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Fitting conic sections to "very scattered" data: An iterative refinement of the bookstein algorithm
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“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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Research works printed but not linked: 2
- Golub, 1970, Stationary values of the ratio of quadratic forms subject to linear constraints, Z. Angew. Math. Phys., 21, 318, 10.1007/BF01627939 · DOI
- Ramsay, 1977, A comparative study of several robust estimates of slope, intercept, and scale in linear regression, J. Amer. Statist. Assoc., 72, 608, 10.2307/2286228 · DOI
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Items 101–200 of 347
Robust statistics in shape fitting
Stein, A., & Werman, M. (1992) · Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.1992.223138 · Cited by 28
Epipolar Geometry Improves Video Generation ModelsPreprint
Kupyn, O., Uscidda, T., Gazulla, M. T., Manhardt, F., Tombari, F., & Rupprecht, C. (2025) · arXiv (Cornell University) · doi:10.48550/arxiv.2510.21615 · Cited by 29
“Once we have estimated the fundamental matrix, we can measure the geometric consistency using the Sampson epipolar error Sampson (1982): The Sampson error provides a first-order approximation to the geometric distance between a point and its epipolar line.”
Deng, Z., Ruan, Y.-S., Hao, F., & Liu, T. (2024) · Measurement · doi:10.1016/j.measurement.2024.114487 · Cited by 26
Wöhler, C. (2012) · X.media.publishing · doi:10.1007/978-1-4471-4150-1 · Cited by 26
Holst, C., Zeimetz, P., Nothnagel, A., Schauerte, W., & Kuhlmann, H. (2012) · doi:10.1061/(asce)su.1943-5428.0000082 · Cited by 26
Robust detection of straight and circular road segments in noisy aerial images'
Netanyahu, N., Philomin, V., Rosenfeld, A., & Stromberg, A. (1997) · Pattern Recognition · doi:10.1016/s0031-3203(96)00189-6 · Cited by 26
Vectorgraph coding: Efficient coding of line drawings
Landy, M., & Cohen, Y. A. (1985) · Computer Vision Graphics and Image Processing · doi:10.1016/0734-189x(85)90164-1 · Cited by 26
“These techniques include use of cubics [12-14], conics [15-16], polygonal splining [17-22], and hybrids between these techniques [23].”
MethodMaalek, R., & Lichti, D. (2020) · arXiv.org · doi:10.1016/j.isprsjprs.2021.04.010 · Cited by 25
“algebraic [38], Sampson [39], confocal hyperbola [20,40], geometric [41], and etc.”
BackgroundAlgorithms for projecting points onto conics
Chernov, N., & Wijewickrema, S. N. R. (2013) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2013.03.031 · Cited by 25
“Instead, researchers replaced geometric distances di with various (easily computable) algebraic distances and solved the resulting minimization problem [11, 29, 33, 37].”
BackgroundRoMo: Robust Motion Segmentation Improves Structure from Motion
Goli, L., Sabour, S., Matthews, M. J., Brubaker, M. A., Lagun, D., Jacobson, A., Fleet, D., Saxena, S., & Tagliasacchi, A. (2024) · IEEE International Conference on Computer Vision · doi:10.1109/iccv51701.2025.00581 · Cited by 24
“RoDynRF [19] is a 4D pose-free reconstruction method that optimizes cameras by removing scene elements with unreliable epipolar geometry using Sampson error [21, 33] similar to us.”
Invariant fitting of two view geometry
Torr, P., & Fitzgibbon, A. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.5244/c.17.8 · Cited by 24
“The method computes an algebraic fit f by an eigenvalue method, then a new fit is computed as the solution of the weighted moment matrixM0 ¼ P i ziz > i =wi, so that one computes min f Xi¼n i¼1 r2i w2i ¼ min f f>M0f ; subject to f>f ¼ 1: Note that 1) the computation of one or more Sampson…”
MethodFauster, E., Berg, D. C., Abliz, D., Grössing, H., Meiners, D., Ziegmann, G., & Schledjewski, R. (2018) · Journal of composite materials · doi:10.1177/0021998318780209 · Cited by 23
Al-Sharadqah, A., & Chernov, N. (2012) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2012.02.028 · Cited by 23
“This formula is also known as “Sampson error” (Sampson [23] was first to apply it to ellipses).”
