Manifold topological multi-resolution analysis method

In this paper, two significant weaknesses of locally linear embedding (LLE) applied to computer vision are addressed: ‘‘intrinsic dimension’’ and ‘‘eigenvector meanings’’. ‘‘Topological embedding’’ and ‘‘multi-resolution nonlinearity capture’’ are introduced based on mathematical analysis of topological manifolds and LLE. The manifold topological analysis (MTA) method is described and is based on ‘‘topological embedding’’. MTA is a more robust method to determine the ‘‘intrinsic dimension’’ of a manifold with typical topology, which is important for tracking and perception understanding. The manifold multi-resolution analysis (MMA) method is based on ‘‘multi-resolution nonlinearity capture’’. MMA defines LLE eigenvectors as features for pattern recognition and dimension reduction. Both MTA and MMA are proved mathematically, and several examples are provided. Applications in 3D object recognition and 3D object viewpoint space partitioning are also described. & 2011 Elsevier Ltd. All rights reserved.