.
, and
Hoppe
,
H.
, 2002, “
Geometry Images
,”
ACM TOG SIGGRAPH
,
21
(
3
), pp.
355
361
.
12.
Gu
,
X.
, and
Yau
,
S.-T.
, 2003 “
Global Conformal Surface Parameterization
,” in
Proc. SGP03
, June 23–25, Aachen, Germany, pp.
127
137
.
13.
Praun
,
E.
, and
Hoppe
,
H.
, 2003, “
Spherical Parameterization and Remeshing
,”
ACM Trans. Graphics
0730-0301,
22
(
3
), pp.
340
348
.
14.
Hormann
,
K.
, and
Greiner
,
G.
, 2000, “
Quadrilateral Remeshing
,” in
Proc. Vision, Modeling, and Viz 2000
, November 22–24, Saarbrücken, Germany, pp.
153
162
.
15.
Alliez
,
P.
,
Cohen-Steiner
,
D.
,
Devillers
,
O.
,
Lévy
,
B.
, and
Desbrun
,
M.
, 2003, “
Anisotropic Polygonal Remeshing
,”
ACM Trans. Graphics
0730-0301,
22
(
3
), pp.
485
493
.
16.
Krishnamurthy
,
V.
and
Levoy
,
M.
, 1996, “
Fitting Smooth Surfaces to Dense Polygon Meshes
,” in
Proc. SIGGRAPH 96
, August 4–9, New Orleans, LA, pp.
313
324
.
17.
Guskov
,
I.
,
Khodakovsky
,
A.
,
Schröder
,
P.
, and
Sweldens
,
W.
, 2002, “
Hybrid Meshes: Multiresolution Using Regular and Irregular Refinement
,” in
Proc. 18th Annual Symp. Comp. Geom.
, June 5–7, Barcelona, Spain, pp.
264
272
.
18.
Owen
,
S.
,
Staten
,
M.
,
Canann
,
S.
, and
Saigal
,
S.
, 1998, “
A Survey of Unstructured Mesh Generation Technology
,” in
Proc. 7th Int. Meshing Roundtable
, October 26–28, Dearborn, MI, pp.
239
267
.
19.
Bern
,
M. W.
, and
Eppstein
,
D.
, 2002, “
Quadrilateral Meshing by Circle Packing
,”
Int. J. Comput. Geom. Appl.
0218-1959,
10
(
4
), pp.
347
360
.
20.
Katz
,
S.
, and
Tal
,
A.
, 2003, “
Hierarchical Mesh Decomposition Using Fuzzy Clustering and Cuts
,”
ACM Trans. Graphics
0730-0301,
22
(
3
), pp.
954
961
.
21.
Garland
,
M.
,
Willmott
,
A.
, and
Heckbert
,
P.
, 2001, “
Hierarchical Face Clustering on Polygonal Surfaces
,” in
Proc. of ACM Symp. on Interactive 3D Graphics
, March, Raleigh, NC.
22.
Sander
,
P. V.
,
Snyder
,
J.
,
Gortler
,
S. J.
, and
Hoppe
,
H.
, 2001, “
Texture Mapping Progressive Meshes
,” in
Proceedings of SIGGRAPH 01
, August 12–17, Los Angeles, CA, pp.
409
416
.
23.
Lévy
,
B.
,
Petitjean
,
S.
,
Ray
,
N.
, and
Maillot
,
J.
, 2002, “
Least Squares Conformal Maps for Automatic Texture Atlas Generation
,”
ACM TOG SIGGRAPH
, July 23–26, San Antonio, TX, pp.
362
371
.
24.
Cohen-Steiner
,
D.
,
Alliez
,
P.
, and
Desbrun
,
M.
, 2004, “
Variational Shape Approximation
,”
ACM Trans. Graphics
0730-0301,
23
(
3
), pp.
905
914
.
25.
Surazhsky
,
V.
,
Alliez
,
P.
, and
Gotsman
,
C.
, 2003, “
Isotropic Remeshing of Surfaces: A Local Parameterization Approach
,” in
Proc. 12th Intl. Meshing Roundtable
, September 14–17, Santa Fe, NM.
26.
Wasserman
,
J.
, 2003,
Michelangelo’s Florence Pieta
,
Princeton U. P.
,
Princeton, NJ
.
27.
Stumpfel aand Ch. Tchou
,
J.
,
Yun
,
N.
,
Martinez
,
P.
,
Hawkins
,
T.
,
Jones
,
A.
,
Emerson
,
B.
, and
Debev
,
P.
, 2003, “
Digital Reunification of the Parthenon and its Sculptures
,” in
4th International Symposium on Virtual Reality, Archaeology and Intelligent Cultural Heritage
, November 5–7, Brighton, United Kingdom, pp.
41
50
.
28.
Blais
,
F.
, 2004, “
Review of 20years of range sensor development
,”
J. Electron. Imaging
1017-9909,
13
(
1
), pp.
231
240
.
29.
Bernardini
,
F.
,
Martin
,
I. M
, and
Rushmeier
,
H.
, 2001, “
High-Quality Texture Reconstruction From Multiple Scans
,”
IEEE Trans. Vis. Comput. Graph.
