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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 201–300 of 347
Statistical analysis of arch shape with conic sections.
Sampson, P. (1983) · Biometrics · doi:10.2307/2531013 · Cited by 7
Self-citationA Unified and Accurate Subpixel Detector of Control Points for Camera Calibration
He, Q., Ji, Z., Yu, P., & Chen, D.-Y. (2023) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2023.3293870 · Cited by 7
“A common way for conics detection is fitting the edge points of the conics [41], [42], [43].”
BackgroundBackground subtraction with a pan/tilt camera
Tsinko, E. (2010) · doi:10.14288/1.0052028 · Cited by 7
“Secondly, the final matrix H is estimated by using a non-linear least squares minimization algorithm that minimizes Sampson error [28].”
MethodEnsemble ellipse fitting by spatial median consensus
Thurnhofer-Hemsi, K., López-Rubio, E., Blázquez-Parra, E. B., Ladrón-de-Guevara-Muñoz, M. C., & de Cózar-Macías, Ó. D. (2021) · Information Sciences · doi:10.1016/j.ins.2021.08.011 · Cited by 6
VISAR signal analysis with an emphasis on ellipse fitting.
Sur, A., Joshi, K., Sharma, A., & Kaushik, T. (2017) · Review of Scientific Instruments · doi:10.1063/1.4994048 · Cited by 6
Fitting parabolas in noisy images
García-Escudero, L., Mayo-Íscar, A., & Sánchez-Gutiérrez, C. I. (2017) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2017.03.008 · Cited by 6
“In subsequent works, Sampson (1982), Taubin (1991) and Joseph (1994), among others, proposed some modifications to Bookstein’s approach, aiming to minimize (at least approximately) the sum of the so-called “geometric distances” given by n∑ i=1 ∥zi − zpi ∥2 (i.e., the non-trimmed version of our…”
BackgroundTechniques for Generating Analytic Covariance Expressions for Eigenvalues and Eigenvectors
Liounis, A., & Christian, J. A. (2016) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2015.2510970 · Cited by 6
Solutions and evaluations for fitting of concentric circles
Al-Sharadqah, A., & Ho, D. K. C. (2016) · Signal Processing · doi:10.1016/j.sigpro.2015.09.025 · Cited by 6
Hyper Least Squares and Its Applications
Rangarajan, P. V., Kanatani, K., Niitsuma, H., & Sugaya, Y. (2010) · International Conference on Pattern Recognition · doi:10.1109/icpr.2010.10 · Cited by 6
“Hence, the method of Taubin (1991) cannot be applied. However, the use of the above NT as N plays the same role of the method of Taubin (1991) for ellipse fitting and fundamental matrix computation, as first pointed out by Niitsuma et al.”
MethodRobust Techniques for the Estimation of Structure from Motion in the Uncalibrated Case
Brooks, M. J., Chojnacki, W., van den Hengel, A., & Baumela, L. (1998) · European Conference on Computer Vision · doi:10.1007/bfb0055673 · Cited by 6
Hyperaccurate Correction of Maximum Likelihood for Geometric Estimation
Kanatani, K., & Sugaya, Y. (2013) · IPSJ Transactions on Computer Vision and Applications · doi:10.2197/ipsjtcva.5.19 · Cited by 6
“Sampson [23].”
Robust statistics over riemannian manifolds for computer vision
Meer, P., & Subbarao, R. (2008) · Rutgers University Community Repository (Rutgers University) · doi:10.7282/t3736r88 · Cited by 6
“In [84] it is shown that methods such as generalized total least squares [131], the Sampson method [100, 57] and renormalization [65] are special cases of the HEIV formulation.”
MethodLess Biased Noise Scale Estimation for Threshold-Robust RANSAC
Edstedt, J. (2025) · 2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) · doi:10.1109/cvprw67362.2025.00264 · Cited by 5
“…of squared residuals would be distributed as However, since x ∗ is unknown, we try to find the most likely x , through The Sampson [24] error for the Fundamental matrix [18] can be derived by linearizing the constraint and solving a Lagrangian, and is often very close to the optimal solu-tion [23].”
VERF: Runtime Monitoring of Pose Estimation With Neural Radiance Fields
Maggio, D., Mario, C., & Carlone, L. (2023) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2023.3341765 · Cited by 5
“In short, the sampson distance [46] is an approximation of error to the epipolar line for two corresponding points.”