Method3-D shape approximation using parametric geons
Wu, K., & Levine, M. (1997) · Image and Vision Computing · doi:10.1016/s0262-8856(96)01124-9 · Cited by 23
Segmentation of geometric signals using robust fitting
Roth, G., & Levine, M. (1990) · [1990] Proceedings. 10th International Conference on Pattern Recognition · doi:10.1109/icpr.1990.118224 · Cited by 23
Robust automated multiple view inspection
Pizarro, L., Mery, D., Delpiano, R., & Carrasco, M. (2007) · Pattern Analysis and Applications · doi:10.1007/s10044-007-0075-9 · Cited by 21
Real-time geometric fitting and pose estimation for surface of revolution
Liu, C., & Hu, W.-D. (2019) · Pattern Recognition · doi:10.1016/j.patcog.2018.08.002 · Cited by 22
From the Hough Transform to a New Approach for the Detection and Approximation of Elliptical Arcs
Daul, C., Graebling, P., & Hirsch, E. (1998) · Computer Vision and Image Understanding · doi:10.1006/cviu.1998.0696 · Cited by 22
“This least squares procedure provides results with almost the same accuracy as the more complex (and computationally much more costly) procedures described in [46] to [51], as demonstrated experimentally using, for example, a modified version of Bookstein’s method available in our laboratory.”
MethodImage Description and 3-D Reconstruction From Image Trajectories of Rotational Motion
Sawhney, H., Oliensis, J., & Hanson, A. (1993) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.232075 · Cited by 22
Shea, K. (2017) · ACM SIGSPATIAL International Workshop on Advances in Geographic Information Systems · doi:10.1007/978-3-319-17885-1_100125 · Cited by 22
Relative Pose Estimation through Affine Corrections of Monocular Depth Priors
Yu, Y., Liu, S.-H., Pautrat, R., Pollefeys, M., & Larsson, V. (2025) · Computer Vision and Pattern Recognition · doi:10.1109/cvpr52734.2025.01557 · Cited by 21
“We also develop hybrid solutions for scoring and local optimization, where we optimize both the classic Sampson error [53] and depth-induced reprojection error using depth and the solved affine corrections.”
A Visual Positioning System for Indoor Blind Navigation
Zhang, H., & Ye, C. (2020) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra40945.2020.9196782 · Cited by 27
“The Sampson error [20] is the first-order approximation of the reprojection-error-based cost function to be minimized.”
MethodParametric fitting of corneal height data to a biconic surface.
Janunts, E., Kannengießer, M., & Langenbucher, A. (2015) · Zeitschrift für Medizinische Physik · doi:10.1016/j.zemedi.2014.02.005 · Cited by 21
Aigner, M., & Jüttler, B. (2008) · Shape Modeling International Conference · doi:10.1109/smi.2008.4547958 · Cited by 21
“In the following we discuss the use o f the Sampson distance [25], which is also known as Taubin distanc e [30].”
BackgroundMethodTight Fitting of Convex Polyhedral Shapes
Gotsman, C., & Keren, D. (1998) · International journal of shape modeling · doi:10.1142/s021865439800009x · Cited by 21
Second-order implicit polynomials for segmentation of range images
Kaveti, S., Teoh, E., & Wang, H. (1996) · Pattern Recognition · doi:10.1016/0031-3203(95)00137-9 · Cited by 21
Recovery Of Superquadrics From 3-D Information
Boult, T., & Gross, A. (1988) · Other Conferences · doi:10.1117/12.942759 · Cited by 20
Topologically faithful fitting of simple closed curves
Keren, D. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.10006 · Cited by 20
“Better results are achieved by using cost functions which provide a more accurate approximation to the geometric distance between the zero-set and the points [9], [11], [20], [1], [17], [13], [15], [3], [8], [19].”
BackgroundFitting Quadratic Curves to Data Points
Chernov, N., Huang, Q., & Ma, H. (2014) · doi:10.9734/bjmcs/2014/6016 · Cited by 19
“In many areas of human practice one needs to approximate a set of planar points representing experimental data or observations by an ellipse [1], [2], [3], [4] or hyperbola [5], [6] or by any conic including a parabola [7], [8], [9], [10], [11].”
