A new multistage approach to motion and structure estimation by gradually enforcing geometric constraints

Abstract

The standard 2-stage algorithm first estimates the 9 essential parameters defined up to a scale factor and then refines the motion estimation based on some statistically optimal criteria. We propose in this paper a novel approach by introducing an intermediate stage which consists in estimating a 3 x 3 matrix defined up to a scale factor by imposing the rank-2 constraint (the matrix has seven independent parameters). The idea is to gradually project parameters estimated in a high dimensional space onto a slightly lower-dimensional space, namely from 8 dimensions to 7 and finally to 5. Experiments with synthetic and real data show a considerable improvement over the 2-stage algorithm. Our conjecture from this work is that the imposition of the constraints arising from projective geometry should be used as an intermediate step in order to obtain reliable 3D Euclidean motion and structure estimation from multiple calibrated images.