Stiefel and Grassmann manifolds

Correction: Statistical Computations on Grassmann and Stiefel Manifolds for Image and Video-Based Recognition

In this paper, we examine image and video based recognition applications where the underlying models have a special structure – the linear subspace structure. We discuss how commonly used parametric models for videos and image-sets can be described using the unified framework of Grassmann and Stiefel manifolds. We first show that the parameters of linear dynamic models are finite dimensional li...

Recognition of Humans and their Activities using Statistical analysis on Stiefel and Grassmann Manifolds

Many applications in computer vision involve learning and recognition of patterns from exemplars which lie on certain manifolds. Given a database of examples and a query, the following two questions are usually addressed – a) what is the ‘closest’ example to the query in the database ? b) what is the ‘most probable’ class to which the query belongs ? The answer to the first question involves st...

Rolling Stiefel manifolds

In this paper rolling maps for real Stiefel manifolds are studied. Real Stiefel manifolds being the set of all orthonormal k-frames of an n-dimensional real Euclidean space are compact manifolds. They are considered here as rigid bodies embedded in a suitable Euclidean space such that the corresponding Euclidean group acts on the rigid body by rotations and translations in the usual way. We der...

Tangent Bundle Manifold Learning via Grassmann&Stiefel Eigenmaps

One of the ultimate goals of Manifold Learning (ML) is to reconstruct an unknown nonlinear low-dimensional manifold embedded in a high-dimensional observation space by a given set of data points from the manifold. We derive a local lower bound for the maximum reconstruction error in a small neighborhood of an arbitrary point. The lower bound is defined in terms of the distance between tangent s...

Space Forms of Grassmann Manifolds