1077-2626,
7
(
4
), pp.
318
332
.
30.
Hendrik
,
Lensch
,
P. A.
,
Kautz
,
J.
,
Goesele
,
M.
,
Heidrich
,
W.
, and
Seidel
,
H-P.
, 2003, “
Image-Based Reconstruction of Spatial Appearance and Geometric Detail
,”
ACM Trans. Graphics
0730-0301,
22
(
2
), pp.
234
257
.
31.
Sorkine
,
O.
, 2005, Eurographics’05 State-of-the-Art Report.
32.
Zorin
,
D.
,
Schröder
,
P.
,
DeRose
,
T.
,
Kobbelt
,
L.
,
Levin
,
A.
, and
Sweldens
,
W.
, 2000, SIGGRAPH’00 Course Notes.
33.
Du
,
Q.
,
Gunzburger
,
M. D.
, and
Ju
,
L.
, 2003, “
Constrained Centroidal Voronoi Tessellations for Surfaces
,”
SIAM J. Sci. Comput. (USA)
1064-8275,
24
(
5
),
1488
1506
.
34.
Du
,
Q.
,
Faber
,
V.
, and
Gunzburger
,
M.
, 1999, “
Centroidal Voronoi Tessellations: Applications and Algorithms
,”
SIAM Rev.
0036-1445,
41
, pp.
637
676
.
35.
Catmull
,
E.
, and
Clark
,
J.
, 1978, “
Recursively Generated B-spline Surfaces on Arbitrary Topological Meshes
,”
CAD
0010-4485,
10
(
6
), pp.
350
355
.
36.
Biermann
,
H.
,
Martin
,
I.
,
Bernardini
,
F.
, and
Zorin
,
D.
, 2002, “
Cut-and-paste Editing of Multiresolution Surfaces
,” in
Proc. SIGGRAPH 02
, July 23–26, San Antonio, TX, pp.
312
321
.
37.
Biermann
,
H.
,
Martin
,
I.
,
Zorin
,
D.
, and
Bernardini
,
F.
, 2001, “
Sharp Features on Multiresolution Subdivision Surfaces
,” in
Proceedings of Pacific Graphics 01
, October 16–18, Tokyo, Japan,
IEEE
,
New York
.
38.
Boier-Martin
,
I.
,
Ronfard
,
R.
, and
Bernardini
,
F.
, 2004, “
Detail-Preserving Variational Surface Design With Multiresolution Constraints
,” in
Proc. SMI 04
, June 7–9, Genova, Italy, pp.
119
128
.
39.
McQueen
,
J.
, 1967, “
Some Methods for Classification and Analysis of Multivariate Observations
,”
5th Berkeley Symp. Math. Stat. Prob.
, edited by
L.
Le Cam
and
J.
Neyman
, Univ. of California, June 21–July 18, 1965 and December 21, 1965–January 7, 1966,
Univ. of California Press
, Vol.
1
, pp.
281
297
.
40.
Alliez
,
P.
,
de Verdière
,
E. C.
,
Devillers
,
O.
, and
Isenburg
,
M.
, 2003, “
Isotropic Surface Remeshing
,” in
Proc. SMI03
, May 12-16, Seoul, Korea, pp.
49
58
.
41.
Amenta
,
N.
,
Bern
,
M.
, and
Kamvysselis
,
M.
, 1998, “
A New Voronoi-Based Surface Reconstruction Algorithm
,”
Proc. SIGGRAPH 98
, July 19–24, Orlando, FL, pp.
415
421
.
42.
Müller-Hannemann
,
M.
, and
Weihe
,
K.
, 1997, “
Minimum Strictly Convex Quadrangulations of Convex Polygons
,” in
Symp. Comp. Geom.
, June 4–6, Nice, France, pp.
193
202
.
43.
Zorin
,
D.
,
Schröder
,
P.
, and
Sweldens
,
W.
, 1997, “
Interactive Multiresolution Mesh Editing
,”
Proceedings of SIGGRAPH, 97
, August,
Los Angeles, CA
, pp.
259
268
.
44.
Osada
,
R.
,
Funkhouser
,
T.
,
Chazelle
,
B.
, and
Dobkin
,
D.
, 2002, “
Shape Distributions
,”
ACM Trans. Graphics
0730-0301,
21
(
4
), pp.
807
832
.
45.
Cignoni
,
P.
,
Rocchini
,
C.
, and
Scopigno
,
R.
, 1998, “
Metro: Measuring Error on Simplified Surfaces
,”
Comput. Graph. Forum
0167-7055,
17
(
2
), pp.
167
174
.
46.
Ciarlet
,
P. G.
, 1991, “
Basic Error Estimates for Elliptic Problems
,”
Handbook of Numerical Analysis
, North-Holland, Amsterdam.
47.
Hormann
,
K.
and
Greiner
,
G.
, 2000, “
MIPS: An Efficient Global Parametrization Method
,” in
Curve and Surface Design: Saint-Malo 1999 (Innovations in Applied Mathematics
, edited by
P.-J.
Laurent
,
P.
Sabglonniere
, and
L. L.
Schumaker
,
Vanderbilt University Press
, pp.
153
162
.
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