On a sub‐Stiefel Procrustes problem arising in computer vision
On a sub‐Stiefel Procrustes problem arising in computer vision
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关于计算机视觉中出现的亚斯蒂菲尔普罗克拉斯特问题
DOI：
10.1002/nla.1969
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发表时间：
2015
影响因子：
4.3
通讯作者：
K. Zietak
中科院分区：
文献类型：
--
作者：
J. R. Cardoso;K. Zietak
子Stiefel矩阵是通过同时删除正交矩阵的最后一行和最后一列而得到的矩阵。在本文中，我们考虑了n阶次Stiefel矩阵集合上的一个Procrustes问题。对于n = 2，这个问题已经出现在计算机视觉中，以解决R. Fereirra，J. Xavier and J. Costeira.提出了一种计算任意n情形下sub-Stiefel Procrustes问题解的迭代算法，并通过数值实验验证了算法的性能.为了这些目的，我们研究子Stiefel矩阵的性质。特别地，我们得到了矩阵是次Stiefel的两个充分必要条件。我们还将子Stiefel Procrustes问题与Stiefel Procrustes问题联系起来，并将其与正交Procrustes问题进行比较。版权所有© 2015约翰威利父子有限公司.
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.