When imaged through a camera, an illuminated ellipsoid gives rise, in general, to two ellipses on the image plane, namely the limb ellipse and the terminator ellipse. If the direction of illumination is known in the ellipsoid frame, then the full six degrees of freedom pose of the camera can be retrieved, apart from ambiguities which arise due to symmetry, by solving a quadric-to-conic plus conic-to-conic correspondence problem. A solution to such task is proposed in this manuscript. By fitting an ellipse to the imaged planetary limb arc, another ellipse to the terminator points, and exploiting analytical results available from projective geometry, equations for computing the entire pose are formulated. The position is expressed as the least squares solution of an over-determined system of four equations in three unknowns, while the attitude is estimated through a modified orthogonal Procrustes problem, whose solution involves the spectral decomposition of symmetric 3x3 matrices. Preliminary validation using synthetically generated images of illuminated ellipsoids suggests that the proposed algorithm can achieve position relative accuracy up to 10−3, and attitude error within the milli-rad.

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