Multiple Homography Estimation with Full Consistency Constraints

Abstract—A novel approach is presented to estimating a set of interdependent homography matrices linked together by latent variables. The approach allows enforcement of all underlying consistency constraints while accounting for the arbitrariness of the scale of each individual matrix. The input data is assumed to be in the form of a set of homography matrices obtained by estimation from image data with the consistency constraints ignored, appended by a set of error covariances associated with these matrix estimates. A cost function is proposed for upgrading, via optimisation, the input data to a set of homography matrices satisfying the constraints. The function is invariant to a change of any of the individual scales of the input matrices. The proposed approach is applied to the particular problem of estimating a set of homography matrices induced by multiple planes in the 3D scene between two views. Experimental results are given which demonstrate the effectiveness of the approach. Keywords-multiple homographies, consistency constraints, multi-projective parameter estimation, scale invariance, maxi-mum likelihood, covariance. I