BackgroundEfficient 3D Scene Modeling and Mosaicing
Nicosevici, T., & García, R. A. (2013) · Springer Tracts in Advanced Robotics · doi:10.1007/978-3-642-36418-1 · Cited by 19
“3), we estimate the fundamental matrix Fbi using RANSAC-based Least Squares (LS) methods 2 [3], with the cost function given by the Sampson distance [126] (see Figure 3.”
MethodEpipolar geometry estimation based on evolutionary agents
Hu, M.-X., McMenemy, K., Ferguson, S., Dodds, G., & Yuan, B.-Z. (2008) · Pattern Recognition · doi:10.1016/j.patcog.2007.06.016 · Cited by 19
Implicit Polynomial Representation Through a Fast Fitting Error Estimation
Rouhani, M., & Sappa, A. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2011.2170080 · Cited by 18
“Although the fitting method in [16] is precise enough, and even covers some wellknown methods in the literature such as [10] and [20], it is quite time consuming due to the iterations.”
On the complexity of curve fitting algorithms
Chernov, N., Lesort, C., & Simányi, N. (2003) · Journal of Complexity · doi:10.1016/j.jco.2004.01.004 · Cited by 18
A Plumbline Constraint for the Rational Function Lens Distortion Model
Claus, D., & Fitzgibbon, A. (2005) · British Machine Vision Conference · doi:10.5244/c.19.10 · Cited by 18
“We then project the lines into conics in the image using (13) and measure the Sampson distance [19] from the conics to the detected edgels.”
MethodMedian spheres: theory, algorithms, applications
Nievergelt, Y. (2009) · Numerische Mathematik · doi:10.1007/s00211-009-0267-x · Cited by 16
“Computer graphics and vision [6,8,51,54,58–60].”
Active Sensors for Local Planning in Mobile Robotics
Smith, P. P. (2001) · World Scientific Series in Robotics and Intelligent Systems · doi:10.1142/4752 · Cited by 17
Extensions to Object Recognition in the Four-Legged League
Seysener, C. J., Murch, C. L., & Middleton, R. (2004) · Robot Soccer World Cup · doi:10.1007/978-3-540-32256-6_22 · Cited by 17
Efficient conic fitting with an analytical Polar-N-Direction geometric distance
Wu, Y., Wang, H., Tang, F.-L., & Wang, Z. (2019) · Pattern Recognition · doi:10.1016/j.patcog.2019.01.023 · Cited by 16
An Analytical Geometric Calibration Method for Circular Cone-Beam Geometry
Xu, J.-Y., & Tsui, B. M. W. (2013) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2013.2266638 · Cited by 16
“It can be shown [26] that the geometric distance can be approximated by a gradient-weighted algebraic distance”
BackgroundRe-localisation of a biopsy site in endoscopic images and characterisation of its uncertainty
Allain, B., Hu, M.-X., Lovat, L., Cook, R., Vercauteren, T. K. M., Ourselin, S., & Hawkes, D. (2012) · Medical Image Anal. · doi:10.1016/j.media.2011.11.005 · Cited by 16
“We used a cost function that depends on the Sampson’s residual errors (Sampson, 1982) and that is described by Torr (2002).”
MethodAllaire, S., Jacq, J., Burdin, V., Roux, C., & Couture, C. (2007) · IEEE International Conference on Computer Vision · doi:10.1109/iccv.2007.4409163 · Cited by 16
Workpiece localization and computer aided setup system
Xiong, Z.-H., Chu, Y.-X., Liu, G., & Li, Z.-X. (2001) · Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180) · doi:10.1109/iros.2001.976322 · Cited by 16
Maalek, R., & Lichti, D. (2020) · Pattern Recognition · doi:10.1016/j.patcog.2021.107948 · Cited by 15
“…,𝑦𝑦𝑖𝑖) = 𝑑𝑑𝑎𝑎𝑎𝑎𝑎𝑎(𝑥𝑥𝑖𝑖,𝑦𝑦𝑖𝑖) �∇𝑑𝑑𝑎𝑎𝑎𝑎𝑎𝑎(𝑥𝑥𝑖𝑖,𝑦𝑦𝑖𝑖)� (6) where ∇ denotes the gradient function, and 𝑑𝑑𝑆𝑆𝑎𝑎𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆(𝑥𝑥,𝑦𝑦) is commonly referred to as the Sampson distance of points (𝑥𝑥,𝑦𝑦)…”
MethodA Comparison of Ellipse Fitting Methods and Implications for Multiple-View Geometry Estimation
Szpak, Z. L., Chojnacki, W., & van den Hengel, A. (2012) · International Conference on Digital Image Computing: Techniques and Applications · doi:10.1109/dicta.2012.6411722 · Cited by 15
“It is variously called the Sampson, gradient-weighted, and approximated maximum likelihood (AML) distance or cost function, and takes the form JAML(θ) = N∑ n=1 θTAnθ θTBnθ with An = u(xn)u(xn)T and Bn = ∂xu(xn)Λxn∂xu(xn) T for each n = 1, . . . , N .”
