Fitting conic sections to "very scattered" data: An iterative refinement of the bookstein algorithm
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FVD StyleGAN, FVD I3D, and FID are used for visual quality, and TSE and CSE for multi-view consistency.
“We use FVD StyleGAN, FVD I3D, and FID for visual quality (Skorokhodov et al., 2021) and TSE and CSE (Sampson, 1982) for multi-view consistency.”
From World Simulation with Video Foundation Models for Physical AI (2025) · cites this paper as Sampson, 1982
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Direct Least Square Fitting of Ellipses
Fitzgibbon, A., Pilu, M., & Fisher, R. B. (1999) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.765658 · Cited by 2,797 · see citing works
“A simple constraint i s kak = 1 b u t B o o k estein used the algebraic invariant constraint a 2 + 1 2 b 2 + c 2 = 1 Sampson 16] presented an iterative improvement to Bookstein method that replaces the algebraic distance (2) with a better approximation to the geometric distance, which w as adapted by Taubin 17] to tur…”
BackgroundMethodInfluentialMLESAC: A New Robust Estimator with Application to Estimating Image Geometry
Torr, P. H. S., & Zisserman, A. (2000) · Computer Vision and Image Understanding · doi:10.1006/cviu.1999.0832 · Cited by 2,402 · see citing works
“Given a set of correspondences the (unbiased) minimum variance solution for F is that which minimizes the sum of squares of distances orthogonal to the variety from each point (x, y, x ′, y′) inR4 [12, 14, 15, 21, 23, 26, 35].”
BackgroundTaubin, G. (1991) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.103273 · Cited by 1,280 · see citing works
Direct least squares fitting of ellipses
Fitzgibbon, A., Pilu, M., & Fisher, R. B. (1996) · Proceedings of 13th International Conference on Pattern Recognition · doi:10.1109/icpr.1996.546029 · Cited by 853 · see citing works
The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix
Torr, P., & Murray, D. (1997) · International Journal of Computer Vision · doi:10.1023/a:1007927408552 · Cited by 776 · see citing works
“These require a working knowledge of the solution, and so an iteratively re-weighted least squares minimization is required (Bookstein 1979; Sampson 1982).”
BackgroundMethodInfluentialDirect least-squares fitting of algebraic surfaces
Pratt, V. (1987) · International Conference on Computer Graphics and Interactive Techniques · doi:10.1145/37401.37420 · Cited by 675
The fundamental matrix: Theory, algorithms, and stability analysis
Luong, Q., & Faugeras, O. (2004) · International Journal of Computer Vision · doi:10.1007/bf00127818 · Cited by 635 · see citing works
Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola
Ahn, S., Rauh, W., & Warnecke, H. (2001) · Pattern Recognition · doi:10.1016/s0031-3203(00)00152-7 · Cited by 404 · see citing works
A Buyer's Guide to Conic Fitting
Fitzgibbon, A., & Fisher, R. B. (1995) · British Machine Vision Conference · doi:10.5244/c.9.51 · Cited by 393 · see citing works
“A number of authors [1, 6, 8, 9, 12, 13] have proposed alternative algorithms and while these are usually compared by the authors with LIN, there have been, to our knowledge, no comparative studies of the relative accuracy and efficiency of these alternatives.”
BackgroundMethodLeast Squares Fitting of Circles
Chernov, N., & Lesort, C. (2005) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-005-0482-8 · Cited by 320 · see citing works
Image Mosaicing and Super-resolution
Capel, D. P. (2004) · Distinguished Dissertations · doi:10.1007/978-0-85729-384-8 · Cited by 298 · see citing works
“Fortunately, in the 2-view case, it is possible to derive a very good approximation to this log-likelihood function, based on Sampson’s approximation of the distance to a conic [124], which does not require explicit parameterization of the pre-image points.”
MethodEstimation of Subspace Arrangements with Applications in Modeling and Segmenting Mixed Data
Ma, Y., Yang, A. Y., Derksen, H., & Fossum, R. (2008) · SIAM Review · doi:10.1137/060655523 · Cited by 280
Outlier detection and motion segmentation
Torr, P., & Murray, D. (1993) · Other Conferences · doi:10.1117/12.150246 · Cited by 279 · see citing works
Long-term changes in arch form after orthodontic treatment and retention.
