  The effectiveness of Symmetric Positive Definite (SPD) manifold features has
been proven in various computer vision tasks. However, due to the non-Euclidean
geometry of these features, existing Euclidean machineries cannot be directly
used. In this paper, we tackle the classification tasks with limited training
data on SPD manifolds. Our proposed framework, named Manifold Convex Class
Model, represents each class on SPD manifolds using a convex model, and
classification can be performed by computing distances to the convex models. We
provide three methods based on different metrics to address the optimization
problem of the smallest distance of a point to the convex model on SPD
manifold. The efficacy of our proposed framework is demonstrated both on
synthetic data and several computer vision tasks including object recognition,
texture classification, person re-identification and traffic scene
classification.
