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.
Issue Section:
Research Papers
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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