This paper describes a new formulation of solid modeling for treating parts derived from volumetric scans (computed tomography, magnetic resonance, etc.) along with parts from traditional computer-aided design operations. Recent advances in segmentation via level set methods produce voxel grids of signed distance values, and we interpolate the signed distance values using wavelets to produce an implicit or function-based representation called wavelet signed distance function representation that provides inherent support for data compression, multiscale modeling, and skeletal-based operations.

1.
Jones
,
M.
,
Baerentzen
,
J.
, and
Sramek
,
M.
, 2006, “
3D Distance Fields: A Survey of Techniques and Applications
,”
IEEE Trans. Vis. Comput. Graph.
1077-2626,
12
(
4
), pp.
581
599
.
2.
Hu
,
Y.
,
Haynor
,
D.
,
Fassbind
,
M.
,
Rohr
,
E.
, and
Ledoux
,
W.
, 2006, “
Image Segmentation and Registration for the Analysis of Joint Motion From 3D MRI
,”
Proc. SPIE
0277-786X,
6141
, pp.
133
142
.
3.
Boykov
,
Y.
, and
Veksler
,
O.
, 2006, “
Graph Cuts in Vision and Graphics: Theories and Applications
,”
Handbook of Mathematical Models in Computer Vision
,
N.
Paragios
,
Y.
Chen
, and
O.
Faugeras
, eds.,
Springer-Verlag
,
Berlin
, pp.
79
96
.
4.
Sethian
,
J. A.
, 1999,
Level Set Methods and Fast Marching Methods
,
2nd ed.
,
Cambridge University Press
,
New York
.
5.
Osher
,
S.
, and
Fedkiw
,
R.
, 2002,
Level Set Methods and Dynamic Implicit Surfaces
,
Springer-Verlag
,
New York
.
6.
Bloomenthal
,
J.
, 1997,
Introduction to Implicit Surfaces
,
Morgan Kaufmann
,
San Francisco, CA
.
7.
Lorensen
,
W.
, and
Cline
,
H.
, 1987, “
Marching Cubes: A High Resolution 3D Surface Construction Algorithm
,”
Comput. Graph.
0097-8930,
21
(
4
), pp.
163
169
.
8.
Cline
,
H.
,
Lorenson
,
W.
,
Ludke
,
S.
,
Crawford
,
C.
, and
Teeter
,
B.
, 1988, “
Two Algorithms for the Three-Dimensional Reconstruction of Tomograms
,”
Med. Phys.
0094-2405,
15
(
3
), pp.
320
327
.
9.
Rheinboldt
,
W.
, 1988, “
On the Computation of Multi-Dimensional Solution Manifolds of Parametrized Equations
,”
Numer. Math.
0029-599X,
53
, pp.
165
182
.
10.
Allgower
,
E.
, and
Georg
,
K.
, 1990,
Numerical Continuation Methods, An Introduction
(
Springer Series in Computational Mathematics
), Vol.
13
,
Springer-Verlag
,
New York
.
11.
Allgower
,
E.
, and
Gnutzmann
,
S.
, 1991, “
Simplicial Pivoting for Mesh Generation of Implicity Defined Surfaces
,”
Comput. Aided Geom. Des.
0167-8396,
8
(
4
), pp.
305
325
.
12.
Velho
,
L.
,
Gomes
,
J.
, and
de Figueiredo
,
L. H.
, 2002,
Implicit Objects in Computer Graphics
,
Springer-Verlag
,
New York
.
15.
Hoffmann
,
C.
, 1989,
Geometric and Solid Modeling: An Introduction
,
Morgan Kaufmann
,
San Francisco, CA
.
16.
Glassner
,
A.
, 1984, “
Space Subdivision for Fast Ray Tracing
,”
IEEE Comput. Graphics Appl.
0272-1716,
4
(
10
), pp.
15
22
.
17.
Pasko
,
A.
,
Adzhiev
,
V.
,
Sourin
,
A.
, and
Savchenko
,
V.
, 1995, “
Function Representation in Geometric Modeling: Concept, Implementation, and Applications
,”
Visual Comput.
0178-2789,
11
, pp.
429
446
.
18.
Shapiro
,
V.
, 1994, “
Real Functions for Representation of Rigid Solids
,”
Comput. Aided Geom. Des.
0167-8396,
11
, pp.
153
175
.
19.
Ricci
,
A.
, 1973, “
A Constructive Geometry for Computer Graphics
,”
Comput. J.
0010-4620,
16
(
2
), pp.
157
160
.
20.
Sabin
,
M.
, 1968, “
The Use of Potential Surfaces for Numerical Geometry
,” British Aircraft Corporation, Weybridge, UK, Technical Report No. VTO/MS/153.
21.
Ganter
,
M.
, and
Storti
,
D.
, 1995, “
Object Extent Determination for Algebraic Solid Models
,”
ASME J. Mech. Des.
0161-8458,
117
, pp.
20
26
.
22.
Ensz
,
M.
, 1994, “
Implicit Swept Solids
,” MS thesis, University of Washington, Seattle.
23.
Sourin
,
A.
, and
Pasko
,
A.
, 1995, “
Functional Representations for Sweeping by a Moving Solid
,”
Proceedings of the Third Symposium on Solid Modeling and Applications
,
ACM
,
NY
, pp.
383
391
.
24.
Savchenko
,
V.
