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- W2013818565 abstract "We consider the task of estimating the relative pose (position andorientation) between a 3D object and its projection on a 2D imageplane from a set of point correspondences. Our approach is toformulate the task as an unconstrained optimization problem on theintersection of the special orthogonal group and a cone, andexploit as much as possible the geometry of the underlyingparameter space. The optimization does not require Riemanniangeometry. It involves successive parameterization of theconstraint manifold and is based on Newton-type iterations inlocal parameter space. A direct proof of local quadraticalconvergence to the optimum is provided. A key feature of theproposed approach, not used in earlier studies, is an analyticgeodesic search, alternating between gradient, Gauss, Newton andrandom directions, which ensures the escape from local minima andconvergence to a global minimum without the need to reinitializethe algorithm. Indeed, for a prescribed number of iterations, theproposed algorithm achieves significantly lower pose estimationerrors than earlier methods and it converges to a global minimumin typically 5--10 iterations." @default.
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- W2013818565 date "2005-01-01" @default.
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- W2013818565 title "Gauss-Newton-on-manifold for pose estimation" @default.
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- W2013818565 doi "https://doi.org/10.3934/jimo.2005.1.565" @default.
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