Reconstruction of a Scene with Multiple Linearly Moving Objects

In this paper we describe an algorithm to recover the scene structure, the trajectories of the moving objects and the camera motion simultaneously given a monocular image sequence. The number of the moving objects is automatically detected without prior motion segmentation. Assuming that the objects are moving linearly with constant speeds, we propose a unified geometrical representation of the static scene and the moving objects. This representation enables the embedding of the motion constraints into the scene structure, which leads to a factorization-based algorithm. We also discuss solutions to the degenerate cases which can be automatically detected by the algorithm. Extension of the algorithm to weak perspective projections is presented as well. Experimental results on synthetic and real images show that the algorithm is reliable under noise.