Motion averaging in 3d reconstruction problems

Abstract

We consider the problem of recovering individual motions for a set of cameras when we are given a number of relative motion estimates between camera pairs. Typically, the number of such relative motion pairs exceeds the number of unknown camera motions, resulting in an overdetermined set of relationships that needs to be averaged. This problem occurs in a variety of contexts and in this chapter we consider sensor localization in 3D reconstruction problems where the camera motions belong to specific finite-dimensional Lie groups or motion groups. The resulting problem has a rich geometric structure that leads to efficient and accurate algorithms that are also robust to the presence of outliers. We develop the motion averaging framework and demonstrate its utility in 3D motion estimation using images or depth scans. A number of real-world examples exemplify the motion averaging principle as well as elucidate its advantages over conventional approaches for 3D reconstruction.