11.3.7 Fitting Curved Surfaces

Dube, R.P.[R. Peter],
Tension In A Bicubic Surface Patch,
CGIP(5), No. 4, December 1976, pp. 496-502.
Elsevier DOI BibRef 7612

Dube, R.P.[R. Peter],
Univariate Blending Functions and Alternatives,
CGIP(6), No. 4, August 1977, pp. 394-408.
Elsevier DOI 0501
Bases for fitting curves. BibRef

Midgley, J.E.[James E.],
Isotropic Four-Point Interpolation,
CGIP(11), No. 2, October 1979, pp. 192-196.
Elsevier DOI Smooth curve through arbitrary data points. More work:
See also Isotropic Four-Point Interpolation Based on Cubic Splines, An. 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.[Ehud],
Display of Three-Dimensional Information in Computed Tomography,
CGIP(9), No. 2, February 1979, pp. 196-198.
Elsevier DOI BibRef 7902

Artzy, E.[Ehud], Frieder, G.[Gideon], Herman, G.T.[Gabor T.],
The Theory, Design, Implementation and Evaluation of a 3D Surface Detection Algorithm,
CGIP(15), No. 1, January 1981, pp. 1-24.
Elsevier DOI Evaluation, Reconstruction. BibRef 8101

Herman, G.T.[Gabor T.], Liu, H.K.[Hsun Kao],
Dynamic Boundary Surface Detection,
CGIP(7), No. 1, February 1978, pp. 130-138.
Elsevier DOI Dynamic surfaces. BibRef 7802

Herman, G.T.[Gabor T.], Liu, H.K.[Hsun Kao],
3D Display of Human Organs from Computed Tomograms,
CGIP(9), No. 1, 1979, pp. 1-21.
Elsevier DOI Hidden surfaces for CT data. BibRef 7900

Gullberg, G.T.[Grant T.],
The Reconstruction of Fan-Beam Data by Filtering the Back-Projection,
CGIP(10), No. 1, May 1979, pp. 30-47.
Elsevier DOI More efficient computation. BibRef 7905

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

Verly, J.G.[Jacques G.],
High-Resolution Imaging in 3-D Reconstructive Tomography,
CGIP(16), No. 1, May 1981, pp. 1-19.
Elsevier DOI BibRef 8105

Gillman, G.[Geoff], Macleod, I.[Iain],
Reconstruction of X-Ray Sources from Penumbral images,
CGIP(11), No. 3, November 1979, pp. 227-241.
Elsevier DOI 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

Xu, S.B., Lu, W.X.,
Surface Reconstruction of 3D Objects in Computerized Tomography,
CVGIP(44), No. 3, December 1988, pp. 270-278.
Elsevier DOI 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.
Elsevier DOI Errors in edge detector output. BibRef 9210

Lee, C.H.[Chia-Hoang], Seidman, T.[Thomas], Rosenfeld, A.[Azriel],
Generation Process for the Reconstruction of Space Curves,
IVC(8), No. 2, May 1990, pp. 99-107.
Elsevier DOI Line drawings. Generate, decide. 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 File. 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.
DOI Link
PDF File. 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 File. BibRef
And:
Simultaneous Segmentation and Approximation of Complex Patterns,
CVPR94(617-623).
IEEE DOI 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 BibRef 9200

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

Best, L.[Leland], Mageo, M.[Michael],
Autonomous Construction of 3-Dimensional Models from Range Data,
PR(31), No. 2, February 1998, pp. 121-136.
Elsevier DOI 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.
DOI Link
See also Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data, A. BibRef 9909

Keren, D.[Daniel], Werman, M.[Michael],
Probabilistic Analysis of Regularization,
PAMI(15), No. 10, October 1993, pp. 982-995.
IEEE DOI BibRef 9310
Earlier:
Variations on Regularization,
ICPR90(I: 93-98).
IEEE DOI Regularization applied to 3-D surface fitting of range points. BibRef

Keren, D.[Daniel], Werman, M.[Michael], Feinberg, J.[Joshua],
A Probabilistic Approach to Pattern Matching in the Continuous Domain,
PAMI(34), No. 10, October 2012, pp. 1873-1885.
IEEE DOI 1208
Compute the complete probability distribution of the signal, not just the dicerete value. 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 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.
DOI Link 0012
BibRef
Earlier:
Model Selection and Surface Merging in Reconstruction Algorithms,
ICCV98(895-902).
IEEE DOI 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 DOI 0012
BibRef
And:
Estimating Vision Parameters given Data with Covariances,
BMVC00(xx-yy).
PDF File. 0009
Estimate parameters of the model.
See also Revisiting Hartley's normalized eight-point algorithm. BibRef

