Convex class model on symmetric positive definite manifolds

Abstract

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.