Comment calibrer extrinsèquement des caméras à champs non-recouvrants ? Application pour un robot mobile

National audienceMulti-camera systems are more and more used in visionbased robotics. An accurate extrinsic calibration (camera relative poses) is usually required. In most of cases, this task is done by matching features through different views of the same scene. However, if the camera fields of view do not overlap, such a matching procedure is not feasible anymore. This article deals with a simple and flexible extrinsic calibration method, for non-overlapping camera rig. The aim is the calibration of non-overlapping cameras embedded on a vehicle, for visual navigation purpose in urban environment. The cameras do not see the same area at the same time. The calibration procedure consists in manoeuvring the vehicle while each camera observes a static scene. Previously, the camera were intrinsically calibrated. The main contributions are a study of the singular motions and a specific bundle adjustment which both reconstructs the scene and calibrates the cameras. Solutions to handle the singular configurations, such as planar motions, are exposed. The proposed approach has been validated with synthetic and real data. This article is translated from [19].Les systèmes multi-caméras sont de plus en plus utilisés en robotique mobile. Il est souvent nécessaire que l'étalonnage extrinsèque (poses relatives des caméras) soit précis. Pour cela, on utilise généralement des appariements entre différentes vues, ce qui est impossible à réaliser si les champs de vue des caméras sont disjoints. Dans cet article, nous exposons une méthode simple et flexible pour étalonner extrinsèquement un système multicaméras dont les champs de vue sont disjoints. Le but est de calibrer des caméras embarquées sur un véhicule pour des applications de navigation en milieu urbain. Les caméras observent donc des régions différentes à un instant donné. La procédure d'étalonnage consiste à manoeuvrer le véhicule pendant que chaque caméra, intrinsèquement calibrée au préalable, observe une scène statique. Les principales contributions sont l'étude des mouvements singuliers, et un ajustement de faisceaux spécifique qui affine les scènes, les poses du système multi-caméras, et calibre extrinsèquement les caméras. Nous étudions comment traiter les mouvements singuliers, comme les mouvements plans. La méthode proposée est validée avec des données synthétiques et réelles. Traduction depuis l'anglais de l'article [19]

Principled bundle block adjustment with multi-head cameras

This paper examines the effects of implementing relative orientation constraints on bundle adjustment, as well as provides a full derivation of the Jacobian matrix for such an adjustment, that can be used to facilitate other implementations of bundle adjustment with constrained cameras. We present empirical evidence demonstrating improved accuracy and reduced computational load when these constraints are imposed

Generalized Weiszfeld algorithms for Lq optimization

In many computer vision applications, a desired model of some type is computed by minimizing a cost function based on several measurements. Typically, one may compute the model that minimizes the L₂ cost, that is the sum of squares of measurement errors with respect to the model. However, the Lq solution which minimizes the sum of the qth power of errors usually gives more robust results in the presence of outliers for some values of q, for example, q = 1. The Weiszfeld algorithm is a classic algorithm for finding the geometric L1 mean of a set of points in Euclidean space. It is provably optimal and requires neither differentiation, nor line search. The Weiszfeld algorithm has also been generalized to find the L1 mean of a set of points on a Riemannian manifold of non-negative curvature. This paper shows that the Weiszfeld approach may be extended to a wide variety of problems to find an Lq mean for 1 ≤ q <; 2, while maintaining simplicity and provable convergence. We apply this problem to both single-rotation averaging (under which the algorithm provably finds the global Lq optimum) and multiple rotation averaging (for which no such proof exists). Experimental results of Lq optimization for rotations show the improved reliability and robustness compared to L₂ optimization.This research has been funded by National ICT Australia

Cascaded Filtering Using the Sigma Point Transformation (Extended Version)

It is often convenient to separate a state estimation task into smaller "local" tasks, where each local estimator estimates a subset of the overall system state. However, neglecting cross-covariance terms between state estimates can result in overconfident estimates, which can ultimately degrade the accuracy of the estimator. Common cascaded filtering techniques focus on the problem of modelling cross-covariances when the local estimators share a common state vector. This letter introduces a novel cascaded and decentralized filtering approach that approximates the cross-covariances when the local estimators consider distinct state vectors. The proposed estimator is validated in simulations and in experiments on a three-dimensional attitude and position estimation problem. The proposed approach is compared to a naive cascaded filtering approach that neglects cross-covariance terms, a sigma point-based Covariance Intersection filter, and a full-state filter. In both simulations and experiments, the proposed filter outperforms the naive and the Covariance Intersection filters, while performing comparatively to the full-state filter.Comment: This is an extended version of the original letter to be published in the IEEE Robotics and Automation Letter

Statistical methods for random rotations

The analysis of orientation data is a growing field in statistics. Though the rotationally symmetric location model for orientation data is simple, statistical methods for estimation and inference for the location parameter, S are limited. In this dissertation we develop point estimation and confidence region methods for the central orientation. Both extrinsic and intrinsic approaches to estimating the central orientation S have been proposed in the literature, but no rigorous comparison of the approaches is available. In Chapter 2 we consider both intrinsic and extrinsic estimators of the central orientation and compare their statistical properties in a simulation study. In particular we consider the projected mean, geometric mean and geometric median. In addition we introduce the projected median as a novel robust estimator of the location parameter. The results of a simulation study suggest the projected median is the preferred estimator because of its low bias and mean square error. Non-parametric confidence regions for the central orientation have been proposed in the literature, but they have undesirable coverage rates for small samples. In Chapter 3 we propose a nonparametric pivotal bootstrap to calibrate confidence regions for the central orientation. We demonstrate the benefits of using calibrated confidence regions in a simulation study and prove the proposed bootstrap method is consistent. Robust statistical methods for estimating the central orientation has received very little attention. In Chapter 4 we explore the finite sample and asymptotic properties of the projected median. In particular we derive the asymptotic distribution of the projected median and show it is SB-robust for the Cayley and matrix Fisher distributions. Confidence regions for the central orientation S are proposed, which can be shown to have preferable finite sample coverage rates compared to those based on the projected mean. Finally the rotations package is developed in Chapter 5, which contains functions for the statistical analysis of rotation data in SO(3)