BackgroundRobust Pan/Tilt Compensation for Foreground–Background Segmentation
Allebosch, G., Hamme, D. V., Veelaert, P., & Philips, W. R. (2019) · Sensors · doi:10.3390/s19122668 · Cited by 5
“In [33], an alternative cost function was proposed, which is much simpler to determine, while still providing a close approximation to the true geometric error.”
BackgroundOptimization Techniques for Geometric Estimation: Beyond Minimization
Kanatani, K. (2012) · SSPR/SPR · doi:10.1007/978-3-642-34166-3_2 · Cited by 5
Simultaneously Estimating the Fundamental Matrix and Homographies
Chen, P., & Suter, D. (2009) · IEEE Transactions on robotics · doi:10.1109/tro.2009.2030224 · Cited by 5
“Based on the above fact, we extend the Sampson error [10], [20], [23], [24] to the case of simultaneously estimating the FM and homographies.”
MethodMotion Recovery by Integrating over the Joint Image Manifold
Goshen, L., Shimshoni, I., Anandan, P., & Keren, D. (2005) · International Journal of Computer Vision · doi:10.1007/s11263-005-3673-2 · Cited by 5
“(3) is correct as the 1’s cancel out.”
BackgroundMethodStereo Camera Re-calibration and the Impact of Pixel Location Uncertainty
Oberle, W. (2003) · doi:10.21236/ada415369 · Cited by 5
“Torr (2002) recommends the use of a method adapted from Sampson (1982) and essentially, this is the error matrix recommended for the algorithm. The actual metric used is the sum of the absolute values of the Sampson error computed for each of the points in the data set. Thus, the metric is a single value referred to a…”
MethodMoment-Based Invariant Fiting of Elliptical Segments
Voss, K., Süße, H., & Neubauer, R. (1995) · International Conference on Computer Analysis of Images and Patterns · doi:10.1007/3-540-60268-2_345 · Cited by 5
Regularised Energy Model for Robust Monocular Ego-motion Estimation
Chien, H.-J., & Klette, R. (2017) · VISIGRAPP · doi:10.5220/0006100303610368 · Cited by 5
“This first-order approximation to the geometric error is known as the Sampson distance (Sampson, 1982), which has also been used to provide iterative solutions to the optimal triangulation problem as formulated by Eq.”
MethodCheng, H., Shi, Q., Li, K., Wei, W., & Wang, H. (2025) · Sensors and Actuators A-Physical · doi:10.1016/j.sna.2025.116795 · Cited by 4
Diverse Consensuses Paired with Motion Estimation-Based Multi-Model Fitting
Yin, W.-Y., Lin, S., Lu, Y., & Wang, H.-Z. (2024) · ACM Multimedia · doi:10.1145/3664647.3681646 · Cited by 4
“Therefore, the tangent inverse function is designed for 𝐶 : where 𝐽 𝑖 and 𝐽 𝑗 ∈ R 2 × 2 are the Jacobians of 𝑝 𝑖 and 𝑝 𝑗 with respect to the epipolar constraint, and × denotes the cross product.”
Combining Absolute and Semi-Generalized Relative Poses for Visual Localization
Panek, V., Sattler, T., & Kukelova, Z. (2024) · International Journal of Computer Vision · doi:10.1007/s11263-026-02914-z · Cited by 4
“For 2D-2D matches, we measure the Sampson error [53, 22].”
A closed-form general solution for the distance of point-to-ellipse in two dimensions
Chou, C.-C. (2019) · Journal of Interdisciplinary Mathematics · doi:10.1080/09720502.2019.1624064 · Cited by 4
Stets, J. D., Corso, A. D., Nielsen, J., Lyngby, R., Jensen, S., Wilm, J., Doest, M. B., Gundlach, C., Eiríksson, E., Conradsen, K., et al. (2017) · Applied Optics · doi:10.1364/ao.56.007679 · Cited by 4
“We match markers in the left and the right images via Sampson distance [45].”
MethodMetric problems for algebraic manifolds: Analytical approach
Uteshev, A., & Goncharova, M. (2017) · Conference on Network Security & Applications · doi:10.1109/cnsa.2017.7974027 · Cited by 4
“Formula (5) is known as Sampson’s approximation [5].”
BackgroundHourdakis, E., & Lourakis, M. (2015) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2015.7353362 · Cited by 5
“This is achieved by computing the points on the epipolar lines that are closest to the original ones, using the Sampson approximation of the distance of points to epipolar lines [20] .”
