3D rigid structure from video: what are "easy" shapes and "good" motions?

Factorization algorithms are increasingly popular to recover 3D rigid structure from video. In this paper, we analyze the rank 1 factorization algorithm to determine what are the most suitable 3D shapes or the best 3D motions to recover the 3D structure from the 2D trajectories of the features. We show that the shape is best retrieved from orthogonal views aligned with the longest and smallest axes of inertia of the object.