Conjugate gradient on Grassmann manifolds for robust subspace estimation

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.

Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (205 K)Download as PowerPoint slideHighlights► The problem of subspace estimation is formulated as an optimization problem over Grassmann manifold. ► Conjugate gradient algorithm is used in conjunction with generalized projection based M-estimator (gpbM). ► Improved performance as compared to the original gpbM algorithm is demonstrated.