Multi-scale Topological Features for Hand Posture Representation and Analysis

In this paper, we propose a multi-scale topological feature representation for automatic analysis of hand posture. Such topological features have the advantage of being posture-dependent while being preserved under certain variations of illumination, rotation, personal dependency, etc. Our method studies the topology of the holes between the hand region and its convex hull. Inspired by the principle of Persistent Homology, which is the theory of computational topology for topological feature analysis over multiple scales, we construct the multi-scale Betti Numbers matrix (MSBNM) for the topological feature representation. In our experiments, we used 12 different hand postures and compared our features with three popular features (HOG, MCT, and Shape Context) on different data sets. In addition to hand postures, we also extend the feature representations to arm postures. The results demonstrate the feasibility and reliability of the proposed method.