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This report presents two efficient solutions to the two-view, relative pose problem from three image point correspondences and one common reference direction. This three-plus-one problem can be used either as a substitute for the classic five-point algorithm using a vanishing point for the reference direction, or to make use of an inertial measurement unit commonly available on robots and mobile devices, where the gravity vector becomes the reference direction. We provide a simple closed-form solution and a solution based on techniques from algebraic geometry and investigate numerical and computational advantages of each approach. In a set of real experiments, we demonstrate the power of our approach by comparing it to the five-point method in a hypothesize-and-test visual odometry setting.
Date Posted: 22 December 2011