Manifold convex hull (MACH): Satisfying a need for SPD

Abstract

In this paper, we extend the nearest convex hull classifier to Symmetric Positive Definite (SPD) manifolds. SPD manifold features have been shown to have excellent performance in various image/video classification tasks. Unfortunately, SPD manifolds naturally possess non-Euclidean geometry, so existing Euclidean machineries such as the nearest convex hull classifier cannot be used directly. To that end, we propose a novel mathematical framework, named Manifold Convex Hull (MACH), that extends the nearest convex hull classifier to SPD Manifolds. The superior performance of our nearest convex hull framework on SPD manifolds is demonstrated in several computer vision applications including object recognition, pedestrian detection and texture classification.