Delacruz, A., Sampson, P., Little, R. M., Årtun, J., & Shapiro, P. (1995) · American Journal of Orthodontics and Dentofacial Orthopedics · doi:10.1016/s0889-5406(95)70119-2 · Cited by 251 · see citing works
Self-citationA rational function lens distortion model for general cameras
Claus, D., & Fitzgibbon, A. (2005) · Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2005.43 · Cited by 248 · see citing works
“The RMS value of the Sampson distances [14] from the points to their epipolar conics was used as the error measure.”
MethodNonparametric Segmentation of Curves into Various Representations
Rosin, P. L., & West, G. (1995) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.476507 · Cited by 246
A note on the least squares fitting of ellipses
Rosin, P. L. (1993) · Pattern Recognition Letters · doi:10.1016/0167-8655(93)90062-i · Cited by 239 · see citing works
SIFT, SURF & seasons: Appearance-based long-term localization in outdoor environments
Valgren, C., & Lilienthal, A. J. (2009) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2009.09.010 · Cited by 195 · see citing works
Describing Complicated Objects by Implicit Polynomials
Keren, D., Cooper, D., & Subrahmonia, J. (1994) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.273718 · Cited by 219
Krishnapuram, R., Frigui, H., & Nasraoui, O. (1995) · IEEE transactions on fuzzy systems · doi:10.1109/91.366570 · Cited by 218
Direct least-squares fitting of algebraic surfaces
Pratt, V. (1987) · doi:10.1145/37402.37420 · Cited by 191
An Extremum Principle for Shape from Contour
Brady, M., & Yuille, A. (1984) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1984.4767521 · Cited by 158 · see citing works
Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space
Ahn, S. (2004) · Lecture Notes in Computer Science · doi:10.1007/b104017 · Cited by 184
“8) which has been described in literature [71], [76] as a good approximation of the minimum distance error (geometric error) vector.”
BackgroundMethodHeteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint
Leedan, Y., & Meer, P. (2000) · International Journal of Computer Vision · doi:10.1023/a:1008185619375 · Cited by 181 · see citing works
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
Taubin, G., Cukierman, F., Sullivan, S., Ponce, J., & Kriegman, D. (1994) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.276128 · Cited by 178
Statistical Bias of Conic Fitting and Renormalization
Kanatani, K. (1994) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.276132 · Cited by 171
Robust Detection of Degenerate Configurations while Estimating the Fundamental Matrix
Torr, P. H. S., Zisserman, A., & Maybank, S. J. (1998) · Computer Vision and Image Understanding · doi:10.1006/cviu.1997.0559 · Cited by 121 · see citing works
Suri, J. S. (2000) · Pattern Analysis and Applications · doi:10.1007/s100440070008 · Cited by 117 · see citing works
Recognition and positioning of rigid objects using algebraic moment invariants
Taubin, G., & Cooper, D. B. (1991) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.48423 · Cited by 104 · see citing works
“The reweight procedure is similar in spirit to Sampson’s algorithm [118] and those iterative weighted least squares algorithms that appear in the regression literature [111].”
BackgroundMethodInfluentialEllipse-specific direct least-square fitting
Pilu, M., Fitzgibbon, A., & Fisher, R. B. (1996) · Proceedings of IEEE international conference on image processing · doi:10.1109/icip.1996.560566 · Cited by 142
Continuous Stereo Self-Calibration by Camera Parameter Tracking
Dang, T., Hoffmann, C., & Stiller, C. (2009) · IEEE Transactions on Image Processing · doi:10.1109/tip.2009.2017824 · Cited by 124 · see citing works
“Please note that (59)–(62) are equivalent to the standard Kalman filter innovation equations for a transformed observation model with measurement vector and correspond to the minimization of a normalized Sampson error [55].”
