Manifold optimisation for motion factorisation

Abstract

This paper presents a novel formulation for the popular factorisation based solution for Structure from Motion. Since our measurement matrices are populated with incomplete and inaccurate data, SVD based total least squares solution are less than appropriate. Instead, we approach the problem as a non-linear unconstrained minimisation problem on the product manifold of the Special Euclidean Group (SE3). The restriction of the domain of optimisation to the SE3 product manifold not only implies that each intermediate solution is a plausible object motion, but also ensures better intrinsic stability for the minimisation algorithm. We compare our method with existing state of art, and show that our algorithm exhibits superior performance.