BackgroundAn automatic tube inspection system that finds cylinders in range data
Grimson, W., Lozano-Perez, T., Noble, N., & White, S. J. (1993) · Proceedings of IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.1993.341092 · Cited by 15
A versatile method for trifocal tensor estimation
Matei, B., Georgescu, B., & Meer, P. (2001) · Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001 · doi:10.1109/iccv.2001.937678 · Cited by 15
“387] since it is based on an old technique proposed for ellipse fitting [13].”
Fast iterative five point relative pose estimation
Hedborg, J., & Felsberg, M. (2013) · 2013 IEEE Workshop on Robot Vision (WORV) · doi:10.1109/worv.2013.6521915 · Cited by 14
“Note that the symmetric variant of (6) is the Sampson distance, [13].”
BackgroundReconstruction from six-point sequences
Hartley, R., & Dano, N. Y. (2000) · Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662) · doi:10.1109/cvpr.2000.854888 · Cited by 14
“The Sampson method is named after the author of a wellknown paper on conic fitting ([9]).”
MethodApproximate Implicitization of Space Curves and of Surfaces of Revolution
Shalaby, M., & Jüttler, B. (2008) · doi:10.1007/978-3-540-72185-7_12 · Cited by 14
Efficient transformation from Cartesian to geodetic coordinates
Claessens, S. J. (2019) · Computers & Geosciences · doi:10.1016/j.cageo.2019.104307 · Cited by 16
“The inverse geodetic transformation problem can be solved in an approximate fashion by applying Sampson’s distance formula (Sampson 1982).”
MethodInfluentialAutomated Alignment of Robotic Pan-Tilt Camera Units Using Vision
Knight, J., & Reid, I. (2006) · International Journal of Computer Vision · doi:10.1007/s11263-005-5032-8 · Cited by 13
Circular motion geometry by minimal 2 points in 4 images
Jiang, G., Quan, L., & Tsui, H.-T. (2003) · Proceedings Ninth IEEE International Conference on Computer Vision · doi:10.1109/iccv.2003.1238345 · Cited by 13
“an approximate point-conic distance is defined to be [2, 15, 10]”
BackgroundGeometric modelling of IC die bonds for inspection
Ngan, K., & Kang, S.-B. (1989) · Pattern Recognition Letters · doi:10.1016/0167-8655(89)90017-2 · Cited by 13
Least-squares fitting of a three-dimensional ellipsoid to noisy data
Malyugina, A., Igudesman, K., & Chickrin, D. (2014) · doi:10.12988/ams.2014.49733 · Cited by 13
Detection and localization of specular surfaces using image motion cues
Yilmaz, O., & Doerschner, K. (2014) · Machine Vision and Applications · doi:10.1007/s00138-014-0610-9 · Cited by 12
Multicriteria Robust Fitting of Elliptical Primitives
Muñoz-Pérez, J., de Cózar-Macías, Ó. D., Blázquez-Parra, E. B., & de Guevara-López, I. L. (2014) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-013-0480-1 · Cited by 12
Effects of surface reflectance and 3D shape on perceived rotation axis.
Doerschner, K., Yilmaz, O., Kucukoglu, G., & Fleming, R. (2013) · Journal of Vision · doi:10.1167/13.11.8 · Cited by 12
“We then used Sampson error (Sampson, 1982) to label inconsistent features as outliers.”
