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.

The Anti-Nuclear Antibody (ANA) clinical pathology test is commonly used to identify the existence of various diseases. A hallmark method for identifying the presence of ANAs is the Indirect Immunofluorescence method on Human Epithelial (HEp-2) cells, due to its high sensitivity and the large range of antigens that can be detected. However, the method suffers from numerous shortcomings, such as being subjective as well as time and labour intensive. Computer Aided Diagnostic (CAD) systems have been developed to address these problems, which automatically classify a HEp-2 cell image into one of its known patterns (eg., speckled, homogeneous). Most of the existing CAD systems use handpicked features to represent a HEp-2 cell image, which may only work in limited scenarios. In this paper, we propose a cell classification system comprised of a dual-region codebookbased descriptor, combined with the Nearest Convex Hull Classifier. We evaluate the performance of several variants of the descriptor on two publicly available datasets: ICPR HEp-2 cell classification contest dataset and the new SNPHEp-2 dataset. To our knowledge, this is the first time codebook-based descriptors are applied and studied in this domain. Experiments show that the proposed system has consistent high performance and is more robust than two recent CAD systems.