A QCQP Approach to Triangulation
Abstract: Triangulation of a three-dimensional point from $n\ge 2$ two-dimensional images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite programming relaxations. We then describe a sufficient condition and a polynomial time test for certifying when such a solution is optimal. This test has no false positives. Experiments indicate that false negatives are rare, and the algorithm has excellent performance in practice. We explain this phenomenon in terms of the geometry of the triangulation problem.
Keywords: QCQP, Computer Vision, Triangulation, SDP
Category 1: Convex and Nonsmooth Optimization (Convex Optimization )
Category 2: Nonlinear Optimization (Quadratic Programming )
Citation: To appear in the proceedings of the 12th European Conference on Computer Vision (ECCV 2012).
Entry Submitted: 07/31/2012
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