HyperLS for Parameter Estimation in Geometric Fitting
Kanatani, K., Rangarajan, P. V., Sugaya, Y., & Niitsuma, H. (2011) · IPSJ Transactions on Computer Vision and Applications · doi:10.2197/ipsjtcva.3.80 · Cited by 12
Robust fitting of implicitly defined surfaces using Gauss–Newton-type techniques
Aigner, M., & Jüttler, B. (2009) · The Visual Computer · doi:10.1007/s00371-009-0361-1 · Cited by 12
“Taubin [34] proposed to use the Sampson distance [28] as an approximation to the exact geometric distance.”
MethodA predictor–corrector-type technique for the approximate parameterization of intersection curves
Bert Jüttler, B., & Chalmovianský, P. (2006) · Applicable Algebra in Engineering Communication and Computing · doi:10.1007/s00200-006-0031-8 · Cited by 11
“Following [14], one may use the Sampson distance”
MethodWhen are Simple LS Estimators Enough? An Empirical Study of LS, TLS, and GTLS
Nayak, A., Trucco, E., & Thacker, N. (2006) · International Journal of Computer Vision · doi:10.1007/s11263-006-6486-z · Cited by 12
“Estimation problems are ubiquitous in computer vision (CV), and considerable effort has been directed towards devising reliable algorithms.”
BackgroundMethodHyper-renormalization: Non-minimization Approach for Geometric Estimation
Kanatani, K., Al-Sharadqah, A., Chernov, N., & Sugaya, Y. (2014) · IPSJ Transactions on Computer Vision and Applications · doi:10.2197/ipsjtcva.6.143 · Cited by 12
Shi, Z.-L., Wang, H., Leung, A., So, H. C., Liang, J.-L., Tsang, K., & Constantinides, A. (2020) · Neurocomputing · doi:10.1016/j.neucom.2020.02.100 · Cited by 11
A novel Bayesian method for fitting parametric and non-parametric models to noisy data
Werman, M., & Keren, D. (1999) · Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149) · doi:10.1109/cvpr.1999.784964 · Cited by 11
“There are also many papers with di erent solutions and heuristics to tting circles, ellipses and other parametric curves using di erent statistical or optimization techniques; see, for example [14, 11, 12, 3, 13].”
MethodA Bayesian Approach Toward Robust Multidimensional Ellipsoid-Specific Fitting
Zhao, M.-Y., Jia, X.-H., Ma, L., Shi, Y., Jiang, J., Li, Q.-Z., Yan, D.-M., & Huang, T.-J. (2024) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2024.3432913 · Cited by 10
“Here, ( x 0 , y 0 , z 0 ) represents the center of the ellipsoid, ( a, b, c ) denote the lengths of its three semi-axes, and ( α, β, γ ) correspond to the Euler angles, defining the orientation of the ellipsoid’s major axis relative to the x , y , and z axes.”
BackgroundEllipse fitting for imaged cross sections of a surface of revolution
Liu, C., & Hu, W.-D. (2015) · Pattern Recognition · doi:10.1016/j.patcog.2014.09.028 · Cited by 10
Ellipse fitting for interferometry. Part 1: static methods.
Collett, M., & Tee, G. (2014) · Journal of The Optical Society of America A-optics Image Science and Vision · doi:10.1364/josaa.31.002573 · Cited by 10
Detection and identification of elliptical structure arrangements in images : theory and algorithms
Pătrăucean, V. (2012) · doi:10.70675/cb7ecfb8z8abfz4897z9dbfz1d3ba0da04df · Cited by 8
A New Method for Ellipse Fitting in Satellite Images
Soh, Y., Bae, J., Kim, D., & Kim, H. (2009) · 2009 Second International Conference on Intelligent Computation Technology and Automation · doi:10.1109/icicta.2009.128 · Cited by 10
Estimation of epipolar geometry by linear mixed-effect modelling
Zhou, H.-Y., Green, P., & Wallace, A. (2009) · Neurocomputing · doi:10.1016/j.neucom.2009.04.018 · Cited by 10
“Sampson’s method is one of the well studied schemes [14].”
MethodDetection of surface defects on raw milled steel blocks using range imaging
Pernkopf, F., Pernkopf, F., & O'Leary, P. (2002) · IS&T/SPIE Electronic Imaging · doi:10.1117/12.460195 · Cited by 10
Circular Arcs Fitted on a Riemann Sphere
Lillekjendlie, B. (1997) · Computer Vision and Image Understanding · doi:10.1006/cviu.1997.0529 · Cited by 10
Robust Ellipsoid Fitting Using Combination of Axial and Sampson Distances
Han, M., Kan, J.-M., Yang, G.-P., & Li, X.-H. (2023) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2023.3315361 · Cited by 10
“The Sampson distance is the first-order approximation of the orthogonal distance and is calculated based on the orthogonality of the measured point to the contour of the measured model [34], [40].”
