Reference

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Bibliography

Books and papers that the algorithms in Algorithms are adapted from or that describe the theory behind them.

Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (2007)

Numerical Recipes: The Art of Scientific Computing, 3rd ed. New York: Cambridge University Press. ISBN 978-0-521-88068-8. Source of the classical root-finding, optimization, integration, interpolation, and least-squares algorithms (linear and nonlinear, including the Levenberg-Marquardt method of Levenberg-Marquardt Fitting Algorithm) that several estimators and fitters in this library are adapted from.

Wikipedia contributors

Quadratic function. Wikipedia, The Free Encyclopedia. Source of the quadratic formula used by SecondDegreePolynomialRootsEstimator, described in Closed-Form Polynomial Roots.

Wikipedia contributors

Cubic function and Cubic equation. Wikipedia, The Free Encyclopedia. Source of the discriminant-based cubic solution used by ThirdDegreePolynomialRootsEstimator, described in Closed-Form Polynomial Roots.

Fischler, M.A., and Bolles, R.C. (1981)

"Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography." Communications of the ACM, 24(6), 381–395. The original RANSAC paper, source of the algorithm implemented by RANSACRobustEstimator, described in RANSAC (Random Sample Consensus).

Rousseeuw, P.J. (1984)

"Least Median of Squares Regression." Journal of the American Statistical Association, 79(388), 871–880. DOI: 10.1080/01621459.1984.10477105. Source of the LMedS criterion and its scale-estimation constant (1.4826) used by LMedSRobustEstimator, described in LMedS (Least Median of Squares).

Torr, P.H.S., and Zisserman, A. (2000)

"MLESAC: A New Robust Estimator with Application to Estimating Image Geometry." Computer Vision and Image Understanding, 78(1), 138–156. Introduces MSAC (M-estimator SAmple Consensus) as a bounded-loss refinement of RANSAC’s scoring function, prior to the full maximum-likelihood MLESAC estimator; source of the algorithm implemented by MSACRobustEstimator, described in MSAC (M-estimator Sample Consensus).

Chum, O., and Matas, J. (2005)

"Matching with PROSAC – Progressive Sample Consensus." Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), 220–226. The original PROSAC paper, source of the algorithm implemented by PROSACRobustEstimator, described in PROSAC (Progressive Sample Consensus). This library’s implementation is itself based on a reference C implementation by Frédéric Devernay, cited directly in the class’s source code.

Irurueta, A., and Morros, J.R. (2012)

"PROMEDS: An Adaptive Robust Fundamental Matrix Estimation Approach." 3DTV-Conference: The True Vision - Capture, Transmission and Display of 3D Video (3DTV-CON). Combines PROSAC’s progressive, quality-guided sampling with the LMedS criterion; source of the algorithm implemented by PROMedSRobustEstimator, described in PROMedS (Progressive Least Median of Squares). This paper is by this library’s own author.

Wikipedia contributors

Convolution. Wikipedia, The Free Encyclopedia. Describes the discrete convolution operation implemented by Convolver1D, described in 1D Discrete Convolution.

Kalman, R.E. (1960)

"A New Approach to Linear Filtering and Prediction Problems." Journal of Basic Engineering, 82(1), 35–45. DOI: 10.1115/1.3662552. The original paper introducing the recursive predict/correct filter implemented by KalmanFilter, described in Kalman Filter.

Welch, G., and Bishop, G. (1995)

"An Introduction to the Kalman Filter." Technical Report TR 95-041, University of North Carolina at Chapel Hill. cs.unc.edu/welch/kalman. Cited directly in KalmanFilter’s own source code as `[Welch95]; its notation for the state transition, control, and measurement matrices and the process/measurement noise covariances is the notation `KalmanFilter’s API follows, described in Kalman Filter.

Wikipedia contributors

Algorithms for calculating variance. Wikipedia, The Free Encyclopedia. General background on incremental (one-sample-at-a-time) mean and covariance updates, the approach taken by MeasurementNoiseCovarianceEstimator, described in Measurement Noise Covariance Estimation.