MethodEllipse-specific fitting by relaxing the 3L constraints with semidefinite programming
Rong, J., Yang, S., Mei, X., Ying, X., Huang, S., & Zha, H. (2015) · International Conference on Information Photonics · doi:10.1109/icip.2015.7350891 · Cited by 4
Motion Flow Estimation from Image Sequences with Applications to Biological Growth and Motility
Dong, G., Baskin, T., & Palaniappan, K. (2006) · International Conference on Information Photonics · doi:10.1109/icip.2006.312551 · Cited by 4
“Sampson PD. Fitting conics sections to ‘very scattered’ data: An iterative refinement of the Bookstein algorithm.”
MethodInfluentialApproximate Rational Parameterization of Implicitly Defined Surfaces
Wurm, E., Jüttler, B., & Kim, M.-S. (2005) · IMA Conference on the Mathematics of Surfaces · doi:10.1007/11537908_26 · Cited by 4
“whose integrand is the so-called squared “Sampson distance” [16].”
BackgroundHuang, J.-B., & Menq, C. (2002) · Journal of Computing and Information Science in Engineering · doi:10.1115/1.1509075 · Cited by 4
Suri, J. S., Singh, S., Setarehdan, S., Sharma, R., Bovis, K., Comaniciu, D., & Reden, L. (2001) · doi:10.1007/978-0-85729-333-6_11 · Cited by 4
Is covariance information useful in estimating vision parameters?
Brooks, M. J., Chojnacki, W., Gawley, D., & van den Hengel, A. (2000) · IS&T/SPIE Electronic Imaging · doi:10.1117/12.410875 · Cited by 4
On the Geometries of Conic Section Representation of Noisy Object Boundaries
Zhu, Q.-M. (1999) · Journal of Visual Communication and Image Representation · doi:10.1006/jvci.1999.0419 · Cited by 4
Reliable identification of sphere-shaped femoral heads in 3D image data
Overhoff, H. M., Ehrich, S., & von Jan, U. (1999) · Medical Imaging · doi:10.1117/12.348536 · Cited by 4
G1 interpolation using piecewise quadric and cubic surfaces
Bajaj, C. (1990) · Other Conferences · doi:10.1117/12.19736 · Cited by 4
“Exact and approximate fitting of curves (primarily conics) has been considered by several authors, see for eg [7] [8] [13] [16] [19].”
BackgroundStepanov, D. (2019) · Computer optics · doi:10.18287/2412-6179-2019-43-1-105-114 · Cited by 4
GeoFlow: Enforcing Implicit Geometric Consistency in Video GenerationPreprint
Ackermann, J., Cai, S., Deng, B., Kuang, Z., Peng, S., & Wetzstein, G. (2026) · arXiv (Cornell University) · doi:10.48550/arxiv.2605.18365 · Cited by 3
“We measure consistency using established metrics for static videos, specifically MEt3R [1] and the Sampson Error [55].”
Rydell, F., Bökman, G., Kahl, F., & Kohn, K. (2025) · International Conference on 3D Vision · doi:10.1109/3dv69130.2026.00032 · Cited by 3
“We consider geometric vision problems involving 3D points, their image projections, and the cameras.”
Driver, T., Vaughan, A., Cheng, Y., Ansar, A., Christian, J., & Tsiotras, P. (2023) · arXiv.org · doi:10.48550/arxiv.2312.06865 · Cited by 3
“Finally, densification of the sparse GTSfM solution is conducted by computing the squared Sampson error [56] of each of the putative correspondences and adding the match if its error is below 1.”
MethodEfficient Time-of-Arrival Self-Calibration using Source Implicitization
Larsson, M., Larsson, V., & Oskarsson, M. (2023) · European Signal Processing Conference · doi:10.23919/eusipco58844.2023.10289933 · Cited by 3
“The problem is now a quadratic optimization problem with a single linear constraint, having the closed form solution (see e.g. [15]) This provides a first-order approximation of (9) which is cheap to compute (only requiring a few polynomial evaluations), and that only depends on the receiver…”
BackgroundMethodSampson Distance: A New Approach to Improving Visual-Inertial Odometry's Accuracy
Zhang, H., & Ye, C. (2021) · IEEE/RJS International Conference on Intelligent RObots and Systems · doi:10.1109/iros51168.2021.9636115 · Cited by 3
“SD was originally introduced by Sampson [14] for conic fitting to scattered data, where an iterative weighted least-square method was used to estimate the parameters of a conic model.”