BackgroundMethodInfluentialRobust statistics for computer vision : model fitting, image segmentation and visual motion analysis
Wang, H. (2017) · doi:10.4225/03/59d42777919fb · Cited by 6
“Thus ellipses are frequently used in computer vision for model matching (Sampson 1982; Fitzgibbon, Pilu et al. 1999; Robin 1999).”
MethodSingle View-Based Pose Estimation of Unknown Circular Object With RGB-D Camera
Li, Z.-X., Meng, C., Li, D., Liu, L., Yuan, W., & Huang, Z.-W. (2024) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2024.3373564 · Cited by 9
“Inspired by a general cost function for fitting conic sections proposed by Sampson [39], the cost C S is proposed to optimize the orientation and takes the form as follows: wherein The problem of minimizing the cost function (5) is a nonlinear least-squares optimization problem.”
MethodImproving ellipse fitting via multi-scale smoothing and key-point searching
Chen, X.-D., Qian, C., Zhao, M.-Y., Yong, J.-H., & Yan, D.-M. (2024) · Pattern Recognition · doi:10.1016/j.patcog.2024.110432 · Cited by 9
The location method of blade vibration events based on the tip-timing signal
Liu, Z., Duan, F., Niu, G., Jiang, J., Zhi, F.-Y., Cheng, Z.-H., Feng, J., & Xiong, B. (2021) · Measurement science and technology · doi:10.1088/1361-6501/abf8ec · Cited by 9
Robust and accurate computation of geometric distance for Lipschitz continuous implicit curves
Hu, M.-X., Zhou, Y., & Li, X. (2017) · The Visual Computer · doi:10.1007/s00371-017-1370-0 · Cited by 9
Motion-based segmentation of objects using overlapping temporal windows
Dimitriou, N., & Delopoulos, A. (2013) · Image and Vision Computing · doi:10.1016/j.imavis.2013.06.005 · Cited by 9
Methods for space line localization from single catadioptric images: new proposals and comparisons
Caglioti, V., Gasparini, S., & Taddei, P. (2007) · IEEE International Conference on Computer Vision · doi:10.1109/iccv.2007.4409195 · Cited by 9
“Thus we may use the following normalized squared sum as error function: e(lx) = ∑ i side(lx, li) 2 ||lx||2 The minimization is subject to a set of constraints which state that the candidate solution intersects each ray externally w.r.t. the mirror surface.”
MethodRobust detection and ordering of ellipses on a calibration pattern
Álvarez, L., Salgado, A., & Sánchez, J. (2007) · Pattern Recognition and Image Analysis · doi:10.1134/s1054661807040098 · Cited by 9
“This method is similar to other related ellipse or general conic fitting methods like [4, 5, 11, 12].”
MethodDirect Estimation of Homogeneous Vectors: An Ill-Solved Problem in Computer Vision
Harker, M., & O'Leary, P. (2006) · Indian Conference on Computer Vision, Graphics & Image Processing · doi:10.1007/11949619_82 · Cited by 9
“Gradient-Weighted Fitting: Sampson [6] proposed that the so-called algebraic distance weighted by its gradient would provide an improved metric for fitting conics, although his approach to attempt to minimize said cost function was iterative.”
Approximate algebraic methods for curves and surfaces and their applications
Jüttler, B., Chalmovianský, P., Shalaby, M., & Wurm, E. (2005) · Spring conference on Computer graphics · doi:10.1145/1090122.1090124 · Cited by 9
Efficient Suboptimal Solutions to the Optimal Triangulation
Wu, F.-C., Zhang, Q., & Hu, Z.-Y. (2010) · International Journal of Computer Vision · doi:10.1007/s11263-010-0378-y · Cited by 9
“By considering the Sampson approximation (Sampson 1982; Torr and Zisserman 1998; Hartley and Zisserman 2003), we define a Sampson sequence for the measured point pair and propose another suboptimal triangulation, called the Sampson suboptimal triangulation.”