MethodAn optimum design for 3-D fixture synthesis in a point set domain
Wang, M. Y. (2000) · IEEE Trans. Robotics Autom. · doi:10.1109/70.897795 · Cited by 136
“Here, gi is known as the algebraic distance of a point separated from a geometric surface [20].”
BackgroundVisual Motion and the Perception of Surface Material
Doerschner, K., Fleming, R., Yilmaz, O., Schrater, P., Hartung, B. M., & Kersten, D. (2011) · Current Biology · doi:10.1016/j.cub.2011.10.036 · Cited by 125
“Vectors with Sampson error [46] less than 1 were accepted as inliers.”
Orthogonal Distance Fitting of Implicit Curves and Surfaces
Ahn, S., Rauh, W., Cho, H., & Warnecke, H. (2002) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.1000237 · Cited by 119 · see citing works
An automatic procedure for co-registration of terrestrial laser scanners and digital cameras
González-Aguilera, D., Rodríguez-Gonzálvez, P., & Gómez-Lahoz, J. (2009) · ISPRS Journal of Photogrammetry and Remote Sensing · doi:10.1016/j.isprsjprs.2008.10.002 · Cited by 117 · see citing works
An improved algorithm for algebraic curve and surface fitting
Taubin, G. (1993) · Vision · doi:10.1109/iccv.1993.378149 · Cited by 114
“In the past we have used a simple first order approximation of the Euclidean distance from a point to an implicit curve or surface which yielded good results in the case of unconstrained algebraic curves or surfaces, and reasonable results in the case of bounded algebraic curves and surfaces.”
MethodThe geometric error for homographies
Chum, O., Pajdla, T., & Sturm, P. F. (2004) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2004.03.004 · Cited by 101 · see citing works
“The first order approximation of this error measure, called Sampson’s error , was first used by Sampson in [9] for conics.”
MethodKanatani, K. (2008) · International Journal of Computer Vision · doi:10.1007/s11263-007-0098-0 · Cited by 108 · see citing works
“All of them are designed so as to make F(xα;u) approximately 0 for all α and at the same time let the solution û have desirable properties (Bookstein 1979; Sampson 1982; Taubin 1991).”
BackgroundDistance approximations for rasterizing implicit curves
Taubin, G. (1994) · ACM Transactions on Graphics · doi:10.1145/174462.174531 · Cited by 107
Subrahmonia, J., Cooper, D., & Keren, D. (1996) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.494640 · Cited by 103
“A much better distance measure [18, 23] is the approximate distance dist2(S; f) = X (xi;yi;zi)2S f2(xi; yi; zi) k 5f(xi; yi; zi) k2 (2) where k 5f(xi; yi; zi) k2 denotes the square of the norm of the gradient.”
BackgroundError Of Fit Measures For Recovering Parametric Solids
Gross, A., & Boult, T. (1988) · [1988 Proceedings] Second International Conference on Computer Vision · doi:10.1109/ccv.1988.590052 · Cited by 99
Mirrors in motion: epipolar geometry and motion estimation
Geyer, C., & Daniilidis, K. (2003) · Proceedings Ninth IEEE International Conference on Computer Vision · doi:10.1109/iccv.2003.1238426 · Cited by 95 · see citing works
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
Bajaj, C., Ihm, I., & Warren, J. (1993) · ACM Transactions on Graphics · doi:10.1145/159730.159734 · Cited by 93
Optical Navigation Using Planet’s Centroid and Apparent Diameter in Image
Christian, J. A. (2015) · Journal of Guidance Control and Dynamics · doi:10.2514/1.g000872 · Cited by 92 · see citing works
“This difficulty has led to a variety of algorithms being developed over the last 40 years [27–34].”
BackgroundMethodRegion-based template deformation and masking for eye-feature extraction and description
Deng, J.-Y., & Lai, F. (1997) · Pattern Recognition · doi:10.1016/s0031-3203(96)00086-6 · Cited by 91
Ellipse fitting by accumulating five-point fits
Rosin, P. L. (1993) · Pattern Recognition Letters · doi:10.1016/0167-8655(93)90052-f · Cited by 91
Projectively invariant representations using implicit algebraic curves
Forsyth, D., Mundy, J., Zisserman, A., & Brown, C. (1990) · Image and Vision Computing · doi:10.1016/0262-8856(91)90023-i · Cited by 91
Dental arch shape: a statistical analysis using conic sections.
