Electrical and Computer Engineering, Dept. ofhttp://jhir.library.jhu.edu/handle/1774.2/334292021-06-22T08:12:26Z2021-06-22T08:12:26ZResults on an Intrinsic Consensus Algorithm on SO(3) with Almost-Global ConvergenceVidal, RenéAsfari, BijanTron, Robertohttp://jhir.library.jhu.edu/handle/1774.2/361392020-05-20T01:27:24Z2012-01-01T00:00:00ZResults on an Intrinsic Consensus Algorithm on SO(3) with Almost-Global Convergence
Vidal, René; Asfari, Bijan; Tron, Roberto
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.
2012-01-01T00:00:00ZDistributed Image-Based 3-D Localization of Camera Sensor NetworksTron, RobertoVidal, Renéhttp://jhir.library.jhu.edu/handle/1774.2/335132017-07-03T19:53:31Z2009-01-01T00:00:00ZDistributed Image-Based 3-D Localization of Camera Sensor Networks
Tron, Roberto; Vidal, René
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.
2009-01-01T00:00:00ZAutomatic Calibration of Cameras with Special MotionsVidal, RenéElhamifar, Ehsanhttp://jhir.library.jhu.edu/handle/1774.2/334632017-07-03T19:53:30Z2009-01-01T00:00:00ZAutomatic Calibration of Cameras with Special Motions
Vidal, René; Elhamifar, Ehsan
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.
2009-01-01T00:00:00Z