Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Using Robust Estimation Algorithms for Tracking Explicit Curves
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Multi-scale EM-ICP: A Fast and Robust Approach for Surface Registration
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part IV
Neural Computation
Curve Finder Combining Perceptual Grouping and a Kalman Like Fitting
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Mean Shift Is a Bound Optimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Pose Estimation and Recognition Using Non-Gaussian Modeling of Appearance Subspaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Cognitive Neuroscience
Backward segmentation and region fitting for geometrical visibility range estimation
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
The estimation of the gradient of a density function, with applications in pattern recognition
IEEE Transactions on Information Theory
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Deterministic edge-preserving regularization in computed imaging
IEEE Transactions on Image Processing
Nonlinear image recovery with half-quadratic regularization
IEEE Transactions on Image Processing
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We consider the problem of fitting linearly parameterized models, that arises in many computer vision problems such as road scene analysis. Data extracted from images usually contain non-Gaussian noise and outliers, which makes non-robust estimation methods ineffective. In this paper, we propose an overview of a Lagrangian formulation of the Half-Quadratic approach by, first, revisiting the derivation of the well-known Iterative Re-weighted Least Squares (IRLS) robust estimation algorithm. Then, it is shown that this formulation helps derive the so-called Modified Residuals Least Squares (MRLS) algorithm. In this framework, moreover, standard theoretical results from constrained optimization can be invoked to derive convergence proofs easier. The interest of using the Lagrangian framework is also illustrated by the extension to the problem of the robust estimation of sets of linearly parameterized curves, and to the problem of robust fitting of linearly parameterized regions. To demonstrate the relevance of the proposed algorithms, applications to lane markings tracking, road sign detection and recognition, road shape fitting and road surface 3D reconstruction are presented.