Sampson, P. (1981) · American Journal of Orthodontics · doi:10.1016/s0002-9416(81)90464-4 · Cited by 91
Self-citationEfficient three‐dimensional scene modeling and mosaicing
Nicosevici, T., Gracias, N., Negahdaripour, S., & García, R. (2009) · Journal of Field Robotics · doi:10.1002/rob.20305 · Cited by 75 · see citing works
“Using the feature correspondences between images Journal of Field Robotics DOI 10.1002/rob Ib and Ii , we estimate the fundamental matrix Fbi using a RANSAC-based least squares (LS) method1 (Armangue & Salvi, 2003), with the cost function represented by the Sampson distance (Sampson, 1982).”
MethodInfluentialA Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data
Werman, M., & Keren, D. (2001) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.922710 · Cited by 86
Estimation of Nonlinear Errors-in-Variables Models for Computer Vision Applications
Matei, B., & Meer, P. (2006) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2006.205 · Cited by 82 · see citing works
“we will show that different particular cases of (40) appear in several techniques used in computer vision: the generalized total least squares (GTLS) [18], the Sampson method [35], [16, p.”
MethodEllipse detection and matching with uncertainty
Ellis, T., Abbood, A., & Brillault-O'Mahony, B. (1992) · Image and Vision Computing · doi:10.1016/0262-8856(92)90041-z · Cited by 84
Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer
Požar, T., & Mozina, J. (2011) · doi:10.1088/0957-0233/22/8/085301 · Cited by 80
A stereo vision-based obstacle detection system in vehicles
Huh, K., Jaehak, P., Hwang, J., & Hong, D. (2007) · Optics and Lasers in Engineering · doi:10.1016/j.optlaseng.2007.08.002 · Cited by 70 · see citing works
Direct and specific least-square fitting of hyperbolæ and ellipses
O'Leary, P., & Zsombor-Murray, P. (2004) · J. Electronic Imaging · doi:10.1117/1.1758951 · Cited by 76
“Journal of Electronic Imaging 13(3), 492–503 (July 2004).”
BackgroundAnalysing error of fit functions for ellipses
Rosin, P. L. (1996) · Pattern Recognition Letters · doi:10.1016/s0167-8655(96)00102-x · Cited by 74
“2 Gradient weighted algebraic distance The most commonly used improvement over the algebraic distance is to inversely weight Q(xj , yj) by its gradient [1, 11, 13] EOF2 = Q(xj , yj) |∇Q(xj , yj)| .”
BackgroundFitting of circles and ellipses least squares solution
Gander, W., Golub, G., & Strebel, R. (1995) · doi:10.1016/b978-044482107-2/50036-4 · Cited by 72
When to use what feature? SIFT, SURF, ORB, or A-KAZE features for monocular visual odometry
Chien, H.-J., Chuang, C.-C., Chen, C., & Klette, R. (2016) · International Conference on Image and Vision Computing New Zealand (IVCNZ) · doi:10.1109/ivcnz.2016.7804434 · Cited by 79 · see citing works
“Here, δ is the Sampson distance [22] between x and x′ defined by”
BackgroundApproximation of n-dimensional data using spherical and ellipsoidal primitives
Calafiore, G. (2002) · IEEE Trans. Syst. Man Cybern. Part A · doi:10.1109/tsmca.2002.1021114 · Cited by 69 · see citing works
“Several “tricks” and weighting schemes (see again [9], and [2], [24], [18], [7], [22]) have been proposed in the literature in order to force the the solution of the AE-based problem to approximate the solution of the EG problem.”
