On a sub‐Stiefel Procrustes problem arising in computer vision |
| |
| Authors: | João R Cardoso Krystyna Zi?tak |
| |
| Affiliation: | 1. Polytechnic Institute of Coimbra/ISEC, Coimbra, Portugal;2. Institute of Systems and Robotics, University of Coimbra, Coimbra, Portugal;3. Wroc?aw School of Information Technology, Wroc?aw, Poland;4. Wroc?aw University of Technology, Faculty of Fundamental Problems of Technology, Wroc?aw, Poland |
| |
| Abstract: | A sub‐Stiefel matrix is a matrix that results from deleting simultaneously the last row and the last column of an orthogonal matrix. In this paper, we consider a Procrustes problem on the set of sub‐Stiefel matrices of order n. For n = 2, this problem has arisen in computer vision to solve the surface unfolding problem considered by R. Fereirra, J. Xavier and J. Costeira. An iterative algorithm for computing the solution of the sub‐Stiefel Procrustes problem for an arbitrary n is proposed, and some numerical experiments are carried out to illustrate its performance. For these purposes, we investigate the properties of sub‐Stiefel matrices. In particular, we derive two necessary and sufficient conditions for a matrix to be sub‐Stiefel. We also relate the sub‐Stiefel Procrustes problem with the Stiefel Procrustes problem and compare it with the orthogonal Procrustes problem. Copyright © 2015 John Wiley & Sons, Ltd. |
| |
| Keywords: | Procrustes problem orthogonal matrix Stiefel matrix sub‐Stiefel matrix approximation of a matrix computer vision |
|
|