MethodHussain, F. (1989) · doi:10.1007/978-4-431-68093-2_6 · Cited by 9
On Geometric Understanding and Learned Priors in Feed-forward 3D Reconstruction Models
Bratulić, J., Mittal, S., Brox, T., & Rupprecht, C. (2025) · doi:10.48550/arxiv.2512.11508 · Cited by 8
“The Sampson error [28] represents a first-order approximation of the true geometric error: Sampson error approximates the reprojection error, avoiding iterative optimization.”
An improved evolutionary algorithm for fundamental matrix estimation
Li, Y., Velipasalar, S., & Gursoy, M. C. (2013) · 2013 10th IEEE International Conference on Advanced Video and Signal Based Surveillance · doi:10.1109/avss.2013.6636644 · Cited by 8
“Sampson distance [6] is a widely used gradient distance.”
Two-View Geometry estimation using the Rodrigues Rotation Formula
Sorgi, L. (2011) · 2011 18th IEEE International Conference on Image Processing · doi:10.1109/icip.2011.6115593 · Cited by 8
A multimodal approach for 3D face modeling and recognition using 3D deformable facial mask
Ansari, A., Abdel-Mottaleb, M., & Mahoor, M. (2009) · Machine Vision and Applications · doi:10.1007/s00138-008-0123-5 · Cited by 8
“For that we use Sampson’s distance function [41].”
MethodSmith, B. M., Stork, D., & Zhang, L. (2009) · Electronic imaging · doi:10.1117/12.806255 · Cited by 8
Fitting NURBS spherical patches to measured data
Piegl, L., & Tiller, W. (2008) · Engineering computations · doi:10.1007/s00366-007-0076-8 · Cited by 8
Evaluating Harker and O'Leary's distance approximation for ellipse fitting
Rosin, P. L. (2007) · Pattern Recognition Letters · doi:10.1016/j.patrec.2007.05.012 · Cited by 8
Fitting geometric models in image processing using Grassmann manifolds
O'Leary, P. (2002) · IS&T/SPIE Electronic Imaging · doi:10.1117/12.460198 · Cited by 8
“i=1 f(2)(xi; yi; zi) rf xi; yi; zi) 2 : (2)”
Interpretation of conic motion and its applications
Liu, W., & Kanatani, K. (1993) · International Journal of Computer Vision · doi:10.1007/bf01440848 · Cited by 8
Subspace Estimation with Uncertain and Correlated Data
Mühlich, M. (2006) · doi:10.1007/1-4020-3858-8_19 · Cited by 8
“For this problem, one famous early iterative algorithm was developed by Sampson (Sampson, 1982).”
MethodRevisiting Sampson Approximations for Geometric Estimation Problems
Rydell, F., Torres, A., & Larsson, V. (2024) · Computer Vision and Pattern Recognition · doi:10.1109/cvpr52733.2024.00477 · Cited by 7
“The Sampson approximation was first proposed in [21] to approximate the point-conic distance.”
BackgroundMethodInfluentialTangent Sampson Error: Fast Approximate Two-view Reprojection Error for Central Camera Models
Terekhov, M., & Larsson, V. (2023) · IEEE International Conference on Computer Vision · doi:10.1109/iccv51070.2023.00312 · Cited by 7
“The Sampson error was introduced in [23] to approximate the geometric distance from a point to a conic.”
BackgroundMethodEllipse Fitting for Computer Vision: Implementation and Applications
Kanatani, K., Sugaya, Y., & Kanazawa, Y. (2016) · Ellipse Fitting for Computer Vision · doi:10.2200/s00713ed1v01y201603cov008 · Cited by 7
Least Squares Orthogonal Distance Fitting of Implicit Curves and Surfaces
Ahn, S., Rauh, W., & Recknagel, M. (2001) · DAGM-Symposium · doi:10.1007/3-540-45404-7_53 · Cited by 7
A new approach to conic section approximation of object boundaries
Zhu, Q.-M., & Peng, L. (1999) · Image and Vision Computing · doi:10.1016/s0262-8856(98)00148-6 · Cited by 7
“Besides the piecewise straight line segment modeling, the conic sections seem to be the next simplest and most frequently used curve form among the alternatives for approximating an object boundary [1,2,13].”
Background
Metadata
- 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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