,
Pasko
,
A.
,
Okunev
,
O.
, and
Kunii
,
T.
, 1995, “
Function Representation of Solids Reconstructed From Scattered Surface Points and Contours
,”
Comput. Graph. Forum
1067-7055,
14
(
4
), pp.
181
188
.
25.
Lim
,
C. -T.
,
Ensz
,
M. T.
,
Ganter
,
M. A.
, and
Storti
,
D. W.
, 1997, “
Object Reconstruction From Layered Data Using Implicit Solid Modeling
,”
J. Manuf. Syst.
0278-6125,
16
(
4
), pp.
260
272
.
26.
Maneewarn
,
T.
,
Hannaford
,
B.
,
Storti
,
D.
, and
Ganter
,
M.
, 1999, “
Haptic Rendering for Internal Content of an Implicit Object
,”
Proceedings of the ASME IMECE
, Nashville, TN.
29.
Ensz
,
M.
,
Storti
,
D.
, and
Ganter
,
M.
, 1998, “
Implicit Methods for Geometry Creation
,”
Int. J. Comput. Geom. Appl.
0218-1959,
8
(
5-6
), pp.
509
536
.
30.
Ensz
,
M.
, 1997, “
Implicit Solid Modeling Through Manifold Modification
,” Ph.D. thesis, University of Washington, Seattle.
31.
Raviv
,
A.
, and
Elber
,
G.
, 2000, “
Three Dimensional Freeform Sculpting Via Zero Sets of Trivariate Functions
,”
Comput.-Aided Des.
0010-4485,
32
, pp.
513
526
.
32.
Schmitt
,
B.
,
Pasko
,
A.
, and
Schlick
,
C.
, 2004, “
Constructive Sculpting of Heterogeneous Volumetric Objects Using Trivariate B-Splines
,”
Visual Comput.
0178-2789,
20
, pp.
130
148
.
33.
Freytag
,
M.
,
Shapiro
,
V.
, and
Tsukanov
,
I.
, 2006, “
Field Modeling With Sampled Distances
,”
Comput.-Aided Des.
0010-4485,
38
(
2
), pp.
87
100
.
34.
Houston
,
B.
,
Nielsen
,
M.
,
Batty
,
C.
,
Nillson
,
O.
, and
Museth
,
K.
, 2006, “
Hierarchical RLE Level Set: A Compact and Versatile Deformable Surface Representation
,”
ACM Trans. Graphics
0730-0301,
25
(
1
), pp.
151
175
.
35.
Blum
,
H.
, 1973, “
Biological Shape and Visual Science
,”
J. Theor. Biol.
0022-5193,
38
(
1
), pp.
205
287
.
36.
Wolter
,
F.
, 1993, “
Cut Locus and Medial Axis in Global Shape Interrogation and Representation
,” Department of Ocean Engineering, MIT, Cambridge, MA, Design Laboratory Memorandum No. 92-2.
37.
Daubechies
,
I.
, 1992,
Wavelets
(
CBMS-NS Series in Applied Mathematics
),
SIAM
,
Philadelphia, PA
.
38.
Resnikoff
,
H.
, and
Wells
,
R.
, 1998,
Wavelet Analysis: The Scalable Structure of Information
,
Springer-Verlag
,
New York
.
39.
Norton
,
A.
, and
Rockwood
,
A.
, 2003, “
Enabling View-Dependent Progressive Volume Visualization on the Grid
,”
IEEE Comput. Graphics Appl.
0272-1716,
23
, pp.
22
31
.
40.
Garcia
,
A.
, and
Shen
,
H. -W.
, 2005, “
GPU-Based 3D Wavelet Reconstruction With Tileboarding
,”
Visual Comput.
0178-2789,
21
, pp.
755
763
.
42.
Nievergelt
,
Y.
, 1999,
Wavelets Made Easy
,
Birkhauser
,
Boston, MA
.
43.
Storti
,
D.
,
Ganter
,
M.
,
Ledoux
,
W.
,
Ching
,
R.
,
Hu
,
Y. P.
, and
Haynor
,
D.
, 2007, “
Artifact Vs. Anatomy: Dealing With Conflict of Geometric Modeling Descriptions
,”
Proceedings of the SAE Human Modeling Conference
, Seattle, WA, Paper No. 2007-01-2450.
44.
Sachs
,
E.
,
Williams
,
P.
,
Brancazio
,
M.
,
Cima
,
M.
, and
Kremmin
,
K.
, 1990, “
Three-Dimensional Printing: Rapid Tooling and Prototypes Directly From a Cad Model
,”
Proceedings of the Manufacturing International
,
ASME
,
New York
, Vol.
4
, pp.
131
136
.
45.
Storti
,
D.
,
Turkiyyah
,
G.
,
Ganter
,
M.
,
Lim
,
C. -T.
, and
Stal
,
D.
, 1997, “
Skeleton-Based Modeling Operations on Solids
,”
Proceedings of the Third ACM Solid Modeling Conference
, pp.
141
154
.
46.
Blanding
,
R.
,
Brooking
,
C.
,
Ganter
,
M.
, and
Storti
,
D.
, 1999, “
A Skeletal-Based Solid Editor
,”
Proceedings of ACM Fifth Symposium on Solid Modeling
,
W.
Broosvoort
and
D.
Anderson
, eds.,
ACM
,
NY
, pp.
141
150
.
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