Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
MLESAC: a new robust estimator with application to estimating image geometry
Computer Vision and Image Understanding - Special issue on robusst statistical techniques in image understanding
Curve Finder Combining Perceptual Grouping and a Kalman Like Fitting
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Deterministic edge-preserving regularization in computed imaging
IEEE Transactions on Image Processing
Improving the stability of algebraic curves for applications
IEEE Transactions on Image Processing
An extended hyperbola model for road tracking for video-based personal navigation
Knowledge-Based Systems
Combination of Roadside and In-vehicle Sensors for Extensive Visibility Range Monitoring
AVSS '09 Proceedings of the 2009 Sixth IEEE International Conference on Advanced Video and Signal Based Surveillance
Backward segmentation and region fitting for geometrical visibility range estimation
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Pattern Recognition Letters
Recent progress in road and lane detection: a survey
Machine Vision and Applications
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The context of this work is lateral vehicle control using a camera as a sensor. A natural tool for controlling a vehicle is recursive filtering. The well-known Kalman filtering theory relies on Gaussian assumptions on both the state and measure random variables. However, image processing algorithms yield measurements that, most of the time, are far from Gaussian, as experimentally shown on real data in our application. It is therefore necessary to make the approach more robust, leading to the so-called robust Kalman filtering. In this paper, we review this approach from a very global point of view, adopting a constrained least squares approach, which is very similar to the half-quadratic theory, and justifies the use of iterative reweighted least squares algorithms. A key issue in robust Kalman filtering is the choice of the prediction error covariance matrix. Unlike in the Gaussian case, its computation is not straightforward in the robust case, due to the nonlinearity of the involved expectation. We review the classical alternatives and propose new ones. A theoretical study of these approximations is out of the scope of this paper, however we do provide an experimental comparison on synthetic data perturbed with Cauchy-distributed noise.