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Many computer vision applications require robust estimation of the underlyinggeometry, in terms of camera motion and 3D structure of the scene. These robustmethods often rely on running minimal solvers in a RANSAC framework. In thispaper we show how we can make polynomial solvers based on the action matrixmethod faster, by careful selection of the monomial bases. These monomial baseshave traditionally been based on a Gr\"obner basis for the polynomial ideal.Here we describe how we can enumerate all such bases in an efficient way. Wealso show that going beyond Gr\"obner bases leads to more efficient solvers inmany cases. We present a novel basis sampling scheme that we evaluate on anumber of problems.

Beyond Gr\"obner Bases: Basis Selection for Minimal Solvers