BackgroundOn Recovering Hyperquadrics from Range Data
Kumar, S., Han, S., Goldgof, D., & Bowyer, K. (1995) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.473234 · Cited by 68 · see citing works
Assessing Error of Fit Functions for Ellipses
Rosin, P. L. (1996) · CVGIP: Graphical Models and Image Processing · doi:10.1006/gmip.1996.0041 · Cited by 67
Ellipse Fitting with Hyperaccuracy
Kanatani, K. (2006) · IEICE Trans. Inf. Syst. · doi:10.1093/ietisy/e89-d.10.2653 · Cited by 66
Vision-based approach towards lane line detection and vehicle localization
Du, X., & Tan, K.-K. (2015) · Machine Vision and Applications · doi:10.1007/s00138-015-0735-5 · Cited by 63 · see citing works
“Supporting data points will be determined purely based on Sampson’s distance d s [20].”
MethodUsing Line and Ellipse Features for Rectification of Broadcast Hockey Video
Gupta, A., Little, J., & Woodham, R. J. (2011) · Canadian Conference on Computer and Robot Vision · doi:10.1109/crv.2011.12 · Cited by 63 · see citing works
“There is an approximate method called Sampson approximation, initially proposed to fit conics [45], which only requires 9 parameters.”
MethodHessian Matrix vs. Gauss-Newton Hessian Matrix
Chen, P. (2011) · SIAM Journal on Numerical Analysis · doi:10.1137/100799988 · Cited by 60
“Instead, other objective functions are to be minimized, such as the Sampson error [32, 20, 36].”
BackgroundRationalising the Renormalisation Method of Kanatani
Chojnacki, W., Brooks, M. J., & van den Hengel, A. (2001) · Journal of Mathematical Imaging and Vision · doi:10.1023/a:1008355213497 · Cited by 59
“Sampson [18] was the first to propose a scheme aiming to minimi se a function involving fractional expressions, such as JAML (although his cost functions did not incorporate covariance matrices).”
BackgroundCohen, F., & Wang, J.-Y. (1994) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.273720 · Cited by 59 · see citing works
Least squares fitting of circles and lines
Chernov, N., & Lesort, C. (2003) · arXiv.org · doi:10.48550/arxiv.cs/0301001 · Cited by 58
Edgel aggregation and edge description
Nalwa, V. S., & Pauchon, E. (1987) · Computer Vision Graphics and Image Processing · doi:10.1016/0734-189x(87)90057-0 · Cited by 58 · see citing works
Song, X., & Jüttler, B. (2009) · Computers & Graphics · doi:10.1016/j.cag.2009.03.021 · Cited by 55 · see citing works
“[27].”
Guaranteed Ellipse Fitting with the Sampson Distance
Szpak, Z. L., Chojnacki, W., & van den Hengel, A. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-33715-4_7 · Cited by 51 · see citing works
“Another cost function for ellipse fitting, and more generally for conic fitting, was first proposed by Sampson [25] and next popularised, in a broader context, by Kanatani [14].”
BackgroundRenormalization for unbiased estimation
Kanatani, K. (1993) · Vision · doi:10.1109/iccv.1993.378156 · Cited by 53
Szpak, Z. L., Chojnacki, W., & van den Hengel, A. (2014) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-014-0536-x · Cited by 50 · see citing works
“Whilst ellipse fitting methods based on the Sampson distance are typically simple, fast, and accurate at moderate noise levels, most do not guarantee generation of an estimate in the form of an ellipse.”
BackgroundInfluentialSurbeck, B. T., Årtun, J., Hawkins, N. R., & Leroux, B. (1998) · American Journal of Orthodontics and Dentofacial Orthopedics · doi:10.1016/s0889-5406(98)70291-4 · Cited by 52
Using hyperquadrics for shape recovery from range data
Han, S., Goldgof, D., & Bowyer, K. (1993) · IEEE International Conference on Computer Vision · doi:10.1109/iccv.1993.378174 · Cited by 51
Function representation based slicer for 3D printing
Song, Y.-Z., Yang, Z.-W., Liu, Y., & Deng, J.-S. (2018) · Computer Aided Geometric Design · doi:10.1016/j.cagd.2018.03.012 · Cited by 49
Performance evaluation of iterative geometric fitting algorithms
Kanatani, K., & Sugaya, Y. (2007) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2007.05.013 · Cited by 49
“To solve this problem, various algebraic methods were proposed in the past (Bookstein, 1979; Sampson, 1982; Taubin, 1991), but Kanatani (1996) pointed out that the problem can be regarded as statistical estimation and that maximum likelihood (ML) produces an optimal solution.”
