Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter
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TLDR
The extended Kaiman filter in its usual form is shown not to reduce the well known bias to high curvature involved in least squares ellipse fitting, but this problem is overcome by developing a linear bias correction for the extendedKaiman filter.About:
This article is published in Image and Vision Computing.The article was published on 1990-02-01 and is currently open access. It has received 156 citations till now. The article focuses on the topics: Least squares & Kalman filter.read more
Citations
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Journal ArticleDOI
Direct least squares fitting of ellipses
TL;DR: This paper presents a new efficient method for fitting ellipses to scattered data that is ellipse-specific so that even bad data will always return an ellipso, and can be solved naturally by a generalized eigensystem.
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Parameter estimation techniques: a tutorial with application to conic fitting
TL;DR: This tutorial presents what is probably the most commonly used techniques for parameter estimation, including linear least-squares (pseudo-inverse and eigen analysis); orthogonal least- Squares; gradient-weighted least-Squares; bias-corrected renormalization; Kalman filtering; and robust techniques (clustering, regression diagnostics, M-estimators, least median of squares).
Numerically Stable Direct Least Squares Fitting of Ellipses
TL;DR: This paper presents a numerically stable non-iterative algorithm for fitting an ellipse to a set of data points based on a least squares minimization which leads to a simple, stable and robust fitting method which can be easily implemented.
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Invariant descriptors for 3D object recognition and pose
TL;DR: A model-based vision system that recognizes curved plane objects irrespective of their pose is demonstrated and the stability of a range of invariant descriptors to measurement error is treated in detail.
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Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola
TL;DR: The least-squares fitting minimizes the squares sum of error-of-fit in predefined measures by the geometric fitting of circle/sphere/ellipse/hyperbola/parabola and simple and robust nonparametric algorithms are proposed.
References
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Book
Stochastic Processes and Filtering Theory
TL;DR: In this paper, a unified treatment of linear and nonlinear filtering theory for engineers is presented, with sufficient emphasis on applications to enable the reader to use the theory for engineering problems.
Book
Building, registrating, and fusing noisy visual maps
Nicholas Ayache,Olivier Faugeras +1 more
TL;DR: In this paper, the authors deal with the problem of building three-dimensional descriptions (called visual maps) of the environment of a mobile robot using passive vision, and they use these maps to fuse the different visual maps and reduce the uncertainty of geometric primitives which have found correspondents in other maps.
Journal ArticleDOI
Building, registrating, and fusing noisy visual maps
Nicholas Ayache,Olivier Faugeras +1 more
TL;DR: It is shown how visual maps corresponding to different positions of the robot can be registered to compute a better estimate of its displacement between the various viewpoint positions, as suming an otherwise static environment.
Journal ArticleDOI
Optimal combination and constraints for geometrical sensor data
TL;DR: In this paper, a formalism for the statistical combination of geometrical information from multiple sensors is described, and applications to stereo vision are discussed, including the combination of multiple stereo views to increase the accuracy of a wire frame model.