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    Distributed Image-Based 3-D Localization of Camera Sensor Networks
    Tron, Roberto; Vidal, René (Department of Electrical and Computer Engineering, Johns Hopkins University, 2009)
    We consider the problem of distributed estimation of the poses of N cameras in a camera sensor network using image measurements only. The relative rotation and translation (up to a scale factor) between pairs of neighboring cameras can be estimated using standard computer vision techniques. However, due to noise in the image measurements, these estimates may not be globally consistent. We address this problem by minimizing a cost function on S E (3)N in a distributed fashion using a generalization of the classical consensus algorithm for averaging Euclidean data. We also derive a condition for convergence, which relates the step-size of the consensus algorithm and the degree of the camera network graph. While our methods are designed with the camera sensor network application in mind, our results are applicable to other localization problems in a more general setting. We also provide synthetic simulations to test the validity of our approach.
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    Automatic Calibration of Cameras with Special Motions
    Vidal, René; Elhamifar, Ehsan (Department of Electrical and Computer Engineering, Johns Hopkins University, 2009)
    We consider the problem of auto-calibrating the intrinsic parameters of a camera moving with a special motion: the rotation axis of the camera being perpendicular to its translation direction. Our method for calibrating the camera is based on Kruppa’s equation which in general requires solving a set of nonlinear equations. We prove in a theorem how to recover the true scale of the Kruppa’s equation from the eigenvalues of a matrix formed using the fundamental matrix between two views.
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    Results on an Intrinsic Consensus Algorithm on SO(3) with Almost-Global Convergence
    Vidal, René; Asfari, Bijan; Tron, Roberto (Department of Electrical and Computer Engineering, Johns Hopkins University, 2012)
    In this paper we propose a discrete time protocol to align the states of a network of agents evolving in the space of rotations SO(3). The starting point of our work is Riemannian consensus, a general and intrinsic extension of classical consensus algorithms to Riemannian manifolds. Unfortunately, this algorithm is guaranteed to align the states only when the initial states are not too far apart. We show how to modify this algorithm so that the states of the agents can be aligned, in practice, from almost any initial condition. While we focus on the specific case of SO(3), we hope that this work will represent the first step toward more general results.