MethodInfluentialXu, A.-P., Wang, Z., Kong, D.-L., Fu, Z.-J., & Lin, Q. (2018) · Chinese Physics B · doi:10.1088/1674-1056/27/7/070203 · Cited by 3
Wang, H., Leung, C., So, H.-C., Liang, J.-L., Feng, R., & Han, Z.-F. (2018) · doi:10.48550/arxiv.1806.00004 · Cited by 3
Second-Order Performance Analysis and Unbiased Estimation for the Fitting of Concentric Circles
Al-Sharadqah, A., & Ho, D. K. C. (2017) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-016-0681-5 · Cited by 3
“Al-Sharadqah and Ho [3] implemented the so-called gradient weighted algebraic fit (GRAF), a well-known method in estimating the parameters for many subjects, to concentric circles fitting [8,16,22].”
MethodIterative circle fitting based on circular attracting factor
Wang, H.-S., Zhang, Q., & Wang, F.-L. (2013) · Journal of Central South University · doi:10.1007/s11771-013-1782-6 · Cited by 3
Ground moving target geo-location from monocular camera mounted on a micro air vehicle
Guo, L., Ang, H., & Zheng, X.-M. (2011) · Photoelectronic Detection and Imaging · doi:10.1117/12.900106 · Cited by 3
“⊥ d is given by the Sampson approximation to reprojection error[6].”
MethodA new method of fitting conic to scattered data
Li, P.-P., Zhang, C.-M., Wang, K., & Li, X.-M. (2010) · International Congress on Image and Signal Processing · doi:10.1109/cisp.2010.5647606 · Cited by 3
“provided a generic quadric constraint in matrix form, which is substituted to the variable given matrix [15], [16].”
BackgroundA Two-Stage Point Pattern Matching Algorithm Using Ellipse Fitting and Dual Hilbert Scans
Li, T., & Kamata, S. (2008) · IEICE Trans. Inf. Syst. · doi:10.1093/ietisy/e91-d.10.2477 · Cited by 3
A Multimodal Approach for 3D Face Modeling and Recognition Using Deformable Mesh Model
Ansari, A., Abdel-Mottaleb, M., & Mahoor, M. (2006) · 2006 Biometrics Symposium: Special Session on Research at the Biometric Consortium Conference · doi:10.1109/bcc.2006.4341633 · Cited by 3
Specification of Initial Shapes for Dynamic Implicit Curve/Surface Reconstruction
Yang, Z.-W., Wu, C., Deng, J.-S., & Chen, F.-L. (2005) · Journal of Computational Science and Technology · doi:10.1007/s11390-006-0249-8 · Cited by 3
Optimal Estimation of Homogeneous Vectors
Mühlich, M., & Mester, R. (2005) · Scandinavian Conference on Image Analysis · doi:10.1007/11499145_34 · Cited by 3
“For ellipse fitting, the most obvious choice (cf. (9)) was proposed by Sampson [10]; defines a first order approximation to the geometric distance between data point and estimated ellipse.”
BackgroundKaveti, S., Teoh, E., & Wang, H. (1998) · Pattern Recognition · doi:10.1016/s0031-3203(97)00047-2 · Cited by 3
Automatic characterization of spiral and elliptical galaxies from digital images
García, J. A., Molina, R., & de la Blanca, N. P. (1994) · Pattern Recognition Letters · doi:10.1016/0167-8655(94)90147-3 · Cited by 3
“In our case we have adopted a least square t (see Sampson (1982)).”
MethodApproximate Geometric Ellipsoid Fitting: A CG-Approach
Kleinsteuber, M., & Hüper, K. (2010) · doi:10.1007/978-3-642-12598-0_7 · Cited by 3
“[1, 4, 6, 10, 14, 15, 19].”
An algebraic and Bayesian technology for object recognition
Subrahmonia, J., Keren, D., & Cooper, D. (1994) · doi:10.1080/757582974 · Cited by 3
Drift-Resistant Navigation World Model with Anchored Epipolar Guidance
Luan, P.-C., Xia, Z.-M., Li, W., Gao, Y., & Alahi, A. (2026) · arXiv.org · doi:10.48550/arxiv.2605.24761 · Cited by 2
“Specifically, we use epipolar distance (ED) [11] and Sampson error (SE) [27, 17] to measure geometric consistency with the induced viewpoint change, and MEt3R [2] to assess multi-view consistency after geometry-aware alignment.”
