Correspondence of projected 3D points and lines using a continuous GRASP

M.J. Hirsch, P. M. Pardalos, and M. G. C. Resende

International Transactions in Operational Research, vol. 18, pp. 493-511, 2011.


The field of computer vision has experienced rapid growth over the past fifty years. Many computer vision problems have been solved using theory and ideas from algebraic projective geometry. In this research, we look at a previously unsolved problem from object recognition, namely object recognition when the correspondences between the object and image data is not known a priori. We formulate this problem as a mixedinteger nonlinear optimization problem in terms of the unknown projection relating the object and image, as well as the unknown assignments of object points and lines to those in the image. The global optimum of this problem recovers the relationship between the object points and lines with those in the image. When certain assumptions are enforced on the allowable projections mapping the object into the image, a proof is provided which permits one to solve the optimization problem via a simple decomposition. We illustrate this decomposition approach on some example scenarios.

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