Constrained planar motion analysis by decomposition

Abstract

General SFM methods give poor results for images captured by constrained motions such as planar motion. In this paper, we propose new SFM algorithms for images captured under a common but constrained planar motion: the image plane is perpendicular to the motion plane. We show that a 2D image captured under such constrained planar motion can be decoupled into two 1D images: one 1D projective and one 1D affine. We then introduce the 1D affine camera model for completing 1D camera models. Next, we describe new subspace reconstruction methods, and apply these methods to the images captured by concentric mosaics, which undergo a special case of constrained planar motion. Finally, we demonstrate both in theory and experiments the advantage of the decomposition method over the general SFM methods by incorporating the constrained motion into the earliest stage of motion analysis.