MethodDetection of lane markings based on ridgeness and RANSAC
López, A., Cañero, C., Serrat, J., Saludes, J., Lumbreras, F., & Graf, T. (2005) · Proceedings. 2005 IEEE Intelligent Transportation Systems, 2005. · doi:10.1109/itsc.2005.1520139 · Cited by 49
“Since the curves we search are hyperbolas, as first factor of e f we propose Sampson’s distance between a point and a conic [8].”
BackgroundGeometry of Single Axis Motions Using Conic Fitting
Jiang, G., Tsui, H.-T., Quan, L., & Zisserman, A. (2003) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2003.1233910 · Cited by 46
“order approximation as suggested in [2], [15], [6].”
MethodCircular motion geometry using minimal data
Jiang, G., Quan, L., & Tsui, H.-T. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.4 · Cited by 45
Range finding and feature extraction by segmentation of images for mobile robot navigation
Taylor, R. M., & Probert, P. (1996) · Proceedings of IEEE International Conference on Robotics and Automation · doi:10.1109/robot.1996.503579 · Cited by 44
Performance characterization of fundamental matrix estimation under image degradation
Torr, P., & Zissermann, A. (1997) · Machine Vision and Applications · doi:10.1007/s001380050051 · Cited by 43
“Given a set of correspondences the (unbiased) maximum likelihood solution forF is that which minimises the sum of squares of distances orthogonal to the variety from each point (x, y, x′, y′) in R4 [13, 16, 17, 21, 23, 24, 27].”
BackgroundVery Fast Best-Fit Circular and Elliptical Boundaries by Chord Data
Barwick, D. (2009) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2008.279 · Cited by 42
Finding cylinders in range data
Lozano-Perez, T., Grimson, W., & White, S. J. (1987) · Proceedings. 1987 IEEE International Conference on Robotics and Automation · doi:10.1109/robot.1987.1088007 · Cited by 42
Intrusion detection with evolutionary learning classifier systems
Shafi, K., Kovacs, T., Abbass, H., & Zhu, W. (2009) · Natural Computing · doi:10.1007/s11047-007-9053-9 · Cited by 41
“We explored various distance metrics and here present the results of a simple technique based on the geometric distance (Sampson 1982):”
MethodA-splines: local interpolation and approximation using Gk-continuous piecewise real algebraic curves
Bajaj, C., & Xu, G.-L. (1999) · Computer Aided Geometric Design · doi:10.1016/s0167-8396(99)00009-6 · Cited by 40
“In general, spline interpolation has been viewed as a global fitting problem to arbitrary scattered data (Bookstein, 1979; Curry and Schoenberg, 1966; Nürnberger et al., 1984; Pavlidis, 1983; Pratt, 1985; Sampson, 1982; Schoenberg and Whitney, 1953).”
BackgroundMethodInfluentialEllipse Fitting Using Orthogonal Hyperbolae and Stirling's Oval
Rosin, P. L. (1998) · Graphical Models and Image Processing · doi:10.1006/gmip.1998.0471 · Cited by 40
“Therefore, more efficiently computable approximations to this distance are usually used instead, some examples of which are given in [3, 4, 9, 10, 11].”
BackgroundUsing symmetry in robust model fitting
Wang, H., & Suter, D. (2003) · Pattern Recognition Letters · doi:10.1016/s0167-8655(03)00156-9 · Cited by 37
“Thus ellipses are frequently used in computer vision for model matching (Sampson, 1982; Fitzgibbon et al., 1999; Robin, 1999, etc.).”
MethodPoint-to-ellipse and point-to-ellipsoid distance equation analysis
Uteshev, A., & Goncharova, M. (2018) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2017.07.021 · Cited by 36
“The necessity for the analytical (symbolical) representation also stems from the problem of the approximation of scattered data known as the ellipse (ellipsoid) fitting problem [5, 6, 7, 8].”
