Conjugate gradient on Grassmann manifolds for robust subspace estimation

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• 作者：Sushil Mittal ; ^{smittal@caip.rutgers.edu} ; Peter Meer ^{meer@jove.rutgers.edu}
• 关键词：Grassmann manifolds ; Conjugate gradient algorithm ; Generalized projection based M-estimator
• 刊名：Image and Vision Computing
• 出版年：2012
• 期刊代码：68_02628856
• 类别：et
• 出版时间：June, 2012
• 卷：30
• 期：6-7
• 页码：417-427
• 文件大小：1146 K

摘要

Most geometric computer vision problems involve orthogonality constraints. An important subclass of these problems is subspace estimation, which can be equivalently formulated into an optimization problem on Grassmann manifolds. In this paper, we propose to use the conjugate gradient algorithm on Grassmann manifolds for robust subspace estimation in conjunction with the recently introduced generalized projection based M-Estimator (gpbM). The gpbM method is an elemental subset-based robust estimation algorithm that can process heteroscedastic data without any user intervention. We show that by optimizing the orthogonal parameter matrix on Grassmann manifolds, the performance of the gpbM algorithm improves significantly. Results on synthetic and real data are presented.