5D Motion Subspaces for Planar Motions

In practice, rigid objects often move on a plane. The object then rotates around a fixed axis and translates in a plane orthogonal to this axis. For a concrete example, think of a car moving on a street. Given multiple static affine cameras which observe such a rigidly moving object and track feature points located on this object, what can be said about the resulting feature point trajectories in the camera views? Are there any useful algebraic constraints hidden in the data? Is a 3D reconstruction of the scene possible even if there are no feature point correspondences between the different cameras? And if so, how many points are sufficient? Does a closed-form solution to this shape from motion reconstruction problem exist? This paper addresses these questions and thereby introduces the concept of 5 dimensional planar motion subspaces: the trajectory of a feature point seen by any camera is restricted to lie in a $5D subspace. The constraints provided by these motion subspaces ena...

• Type: Conference
• Year: 2010
• Where: ECCV
• Authors: Roland Angst, Marc Pollefeys
• Keywords: 3D Reconstruction, Affine Cameras, ECCV 2010, Feature Point Trajectories, Matrix And Tensor Factorizations, Planar Rigid Motion, Structure From Motion