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We consider the classical camera pose estimation problem that arises in manycomputer vision applications, in which we are given n 2D-3D correspondencesbetween points in the scene and points in the camera image (some of which areincorrect associations), and where we aim to determine the camera pose (theposition and orientation of the camera in the scene) from this data. Wedemonstrate that this posing problem can be reduced to the problem of computing{\epsilon}-approximate incidences between two-dimensional surfaces (derivedfrom the input correspondences) and points (on a grid) in a four-dimensionalpose space. Similar reductions can be applied to other camera pose problems, aswell as to similar problems in related application areas. We describe andanalyze three techniques for solving the resulting {\epsilon}-approximateincidences problem in the context of our camera posing application. The firstis a straightforward assignment of surfaces to the cells of a grid (ofside-length {\epsilon}) that they intersect. The second is a variant of aprimal-dual technique, recently introduced by a subset of the authors [2] fordifferent (and simpler) applications. The third is a non-trivial generalizationof a data structure Fonseca and Mount [3], originally designed for the case ofhyperplanes. We present and analyze this technique in full generality, and thenapply it to the camera posing problem at hand. We compare our methodsexperimentally on real and synthetic data. Our experiments show that for thetypical values of n and {\epsilon}, the primal-dual method is the fastest, alsoin practice.

General techniques for approximate incidences and their application to the camera posing problem