GeCo: Evaluating Geometric Consistency for Video Generation via Motion and Structure
Gu, L., Hur, J., Herrmann, C., Zhan, F.-N., Zickler, T., Sun, D., & Pfister, H. (2025) · doi:10.48550/arxiv.2512.22274 · Cited by 2
“Occlusion TSED [55] SIFT [32] Symmetric epipolar distance [16] ✗ ✓ ✗ Cosmos [1] SuperPoint [9] & LightGlue [28] Sampson error [41] ✗ ✓ ✗ VBench [23,24] None (frame-wise) CLIP feature [37] ✗ ✗ ✗ MEt3R [2] 3D warping (DUSt3R [48]) DINO feature [7] ✓ ✗ ✓ WorldScore [10] Learnt flow (DROID-SLAM [43])…”
Siebert, J. M. U., & Odenbach, S. (2024) · Transport in Porous Media · doi:10.1007/s11242-024-02086-9 · Cited by 2
“Nonetheless, different methods for ellipse fitting have been presented in literature (Bookstein 1979; Fischler and Bolles 1981; Sampson 1982; Yuen et al. 1989; Porrill 1990; Taubin 1991; Dave and Bhaswan 1992; Haralick and Shapiro 1993; Leavers 1992; Yip et al. 1992; Rosin 1993; Wu and Wang 1993;…”
Rodríguez-Rojo, E., Cubas, J., & Pindado, S. (2022) · Social Science Research Network · doi:10.2139/ssrn.4170620 · Cited by 2
Robust Ellipsoid-specific Fitting via Expectation Maximization
Zhao, M.-Y., Jia, X., Ma, L., Qiu, X., Jiang, X., & Yan, D.-M. (2021) · British Machine Vision Conference · doi:10.5244/c.35.99 · Cited by 2
“To circumvent this issue, Taubin [37] uses the second-order Taylor expansion to approximate the orthogonal distance, whereas Sampson [34] weights the algebraic distance by the first-order differential.”
Amafabia, D. M. (2019) · doi:10.18745/th.22488 · Cited by 2
“An iterative approximation method [250] through a better estimated geometric distance [256] can be expressed:”
MethodApproximation of the Distance from a Point to an Algebraic Manifold
Uteshev, A., & Goncharova, M. (2019) · International Conference on Pattern Recognition Applications and Methods · doi:10.5220/0007483007150720 · Cited by 2
“Approximation (2) is known as Sampson’s distance (Sampson, 1982).”
BackgroundOn reducing uncertainty on the Elliptical Plane modal identification method
Montalvão, D., Dupac, M., Amafabia, D. M., David-West, O., & Haritos, G. (2018) · doi:10.1051/matecconf/201821106001 · Cited by 2
Masterenko, D. A. (2015) · Measurement techniques · doi:10.1007/s11018-015-0791-2 · Cited by 2
“This situation is analyzed in [19] and an iterative method of “reweighing” of the initial points to equalize their infl uence is proposed.”
MethodParametric curve with an implicit domain
Zhang, W.-H., Deng, J.-S., Yang, Z.-W., & Liu, L.-G. (2014) · Science China Mathematics · doi:10.1007/s11425-014-4832-0 · Cited by 2
Adapting the RANSAC algorithm to detect 2nd - degree manifolds in 2D and 3D
Luchowski, L. (2012) · doi:10.2478/v10179-012-0007-2 · Cited by 2
A new ellipse fitting method and its application
Qiao, X., Zhang, L., & Liu, R. (2011) · International Conference on Electrical and Control Engineering · doi:10.1109/iceceng.2011.6057675 · Cited by 2
Hypersurface Fitting via Jacobian Nonlinear PCA on Riemannian Space
Fujiki, J., & Akaho, S. (2011) · International Conference on Computer Analysis of Images and Patterns · doi:10.1007/978-3-642-23672-3_29 · Cited by 2
Projective 3D-reconstruction of uncalibrated endoscopic images
Faltin, P., & Behrens, A. (2010) · Acta Polytechnica · doi:10.14311/1225 · Cited by 2
A Novel Approach to Geometric Fitting of Implicit Quadrics
Rouhani, M., & Sappa, A. (2009) · Advanced Concepts for Intelligent Vision Systems Conference · doi:10.1007/978-3-642-04697-1_12 · Cited by 2
“Although this method is precise enough, and even covers some well-known method in the literature, like [12] and [13], it is quite time-consuming due to the iterations.”
