Sio-Song Ieng

Using Robust Estimation Algorithms for Tracking Explicit Curves

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.

On the design of a single lane-markings detectors regardless the on-board camera's position

In this article, we present an algorithm for lane marking features extraction and robust shape estimation of lane markings. The algorithm uses a new lane-marking features extractor followed by the robust fitting algorithm described by Tarel et. al. (2002) to estimate the lane-markings shape as a single analytical curve. The lane-marking features extractor is based on the fact that lane-markings widths are in a small range of possible values, on a road. This implies a geometric constrain on the observed lane-markings widths from a camera on-board a vehicle. The lane-marking features extractor uses this property to select pairs of edge points corresponding with a high probability to a section of lane-marking. This features extractor is especially designed to be robust to lighting conditions as shown by few experiments. The extracted features are then grouped to estimate the parameters of the analytical curve model of these lane-markings. With the proposed approach, the obtained detector is robust to different kinds of noise and perturbations, allowing us to use it with a camera in many positions. Finally, to illustrate this property, we briefly describe two applications of the proposed detector: accurate vehicle location on the road and estimation of the time to line crossing.

Accurate and Robust Image Alignment for Road Profile Reconstruction

In this paper, we propose a novel approach of the two-image alignment problem based on a functional representation of images. This allows us to derive a one-to-several correspondence, multi-scale algorithm. At the same time, it also formalizes the problem as a robust estimation problem between possible matches. We then derive an accurate, robust and faster version for the alignment of edge images. The proposed algorithm is developed and tested in the context of off-line longitudinal road profile reconstruction from stereo images.

Evaluation of Robust Fitting Based Detection

Low-level image processing algorithms generally provide noisy features that are far from being Gaussian. Medium-level tasks such as object detection must therefore be robust to outliers. This can be achieved by means of the well-known M-estimators. However, higher-level systems do not only need robust detection, but also a confidence value associated to the detection. When the detection is cast into the fitting framework, the inverse of the covariance matrix of the fit provides a valuable confidence matrix.

A constrained-optimization based half-quadratic algorithm for robustly fitting sets of linearly parametrized curves

We consider the problem of multiple fitting of linearly parametrized curves, 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 classical estimation methods ineffective. In this paper, we first introduce a family of robust probability density functions which appears to be well-suited to many real-world problems. Also, such noise models are suitable for defining continuation heuristics to escape shallow local minima and their robustness is devised in terms of breakdown point. Second, the usual Iterative Reweighted Least Squares (IRLS) robust estimator is extended to the problem of robustly estimating sets of linearly parametrized curves. The resulting, non-convex optimization problem is tackled within a Lagrangian approach, leading to the so-called Simultaneous Robust Multiple Fitting (SRMF) algorithm, whose global convergence to a local minimum is proved using results from constrained optimization theory.

A Revisited Half-Quadratic Approach for Simultaneous Robust Fitting of Multiple Curves

In this paper, we address the problem of robustly recovering several instances of a curve model from a single noisy data set with outliers. Using M-estimators revisited in a Lagrangian formalism, we derive an algorithm that we call Simultaneous Multiple Robust Fitting (SMRF), which extends the classical Iterative Reweighted Least Squares algorithm (IRLS). Compared to the IRLS, it features an extra probability ratio, which is classical in clustering algorithms, in the expression of the weights. Potential numerical issues are tackled by banning zero probabilities in the computation of the weights and by introducing a Gaussian prior on curves coefficients. Applications to camera calibration and lane-markings tracking show the effectiveness of the SMRF algorithm, which outperforms classical Gaussian mixture model algorithms in the presence of outliers.