The Generalized Trace-Norm and its Application to Structure-from-Motion Problems

In geometric computer vision, the structure from motion (SfM) problem can be formulated as a optimization problem with a rank constraint. It is well known that the trace norm of a matrix can act as a convex proxy for a low rank constraint. Hence, in recent work [7], the trace-norm relaxation has been applied to the SfM problem. However, SfM problems often exhibit a certain structure, for example a smooth camera path. Unfortunately, the trace norm relaxation can not make use of this additional structure. This observation motivates the main contribution of this paper. We present the so-called generalized trace norm which allows to encode prior knowledge about a specific problem into a convex regularization term which enforces a low rank solution while at the same time taking the problem structure into account. While deriving the generalized trace norm and stating its different formulations, we draw interesting connections to other fields, most importantly to the field of compressive ...

• Type: Journal
• Year: 2011
• Where: ICCV
• Authors: Roland Angst, Christopher Zach, Marc Pollefeys
• Keywords: Camera Path, Computer Vision, ICCV 2011, Optimization Problem, Optimization Problems