MethodFeature Correspondences from Multiple Views of Coplanar Ellipses
Barat, C., Menudet, J., Louhichi, H., & Fournel, T. (2006) · International Symposium on Visual Computing · doi:10.1007/11919629_38 · Cited by 2
“Among possible primitives, conics have received a lot of attention because they play a central role in projective geometry and robust algorithms exist to compute them [10, 2].”
BackgroundApplications of an efficient algorithm for locating 3D models in 2D images
Albus, J. (1998) · Defense, Security, and Sensing · doi:10.1117/12.323859 · Cited by 2
Localization and pose estimation of free-form shapes under Euclidean transformation
Kaveti, S., Teoh, E., & Wang, H. (1996) · Proceedings of the 1996 IEEE IECON. 22nd International Conference on Industrial Electronics, Control, and Instrumentation · doi:10.1109/iecon.1996.566027 · Cited by 2
3-D recognition and shape estimation from image contours using invariant 3-D object curve models
Cohen, F., & Wang, J.-Y. (1992) · Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.1992.223190 · Cited by 2
3-D object location determination using line-segments matching
Shao, L., Volz, R., & Walker, M. (1989) · International Workshop on Industrial Applications of Machine Intelligence and Vision, · doi:10.1109/miv.1989.40540 · Cited by 2
Fitting Curves and Surfaces With Constrained Implicit Polynomials
Keren, D., & Gotsman, C. (1999) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.745731 · Cited by 2
World Simulation with Video Foundation Models for Physical AI
NVIDIA, :, Ali, A., Bai, J., Bala, M., Balaji, Y., Blakeman, A., Cai, T., Cao, J., Cao, T., et al. (2025) · arXiv · doi:10.48550/arxiv.2511.00062 · Cited by 1
Non-Minimal Sampling and Consensus for Prohibitively Large Datasets
Lee, S. H., Vandewalle, P., & Civera, J. (2026) · arXiv.org · doi:10.48550/arxiv.2604.22518 · Cited by 1
“We identify the inliers by applying a threshold of (5 σ ) 2 to the Sampson errors [29, 35, 36].”
Visual Sync: Multi-Camera Synchronization via Cross-View Object Motion
Liu, S., Yao, D. Y., Gupta, S., & Wang, S.-L. (2025) · Neural Information Processing Systems · doi:10.48550/arxiv.2512.02017 · Cited by 1
“Among various epipolar-error measures, we adopt the Sampson error [19, 35, 45, 44], which approximates the squared Euclidean distance from a point to its corresponding epipolar line.”
PIS3R: Very Large Parallax Image Stitching via Deep 3D Reconstruction
Zhu, M.-H., Jin, X., Wang, C., Zhang, Y.-C., Xue, Y.-F., Ji, T., & Lao, Y.-Z. (2025) · arXiv.org · doi:10.48550/arxiv.2508.04236 · Cited by 1
Stereophotoclinometry Revisited
Driver, T., Vaughan, A., Cheng, Y., Ansar, A., Christian, J., & Tsiotras, P. (2025) · Journal of Guidance Control and Dynamics · doi:10.48550/arxiv.2504.08252 · Cited by 1
“Next, densification of the sparse GTSfM solution is conducted by computing the squared Sampson error [56] of each of the putative correspondences and adding the match if its error is below 1.”
Bayesian Regression Analysis for Dependent Data with an Elliptical Shape
Yu, Y., Tang, L., Ren, K., Chen, Z., Chen, S.-D., & Shi, J. (2024) · Entropy · doi:10.3390/e26121072 · Cited by 1
A comprehensive Cartesian to geodetic coordinate transformation reference listing
Nilsson, J.-O. (2024) · doi:10.48550/arxiv.2405.05352 · Cited by 1
Efficient 6-DoF camera pose tracking with circular edges
Tang, F.-L., Wu, S., Qian, Z., & Wu, Y. (2023) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2023.103767 · Cited by 1
Robust Ellipsoid Fitting Using Axial Distance and Combination
Han, M., Kan, J., Yang, G., & Li, X.-H. (2023) · arXiv.org · doi:10.48550/arxiv.2304.00517 · Cited by 1
Two-Camera Synchronization and Trajectory Reconstruction for a Touch Screen Usability Experiment
Kuronen, T., Eerola, T., Lensu, L., & Kälviäinen, H. (2018) · Advanced Concepts for Intelligent Vision Systems Conference · doi:10.1007/978-3-030-01449-0_11 · Cited by 1
“The evaluation was performed with confidence levels varying from 90% to 99%, and different Sampson distance [13] thresholds from 5 to 35 pixels.”
