A Lagrangian Half-Quadratic approach to robust estimation and its applications to road scene analysis

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.