11.3.3 Fitting Curved Surfaces

Dube, R.P.,
Tension In A Bicubic Surface Patch,
CGIP(5), No. 4, December 1976, pp. 496-502.
WWW Version. BibRef 7612

Dube, R.P.[R. Peter],
Univariate Blending Functions and Alternatives,
CGIP(6), No. 4, August 1977, pp. 394-408.
WWW Version. 0501 BibRef

Midgley, J.E.,
Isotropic Four-Point Interpolation,
CGIP(11), No. 2, October 1979, pp. 192-196.
WWW Version. BibRef 7910

Bookstein, F.L.,
The Measurement of Biological Shape and Shape Change,
SpringerNew York, 1978. BibRef 7800

Bookstein, F.L.,
A Statistical Method for Biological Shape Comparisons,
Theoretical Biology(107), 1984, pp. 475-520. Tensor methods to compare mean sizes, mean shapes, and shape changes over time. BibRef 8400

Bookstein, F.L.,
Size and Shape Spaces for Landmark Data in Two Dimensions,
Statictical Science(1), No. 2, 1986, pp. 181-242. centroid size variable and shape variables are uncorrelated. BibRef 8600

Bookstein, F.L.,
Morphometric Tools for Landmark Data: Geometry and Biology,
Cambridge University PressCambridge, MA, 1991. BibRef 9100

Bookstein, F.L.,
Landmark Methods for Forms Without Landmarks: Localizing Group Differences in Outline Shapes,
MMBIA96(SHAPE) BibRef 9600

Artzy, E.,
Display of Three-Dimensional Information in Computed Tomography,
CGIP(9), No. 2, February 1979, pp. 196-198.
WWW Version. BibRef 7902

Artzy, E., Frieder, G., and Herman, G.T.,
The Theory, Design, Implementation and Evaluation of a 3D Surface Detection Algorithm,
CGIP(15), No. 1, January 1981, pp. 1-24.
WWW Version. Evaluation, Reconstruction. BibRef 8101

Herman, G.T., and Liu, H.K.,
Dynamic Boundary Surface Detection,
CGIP(7), No. 1, February 1978, pp. 130-138.
WWW Version. BibRef 7802

Herman, G.T., and Liu, H.K.,
3D Display of Human Organs from Computed Tomograms,
CGIP(9), No. 1, 1979, pp. 1-21.
WWW Version. BibRef 7900

Gullberg, G.T.,
The Reconstruction of Fan-Beam Data by Filtering the Back-Projection,
CGIP(10), No. 1, May 1979, pp. 30-47.
WWW Version. BibRef 7905

Minerbo, G.,
MENT: A Maximum Entropy Algorithm for Reconstructing a Source from Projection Data,
CGIP(10), No. 1, May 1979, pp. 48-68.
WWW Version. BibRef 7905

Verly, J.G.,
High-Resolution Imaging in 3-D Reconstructive Tomography,
CGIP(16), No. 1, May 1981, pp. 1-19.
WWW Version. BibRef 8105

Gillman, G., MacLeod, I.,
Reconstruction of X-Ray Sources from Penumbral images,
CGIP(11), No. 3, November 1979, pp. 227-241.
WWW Version. BibRef 7911

Bolle, R.M., and Cooper, D.B.,
Bayesian Recognition of Local 3-D Shape by Approximating Image Intensity Functions with Quadric Polynomials,
PAMI(6), No. 4, July 1984, pp. 418-429. BibRef 8407

Bolle, R.M., Cooper, D.B., and Cernuschi-Frias, B.,
Three-Dimensional Surface Shape Recognition by Approximating Image Intensity Functions with Quadric Polynomials,
PRIP82(611-617). BibRef 8200

Cernuschi-Frias, B., Cooper, D.B., and Bolle, R.M.,
Estimation of Location and Orientation of 3-D Surfaces Using a Single 2-D Image,
PRIP82(605-610). BibRef 8200

Shirman, L., Sequin, C.,
Local Surface Interpolation with Bezier Patches,
CADG(4), 1987, pp. 279-295. BibRef 8700

Xu, S.B., Lu, W.X.,
Surface Reconstruction of 3D Objects in Computerized Tomography,
CVGIP(44), No. 3, December 1988, pp. 270-278.
WWW Version. BibRef 8812