Brooks, M.J.[Michael J.], Chojnacki, W.[Wojciech], Gawley, D.[Darren], van den Hengel, A.J.[Anton J.],
What Value Covariance Information in Estimating Vision Parameters?,
ICCV01(I: 302-308).
IEEE DOI 0106
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 DOI 0101
Curve 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 DOI 0205
Distance-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.
Springer DOI Fitting curves and surfaces. From thesis. BibRef

Ahn, S.J., Rauh, W., Westkämper, E.,
Fitting of Parametric Space Curves and Surfaces by Using the Geometric Error Measure,
DAGM02(548 ff.).
Springer DOI 0303
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 DOI 0205
Fit a surface to data. BibRef

Bing, C.[Cheng], Ying, W.[Wang], Zheng, N.N.[Nan-Ning], Bian, Z.Z.[Zheng-Zhong], Zhang, Y.P.[Yong-Ping],
A two-step method for preprocessing volume data,
CVIU(95), No. 2, August 2004, pp. 150-164.
Elsevier DOI 0409
Create 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.
Elsevier DOI 0611
Surface fitting; Quadric surfaces; Paraboloids; Least-squares BibRef

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

Grimm, C.M.[Cindy M.], Ju, T.[Tao], Phan, L.[Ly], Hughes, J.[John],
Adaptive smooth surface fitting with manifolds,
VC(25), No. 5-7, May 2009, pp. xx-yy.
Springer DOI 0905
BibRef

Rouhani, M.[Mohammad], Sappa, A.D.[Angel D.],
Implicit Polynomial Representation Through a Fast Fitting Error Estimation,
IP(21), No. 4, April 2012, pp. 2089-2098.
IEEE DOI 1204
BibRef
Earlier:
Implicit B-spline fitting using the 3L algorithm,
ICIP11(893-896).
IEEE DOI 1201
BibRef
Earlier:
A fast accurate implicit polynomial fitting approach,
ICIP10(1429-1432).
IEEE DOI 1009
BibRef
And:
Relaxing the 3L algorithm for an accurate implicit polynomial fitting,
CVPR10(3066-3072).
IEEE DOI 1006
BibRef
Earlier: A2, A1:
Efficient distance estimation for fitting implicit quadric surfaces,
ICIP09(3521-3524).
IEEE DOI 0911
BibRef
And: A1, A2:
A Novel Approach to Geometric Fitting of Implicit Quadrics,
ACIVS09(121-132).
Springer DOI 0909
BibRef

Rouhani, M.[Mohammad], Sappa, A.D.[Angel D.], Boyer, E.,
Implicit B-Spline Surface Reconstruction,
IP(24), No. 1, January 2015, pp. 22-32.
IEEE DOI 1502
image reconstruction BibRef

Dai, L., Zhang, F., Mei, X., Zhang, X.,
Fast Minimax Path-Based Joint Depth Interpolation,
SPLetters(22), No. 5, May 2015, pp. 623-627.
IEEE DOI 1411
Complexity theory BibRef

Zhang, F., Dai, L., Xiang, S., Zhang, X.,
Segment Graph Based Image Filtering: Fast Structure-Preserving Smoothing,
ICCV15(361-369)
IEEE DOI 1602
Image edge detection BibRef

Hunyadi, L.[Levente], Vajk, I.[István],
Constrained quadratic errors-in-variables fitting,
VC(30), No. 12, December 2014, pp. 1347-1358.
Springer DOI 1411
Fit conics or quadrics. BibRef

Absil, P.A., Gousenbourger, P.Y.[Pierre-Yves], Striewski, P.[Paul], Wirth, B.[Benedikt],
Differentiable Piecewise-Bézier Surfaces on Riemannian Manifolds,
SIIMS(9), No. 4, 2016, pp. 1788-1828.
DOI Link 1612
BibRef