BackgroundUnified Computation of Strict Maximum Likelihood for Geometric Fitting
Kanatani, K., & Sugaya, Y. (2008) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-010-0206-6 · Cited by 44 · see citing works
“which is called the Sampson error, originating from ellipse fitting by Sampson [29].”
MethodEllipse fitting and parameter assessment of circular object targets for robot vision
Ahn, S., Rauh, W., & Recknagel, M. (1999) · Proceedings 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human and Environment Friendly Robots with High Intelligence and Emotional Quotients (Cat. No.99CH36289) · doi:10.1109/iros.1999.813057 · Cited by 33 · see citing works
Trager, M., Hebert, M., & Ponce, J. (2015) · IEEE International Conference on Computer Vision · doi:10.1109/iccv.2015.110 · Cited by 31
“3 For this reason, approximations of the reprojection error have been considered, for example the so-called Sampson error [15].”
MethodVision-based vehicle detection and tracking algorithm design
Hwang, J.-H., Huh, K., & Lee, D. (2009) · doi:10.1117/1.3269685 · Cited by 31
Compact algorithm for strictly ML ellipse fitting
Kanatani, K., & Sugaya, Y. (2008) · International Conference on Pattern Recognition · doi:10.1109/icpr.2008.4761605 · Cited by 31
“Most of the methods presented in early days were based on heuristics combining voting and least squares in many different forms [1, 3, 16, 19, 21].”
MethodImage-Based Lunar Terrain Relative Navigation Without a Map: Measurements
Christian, J. A., Hong, L., McKee, P., Christensen, R., & Crain, T. P. (2021) · Journal of Spacecraft and Rockets · doi:10.2514/1.a34875 · Cited by 31 · see citing works
Automated As-Built Model Generation of Subway Tunnels from Mobile LiDAR Data
Arastounia, M. (2016) · Italian National Conference on Sensors · doi:10.3390/s16091486 · Cited by 30
Measure dimension of rotating large hot steel shell using pulse laser on PRRR robot
He, J., Gao, F., Wu, S.-F., Liu, R.-Q., & Zhao, X.-C. (2012) · doi:10.1016/j.measurement.2012.04.001 · Cited by 30
Moving Forward in Structure From Motion
Vedaldi, A., Guidi, G., & Soatto, S. (2007) · 2007 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2007.383117 · Cited by 30
Type-Constrained Direct Fitting of Quadric Surfaces
Andrews, J., & Séquin, C. (2014) · doi:10.1080/16864360.2013.834155 · Cited by 30
First Order Geometric Distance (The Myth of Sampsonus)
Harker, M., & O'Leary, P. (2006) · British Machine Vision Conference · doi:10.5244/c.20.10 · Cited by 29
“Perhaps the most common of these approximations is the so-called Sampson Error [5], which is a generalized form of that proposed by Sampson for conics [7].”
BackgroundMethod
- Authors
- Sampson, P. D.
- Affiliations
- University of Chicago (US)
- Corresponding author
- Sampson, Paul D
- ORCID
- Sampson, Paul D
- Venue
- Computer Graphics and Image Processing
- Publisher
- Elsevier BV
- Published
- 1982-01
- Volume
- 18
- Issue
- 1
- Pages
- 97-108
- ISSN
- 0146-664X (ISSN-L)
- OpenAlex
- W2045181334
- Cited by
- 358
- References
- 0
- Citations by year
- 2026: 4 · 2025: 5 · 2024: 9 · 2023: 8 · 2022: 1 · 2021: 8 · 2020: 7 · 2019: 11 · 2018: 7 · 2017: 8 · 2016: 10 · 2015: 10 · 2014: 14 · 2013: 14 · 2012: 11
- FWCI
- 2.35
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Computer Graphics and Image Processing (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Object Detection Techniques
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Physical Sciences › Engineering › Computational Mechanics › Advanced Numerical Analysis Techniques
- Keywords
- iterative refinement, curve fitting, geometric interpretation, iteratively reweighted least squares
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