Cao, X.P., Shrikande, N., Hu, G.Z.,
Approximate Orthogonal Distance Regression Method for Fitting Quadric Surfaces to Range Data,
PRL(15), No. 8, August 1994, pp. 781-796. BibRef 9408

Cai, Y.Y., Nee, A.Y.C., Loh, H.T.,
Geometric Feature Detection for Reverse Engineering Using Range Imaging,
JVCIR(7), No. 3, September 1996, pp. 205-216. Quadric Surfaces. Recognition. BibRef 9609

Sankar, P.V., Silbermann, M.J., Ferrari, L.A.,
Curve and Surface Generation and Refinement: Based on a High-Speed Derivative Algorithm,
GMIP(56), No. 1, January 1994, pp. 94-101. BibRef 9401

Snyder, W.E., Groshong, R., Hsiao, M., Boone, K.L., Hudacko, T.,
Closing Gaps in Edges and Surfaces,
IVC(10), No. 8, October 1992, pp. 523-531.
WWW Version. BibRef 9210

Lee, C.H., Seidman, T., Rosenfeld, A.,
Generation Process for the Reconstruction of Space Curves,
IVC(8), No. 2, May 1990, pp. 99-107.
WWW Version. BibRef 9005

Baird, L., and Wang, P.,
3D Object Perception Using Gradient Descent,
JMIV(5), No. 2, June 1995, pp. 111-117. BibRef 9506

Lim, Y.S., Cho, T.I., Park, K.H.,
Range Image Segmentation Based on 2D Quadratic Function Approximation,
PRL(11), 1990, pp. 699-708. BibRef 9000

Liao, C.W.[Chia-Wei], Medioni, G.[Gerard],
Surface Approximation of a Cloud of 3D Points,
GMIP(57), No. 1, January 1995, pp. 67-74. Attempt to work on multiple objects and those with holes. Extract the object, then the parts that are not explained right, and generate a CSG representation for the various combinations.
PDF Version. BibRef 9501

Liao, C.W.[Chia-Wei], Medioni, G.[Gerard],
Simultaneous Surface Approximation and Segmentation of Complex Objects,
CVIU(73), No. 1, January 1999, pp. 43-63.
WWW Version.
PDF Version. BibRef 9901

Liao, C.W.[Chia Wei], and Medioni, G.[Gerard],
Surface Approximation Of Complex Multipart Objects,
PBMCV95(SESSION 1). BibRef 9500
Earlier:
Surface Approximation of Complex 3-D Objects,
ARPA94(II:1461-1468).
PDF Version. BibRef
And:
Simultaneous Segmentation and Approximation of Complex Patterns,
CVPR94(617-623).
IEEE Abstract. IEEE Top Reference. BibRef

Liao, C.W.[Chia-Wei], Medioni, G.[Gerard],
Surface Approximation and Segmentation of Objects with Unknown Topology,
ARPA96(1033-1040). BibRef 9600

Liao, C.W.[Chia Wei], and Medioni, G.[Gerard],
Representation of Range Data with B-Spline Surface Patches,
ICPR92(III:745-748).
IEEE DOI may work or IEEE-CS DOI may work. BibRef 9200

Laurentini, A.,
Surface Reconstruction Accuracy for Active Volume,
PRL(17), No. 12, October 25 1996, pp. 1285-1292. 9612 BibRef

Best, L., Magee, M.,
Autonomous Construction of 3-Dimensional Models from Range Data,
PR(31), No. 2, February 1998, pp. 121-136.
WWW Version. 9802 BibRef

Agarwal, P.K.[Pankaj K.], Suri, S.[Subhash],
Surface Approximation and Geometric Partitions,
SIAM_JC(27), No. 4, 1998, pp. 1016-1035. Study of computational complexity. BibRef 9800

Zhang, J.W.[Ji-Wen],
C-Bezier Curves and Surfaces,
GMIP(61), No. 1, January 1999, pp. 2-15. BibRef 9901

Keren, D.[Daniel], Werman, M.[Michael],
A Full Bayesian Approach to Curve and Surface Reconstruction,
JMIV(11), No. 1, September 1999, pp. 27-43.
WWW Version. See also Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data, A. BibRef 9909

