• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.563-571
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• 2008

We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.45 no.6
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• pp.125-132
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• 2008

Omnidirectional camera system with a wide view angle is widely used in surveillance and robotics areas. In general, most of previous studies on estimating a projection model and the extrinsic parameters from the omnidirectional images assume corresponding points previously established among views. This paper presents a novel omnidirectional camera calibration based on automatic contour matching. In the first place, we estimate the initial parameters including translation and rotations by using the epipolar constraint from the matched feature points. After choosing the interested points adjacent to more than two contours, we establish a precise correspondence among the connected contours by using the initial parameters and the active matching windows. The extrinsic parameters of the omnidirectional camera are estimated minimizing the angular errors of the epipolar plane of endpoints and the inverse projected 3D vectors. Experimental results on synthetic and real images demonstrate that the proposed algorithm obtains more precise camera parameters than the previous method.