BackgroundConic Fitting: New Easy Geometric Method and Revisiting Sampson Distance
Wu, Y., Wang, H., & Tang, F.-L. (2017) · Asian Conference on Pattern Recognition · doi:10.1109/acpr.2017.22 · Cited by 1
“Comparisons with typical conic fitting methods were included: Linear least square method (LLS), Sampson distance based method (Sampson) [10], H-circle method of Sturm and Gargallo (SG) [12], and orthogonal distance based method of solving 4th order equations (Orthogonal) n [15].”
BackgroundMethodNiri, E. D., & Singh, T. (2016) · Pattern Recognition · doi:10.1016/j.patcog.2016.02.009 · Cited by 1
LEDs based video camera pose estimation
Sudars, K., Cacurs, R., Homjakovs, I., & Judvaitis, J. (2015) · doi:10.1515/bpasts-2015-0102 · Cited by 1
“As a criteria we have used Sampson distance [27] because it is shown in [1] that it gives good results”
MethodSelf-normalising linear camera resection
Collett, M. (2015) · Image and Vision Computing New Zealand · doi:10.1109/ivcnz.2015.7761560 · Cited by 1
“In the same notation, the optimum choice of C is (from ( 20)) c = [~ o o o From (9) we immediately have that (28) P", = 83"i83",P3, a = 1,2.”
BackgroundMethodInfluentialEuclidean upgrading from segment lengths: DLT-like algorithm and its variants
Shi, K., Dong, Q., & Wu, F.-C. (2014) · Image and Vision Computing · doi:10.1016/j.imavis.2013.12.012 · Cited by 1
“the result calculated by the DLT-like algorithm), and then we weight the constraint equations in the DLT-like algorithm in a similar way to the wellknown “iterative weighted least squares” [26], where the weights on the constraint equations are computed as the inverses of the standard derivations of their residuals.”
Motion segmentation via overlapping temporal windows
Dimitriou, N., & Delopoulos, A. (2013) · 2013 IEEE International Conference on Image Processing · doi:10.1109/icip.2013.6738873 · Cited by 1
“Then, for Sq we compute at each transition the Sampson distance [26, 27] for the Xq point correspondences using F (Xp).”
MethodRobust Hypersurface Fitting Based on Random Sampling Approximations
Fujiki, J., Akaho, S., Hino, H., & Murata, N. (2012) · International Conference on Neural Information Processing · doi:10.1007/978-3-642-34487-9_63 · Cited by 1
Caracterización y optimización del proceso de calibrado de cámaras basado en plantilla bidimensional
Viala, C. R. (2011) · doi:10.4995/thesis/10251/1858 · Cited by 1
“Para la obtención de los puntos qi* y pi* que satisfacen plenamente la matriz de proyección estimada M4 se realiza por métodos iterativos, según explica Sampson [77].”
BackgroundInfluentialA method of conic fitting applied in paracatadioptric system
Wang, M.-Z., & Wang, Y. (2010) · International Conference on Computer, Mechatronics, Control and Electronic Engineering · doi:10.1109/cmce.2010.5609811 · Cited by 1
Application of Structure-from-Motion 3D Reconstruction in Computer-Guided Surgical Training
Wytyczak-Partyka, A., Nikodem, J., & Klempous, R. (2009) · European Conference on the Engineering of Computer-Based Systems · doi:10.1109/ecbs.2009.38 · Cited by 1
Full three-dimensional reconstruction using key-frame selection under circular motion
Kim, S.-H., Seo, Y.-H., Yun, Y.-I., & Choi, J.-S. (2008) · Optical Engineering · doi:10.1117/1.2904004 · Cited by 1
Hu, M.-X., Dodds, G., & Yuan, B.-Z. (2005) · Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005. · doi:10.1109/icassp.2005.1415560 · Cited by 1
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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