Keren, D., and Werman, M.,
Probabilistic Analysis of Regularization,
PAMI(15), No. 10, October 1993, pp. 982-995.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9310
Earlier:
Variations on Regularization,
ICPR90(I: 93-98).
IEEE DOI may work or IEEE-CS DOI may work. Regularization applied to 3-D surface fitting of range points. BibRef

Keren, D.[Daniel], Werman, M.[Michael],
Bayesian Regularization,
ARPA94(II:1607-1609). BibRef 9400
And:
A Bayesian Framework For Regularization,
ICPR94(C:72-76).
IEEE DOI may work or IEEE-CS DOI may work. BibRef

Bubna, K.[Kishore], Stewart, C.V.[Charles V.],
Model Selection Techniques and Merging Rules for Range Data Segmentation Algorithms,
CVIU(80), No. 2, November 2000, pp. 215-245. 0012
WWW Version. BibRef
Earlier:
Model Selection and Surface Merging in Reconstruction Algorithms,
ICCV98(895-902).
IEEE DOI may work or IEEE-CS DOI may work. BibRef

Chojnacki, W.[Wojciech], Brooks, M.J.[Michael J.], van den Hengel, A.J.[Anton J.], Gawley, D.[Darren],
On the Fitting of Surfaces to Data with Covariances,
PAMI(22), No. 11, November 2000, pp. 1294-1303.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0012Estimate parameters of the model. BibRef

Chang, K.Y.[Kui-Yu], Ghosh, J.[Joydeep],
A Unified Model for Probabilistic Principal Surfaces,
PAMI(23), No. 1, January 2001, pp. 22-41.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0101Curve or surface fitting, almost. BibRef

Ahn, S.J.[Sung Joon], Rauh, W.[Wolfgang], Cho, H.S.[Hyung Suck], Warnecke, H.J.[Hans-Jürgen],
Orthogonal Distance Fitting of Implicit Curves and Surfaces,
PAMI(24), No. 5, May 2002, pp. 620-638.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0205Distance-based algorithm. Coordinate-based algorithm. minimize sq sum of orthogonal error distance. BibRef

Ahn, S.J.[Sung Joon],
Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space,
Springer2004. ISBN: 978-3-540-23966-6 BibRef 0400 LNCS3151.
WWW Version. Fitting curves and surfaces. From thesis. BibRef

Sengupta, K.[Kuntal], Burman, P.[Prabir],
A Curve Fitting Problem and Its Application in Modeling Objects in Monocular Image Sequences,
PAMI(24), No. 5, May 2002, pp. 674-686.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0205Fit a surface to data. BibRef

Bing, C.[Cheng], Ying, W.[Wang], Zheng, N.N.[Nan-Ning], Bian, Z.[Zhengzhong], Zhang, Y.P.[Yong-Ping],
A two-step method for preprocessing volume data,
CVIU(95), No. 2, August 2004, pp. 150-164.
WWW Version. 0409Create surfaces to use for rendering. Filter noise, then segment by modeling surface as a PDE. BibRef

Dai, M.[Min], Newman, T.S.[Timothy S.], Cao, C.G.[Chun-Guang],
Least-squares-based fitting of paraboloids,
PR(40), No. 2, February 2007, pp. 504-515.
WWW Version. 0611Surface fitting; Quadric surfaces; Paraboloids; Least-squares BibRef

Faria, L.N.[Lilian N.], Mascarenhas, N.D.A.[Nelson D.A.], Morón, C.E.[Célio E.], Saito, J.H.[José H.], Rosa, R.R.[Reinaldo R.], Sawant, H.S.[Hanumant S.],
A parallel application for 3D reconstruction of coronal loops using image morphing,
IVC(25), No. 1, January 2007, pp. 95-102.
WWW Version. 0611Coronal loops; 3D Reconstruction; Image processing; Image morphing; Parallel system BibRef

Sahin, T.[Turker], Unel, M.[Mustafa],
Stable Algebraic Surfaces for 3d Object Representation,
JMIV(32), No. 2, October 2008, pp. xx-yy.
WWW Version. 0804 BibRef
Earlier:
Fitting Globally Stabilized Algebraic Surfaces to Range Data,
ICCV05(II: 1083-1088).
IEEE DOI may work or IEEE-CS DOI may work. 0510 BibRef
Earlier:
Globally Stabilized 3L Curve Fitting,
ICIAR04(I: 495-502).
WWW Version. 0409 BibRef
And:
An Adaptive Estimation Method for Rigid Motion Parameters of 2D Curves,
ICIAR04(II: 355-362).
WWW Version. 0409 BibRef

