MLPnP - A Real-Time Maximum Likelihood Solution to the Perspective-n-Point Problem

In this paper, a statistically optimal solution to the Perspective-n-Point (PnP) problem is presented. Many solutions to the PnP problem are geometrically optimal, but do not consider the uncertainties of the observations. In addition, it would be desirable to have an internal estimation of the accuracy of the estimated rotation and translation parameters of the camera pose. Thus, we propose a novel maximum likelihood solution to the PnP problem, that incorporates image observation uncertainties and remains real-time capable at the same time. Further, the presented method is general, as is works with 3D direction vectors instead of 2D image points and is thus able to cope with arbitrary central camera models. This is achieved by projecting (and thus reducing) the covariance matrices of the observations to the corresponding vector tangent space.Comment: Submitted to the ISPRS congress (2016) in Prague. Oral Presentation. Published in ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., III-3, 131-13

Une solution analytique au problème « Perspective-N-Points » et son extension aux capteurs catadioptriques

La détermination de la distance entre un capteur d'image unique et une mire constituée d'un ensemble de N points de références est un problème couramment abordé en traitement d'image (souvent appelé Perspective-N-Points). Beaucoup de solutions ont déjà été proposées. À l'aide d'une mise en équation originale, notre approche est, contrairement à la plupart des solutions existantes, strictement analytique. D'une part, cette solution nécessite une charge de calcul minimale et constante, ce qui la rend compatible avec un traitement temps réel et, d'autre part, elle est applicable avec des capteurs non linéaires (en particulier omnidirectionnels)

Computationally Efficient Iterative Pose Estimation for Space Robot Based on Vision

In postestimation problem for space robot, photogrammetry has been used to determine the relative pose between an object and a camera. The calculation of the projection from two-dimensional measured data to three-dimensional models is of utmost importance in this vision-based estimation however, this process is usually time consuming, especially in the outer space environment with limited performance of hardware. This paper proposes a computationally efficient iterative algorithm for pose estimation based on vision technology. In this method, an error function is designed to estimate the object-space collinearity error, and the error is minimized iteratively for rotation matrix based on the absolute orientation information. Experimental result shows that this approach achieves comparable accuracy with the SVD-based methods; however, the computational time has been greatly reduced due to the use of the absolute orientation method

Riccati Observers for the non-stationary PnP problem

This paper revisits the problem of estimating the pose (position and orientation) of a body in 3D space with respect to (w.r.t.) an inertial frame by using i) the knowledge of source points positions in the inertial frame, ii) the measurements of the body velocity, either in the body frame or in the inertial frame, and iii) source points bearing measurements performed in the body frame. An important difference with the much studied static Perspective-n-Point (PnP) problem addressed with iterative algorithms is that body motion is not only allowed but also used as a source of information that improves the estimation possibilities. With respect to the probabilistic framework commonly used in other studies that develop Extended Kalman filter (EKF) solutions, the deterministic approach here adopted is better suited to point out the observability conditions, that involve the number and disposition of the source points in combination with body motion characteristics, under which the proposed observers ensure robust estimation of the body pose. These observers are here named Riccati observers because of the instrumental role played by the Continuous Riccati equation (CRE) in the design of the observers and in the Lyapunov stability and convergence analysis that we develop independently of the well-known complementary (either deterministic or probabilistic) optimality properties associated with Kalman filtering. The set of these observers also encompasses Extended Kalman filter solutions. Another contribution of the present study is to show the importance of using body motion to improve the observers performance and, when this is possible, of measuring the body translational velocity in the inertial frame rather than in the body frame in order to remove the constraint of knowing the positions of the source points in the inertial frame. This latter issue is the link that connects the problem of body pose estimation with single source point bearing measurements and the Simultaneous Localization and Mapping (SLAM) problem in Robotics