Birdal, T.[Tolga], Busam, B.[Benjamin], Navab, N.[Nassir], Ilic, S.[Slobodan], Sturm, P.F.[Peter F.],
Generic Primitive Detection in Point Clouds Using Novel Minimal Quadric Fits,
PAMI(42), No. 6, June 2020, pp. 1333-1347.
IEEE DOI 2005
BibRef
Earlier:
A Minimalist Approach to Type-Agnostic Detection of Quadrics in Point Clouds,
CVPR18(3530-3540)
IEEE DOI 1812
Solid modeling, Shape, Ellipsoids, Surface fitting, Splines (mathematics), Quadrics, minimal problems. Clutter, Pipelines, Fitting, Feature extraction BibRef

Yang, Z.S.[Zhang-Sihao], Litany, O.[Or], Birdal, T.[Tolga], Sridhar, S.[Srinath], Guibas, L.J.[Leonidas J.],
Continuous Geodesic Convolutions for Learning on 3D Shapes,
WACV21(134-144)
IEEE DOI 2106
Matched filters, Shape, Convolution, Neural networks, Sampling methods BibRef

Kanatani, K.[Kenichi], Al-Sharadqah, A.[Ali], Chernov, N.[Nikolai], Sugaya, Y.[Yasuyuki],
Renormalization Returns: Hyper-renormalization and Its Applications,
ECCV12(III: 384-397).
Springer DOI 1210
versus minimization of the reprojection error. 3D from noisy data. BibRef

Fujiki, J.[Jun], Akaho, S.[Shotaro],
Flexible Hypersurface Fitting with RBF Kernels,
CAIP13(286-293).
Springer DOI 1308
BibRef
Earlier:
Hypersurface Fitting via Jacobian Nonlinear PCA on Riemannian Space,
CAIP11(I: 236-243).
Springer DOI 1109
BibRef
Earlier:
Curve fitting by Spherical Least Squares on two-dimensional sphere,
Subspace09(250-255).
IEEE DOI 0910
BibRef

Fujiki, J.[Jun], Akaho, S.[Shotaro], Hino, H.[Hideitsu], Murata, N.[Noboru],
Robust Hyperplane Fitting Based on k-th Power Deviation and a-Quantile,
CAIP11(I: 278-285).
Springer DOI 1109
least median of squares. BibRef

Yang, Y.J.[Yi-Jun], Yong, J.H.[Jun-Hai], Zhang, H.[Hui], Paul, J.C.[Jean-Claude], Sun, J.G.[Jia-Guang],
Optimal Parameterizations of Bézier Surfaces,
ISVC06(I: 672-681).
Springer DOI 0611
BibRef

Wang, W.K.[Wen-Ke], Zhang, H.[Hui], Yong, J.H.[Jun-Hai], Sun, J.G.[Jia-Guang],
Surface Fitting to Curves with Energy Control,
ISVC06(I: 569-578).
Springer DOI 0611
BibRef

Tseng, Y.H.[Yi-Hsing], Tang, K.P.[Kai-Pei], Chou, F.C.[Fu-Chen],
Surface Reconstruction from LiDAR Data with Extended Snake Theory,
EMMCVPR07(479-492).
Springer DOI 0708
BibRef

Cheng, D.C.[Da-Chuan], Jiang, X.Y.[Xiao-Yi],
Object Modeling with Guaranteed Fulfillment of Geometric Constraints,
3DPVT06(639-646).
IEEE DOI 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).
Springer DOI 0509
BibRef

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

Faber, P.[Petko], Fisher, R.B.,
Euclidean Fitting Revisited,
VF01(165 ff.).
Springer DOI 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 DOI 9704
BibRef

Varley, A.[Andrew], Rayner, P.[Peter],
Bézier modelling of cracks,
CIAP97(I: 551-558).
Springer DOI 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). 9608
University of Sheffield BibRef

Fletcher, G.J., Giblin, P.J.,
Class Based Reconstruction Techniques using Singular Apparent Contours,
ECCV96(I:107-116).
Springer DOI 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 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 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).
Springer DOI 9405
BibRef

Fitzgibbon, A.W.[Andrew W.], Fisher, R.B.[Robert B.],
Invariant Fitting of Arbitrary Single-Extremum Surfaces,
BMVC93(569-578).
PDF File. BibRef 9300 Edinburghsurface fitting in range data
PS File. (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 Link. BibRef 8606

Chapter on 3-D Object Description and Computation Techniques, Surfaces, Deformable, View Generation, Video Conferencing continues in
Surface Interpolation, Surface Reconstction .