Sampling Algebraic Varieties for Robust Camera Autocalibration

TLDR: This paper addresses the problem of robustly autocalibrating a moving camera with constant intrinsics by using the Branch-and-Bound (BnB) search paradigm to maximize the consensus of the polynomials.

Abstract: This paper addresses the problem of robustly autocalibrating a moving camera with constant intrinsics. The proposed calibration method uses the Branch-and-Bound (BnB) search paradigm to maximize the consensus of the polynomials. These polynomials are parameterized by the entries of, either the Dual Image of Absolute Conic (DIAC) or the Plane-at-Infinity (PaI). During the BnB search, we exploit the theory of sampling algebraic varieties, to test the positivity of any polynomial within a parameter’s interval, i.e. outliers with certainty. The search process explores the space of exact parameters (i.e. the entries of DIAC or PaI), benefits from the solution of a local method, and converges to the solution satisfied by the largest number of polynomials. Given many polynomials on the sought parameters (with possibly overwhelmingly many from outlier measurements), their consensus for calibration is searched for two cases: simplified Kruppa’s equations and Modulus constraints, expressed in DIAC and PaI, resp. Our approach yields outstanding results in terms of robustness and optimality.