Cheng, D.C.[Da-Chuan], Jiang, X.Y.[Xiao-Yi],
Object Modeling with Guaranteed Fulfillment of Geometric Constraints,
3DPVT06(639-646).
IEEE DOI may work or IEEE-CS DOI may work. 0606 BibRef

Jiang, X.Y.[Xiao-Yi], Cheng, D.C.[Da-Chuan],
A Novel Parameter Decomposition Approach to Faithful Fitting of Quadric Surfaces,
DAGM05(168).
WWW Version. 0509 BibRef

Ahn, S.J., Rauh, W., Westkämper, E.,
Fitting of Parametric Space Curves and Surfaces by Using the Geometric Error Measure,
DAGM02(548 ff.).
HTML Version. 0303 BibRef

Gomes, J., Mojsilovic, A.,
A Variational Approach to Recovering a Manifold from Sample Points,
ECCV02(II: 3 ff.).
HTML Version. 0205 BibRef

Faber, P.[Petko], Fisher, R.B.,
Euclidean Fitting Revisited,
VF01(165 ff.).
HTML Version. BibRef 0100 Edinburgh 0209 BibRef

Faber, P., Fisher, R.B.,
A Buyer's Guide to Euclidean Elliptical Cylindrical and Conical Surface Fitting,
BMVC01(521-530). BibRef 0100 EdinburghUniversity of Edinburgh
HTML Version. 0110 BibRef

Montagnat, J., Delingette, H.,
An Hybrid Framework for Surface Registration and Deformable Models,
CVPR97(1041-1046).
IEEE Abstract. IEEE Top Reference.
WWW Version. 9704 BibRef

Varley, A.[Andrew], Rayner, P.[Peter],
Bézier modelling of cracks,
CIAP97(I: 551-558).
WWW Version. 9709 BibRef

Thacker, N.A., Prendergast, D., and Rockett, P.I.,
B-Fitting: An Estimation Technique with Automatic Parameter Selection,
BMVC96(Model Fitting, Matching, Recognition). 9608University of Sheffield BibRef

Liao, W., Aggarwal, J.K.,
Curve and Surface Interpolation Using Rational Radial Basis Functions,
ICPR96(IV: 8-13).
IEEE DOI may work or IEEE-CS DOI may work. 9608(Univ. of Texas, Austin, USA) BibRef

Fletcher, G.J., Giblin, P.J.,
Class Based Reconstruction Techniques using Singular Apparent Contours,
ECCV96(I:107-116).
WWW Version. Golbal reconstruction of special case surfaces. BibRef 9600

Xie, M.[Ming],
On 3D reconstruction strategy: a case of conics,
ICPR94(A:665-667).
IEEE DOI may work or IEEE-CS DOI may work. 9410 BibRef

Chia, T.L.[Tsorng-Lin], Chen, Z.[Zen],
A vision method for computing 3-D location and shape parameters of a cone,
ICPR94(A:671-673).
IEEE DOI may work or IEEE-CS DOI may work. 9410 BibRef

Fitzgibbon, A.W.[Andrew W.], Fisher, R.B.[Robert B.],
Lack-of-fit detection using the run-distribution test,
ECCV94(B:173-178).
WWW Version. 9405 BibRef

Fitzgibbon, A.W.[Andrew W.], Fisher, R.B.[Robert B.],
Invariant Fitting of Arbitrary Single-Extremum Surfaces,
BMVC93(569-578).
PDF Version. BibRef 9300 Edinburghsurface fitting in range data
Postscript Version. (Edinburgh Univ); BibRef

Harris, J.G.,
A New Approach to Surface Reconstruction: The Coupled Depth/Slope Model,
ICCV87(277-283). BibRef 8700

Harris, J.G.[John G.],
The Coupled Depth/Slope Approach to Surface Reconstruction,
MIT AI-TR-908, June 1986.
WWW Version. BibRef 8606

Chapter on 3-D Object Description and Computation Techniques, Surfaces, Deformable, View Generation, Video Conferencing continues in
Reconstruction, Hierarchical, Multi-Grid Approaches .