An imaging sensor made of multiple light-weight non-overlapping cameras is an effective sensor for a small unmanned aerial vehicle that has strong payload limitation. This paper presents a method for motion estimation by assuming that such a multi-camera system is a spherical imaging system (that is, the cameras share a single optical center). We derive analytically and empirically a condition for a multi-camera system to be modeled as a spherical camera. Interestingly, not only does the spherical assumption simplify the algorithms and calibration procedure, but also motion estimation based on that assumption becomes more accurate.

In this paper, we describe a new optical tracking algorithm for pose estimation of interaction devices in virtual and augmented reality. Given a 3D model of the interaction device and a number of camera images, the primary difficulty in pose reconstruction is to find the correspondence between 2D image points and 3D model points. Most previous methods solved this problem by the use of stereo correspondence. Once the correspondence problem has been solved, the pose can be estimated by determining the transformation between the 3D point cloud and the model. Our approach is based on the projective invariant topology of graph structures. The topology of a graph structure does not change under projection: in this way we solve the point correspondence problem by a subgraph matching algorithm between the detected 2D image graph and the model graph. There are four advantages to our method. First, the correspondence problem is solved entirely in 2D and therefore no stereo correspondence is needed. Consequently, we can use any number of cameras, including a single camera. Secondly, as opposed to stereo methods, we do not need to detect the same model point in two different cameras, and therefore our method is much more robust against occlusion. Thirdly, the subgraph matching algorithm can still detect a match even when parts of the graph are occluded, for example by the users hands. This also provides more robustness against occlusion. Finally, the error made in the pose estimation is significantly reduced as the amount of cameras is increased.

Estimating motions of a multi-camera system which may not have overlapping fields of view is generally complex and computationally expensive because of the non-zero offset between each camera’s center. It is conceivable that if we can assume that multiple cameras share a single optical center, and thus can be modeled as a spherical imaging system, motion estimation and calibration of this system would become simpler and more efficient. In this paper, we analytically and empirically derive the conditions under which a multi-camera system can be modeled as a single spherical camera. Various analyses and experiments using simulated and real images show that spherical approximation is applicable to a surprisingly larger extent than currently expected. Moreover, we show that, when applicable, this approximation even results in improvements in accuracy and stability of estimated motion over the exact algorithm.

Abstract- In this work, we solve the pose estimation problem for robot motion by placing multiple cameras on the robot. In particular, we combine the Extended Kalman Filter (EKF) with the multiple cameras. An essential strength of our approach is that it does not require finding image feature correspondences among cameras which is a difficult classical problem. The initial pose, the tracked features, and their corresponding 3D reconstruction are fed to the multiple-camera EKF which estimates the real-time pose. The reason for using multiple cameras is that the pose estimation problem is more constrained for multiple cameras than for a single camera, which has been verified by simulations and real experiments alike. Different approaches using single and two cameras have been compared, as well as two different triangulation methods for the 3D reconstruction. Both the simulations and the real experiments show that our approach is fast, robust and accurate. 1.

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