A convenient way of analysing Riemannian manifolds is to embed them in Euclidean spaces, with the embedding typically obtained by flattening the manifold via tangent spaces. This general approach is not free of drawbacks. For example, only distances between points to the tangent pole are equal to true geodesic distances. This is restrictive and may lead to inaccurate modelling. Instead of using tangent spaces, we propose embedding into the Reproducing Kernel Hilbert Space by introducing a Riemannian pseudo kernel. We furthermore propose to recast a locality preserving projection technique from Euclidean spaces to Riemannian manifolds, in order to demonstrate the benefits of the embedding. Experiments on several visual classification tasks (gesture recognition, person re-identification and texture classification) show that in comparison to tangentbased processing and state-of-the-art methods (such as tensor canonical correlation analysis), the proposed approach obtains considerable improvements in discrimination accuracy.
Prior to classification, points on the manifold were mapped to an Euclidean space, through Riemannian Locality Preserving Projection REF .
Kernel analysis over Riemannian manifolds for visual recognition of actions, pedestrians and textures
2012 IEEE Workshop on the Applications of Computer Vision (WACV)
2012 IEEE Workshop on the Applications of Computer Vision (WACV)
Computer Science