Ollivier-Ricci Curvature for Head Pose Estimation from a Single Image

Head pose estimation is not only a crucial challenge for many real-world applications, such as driver attention detection analysis, but it represents an interesting strategy to support biometric frameworks as well. This paper aims to estimate head pose from a single image by applying notions of network curvature. In the real world, many complex networks have groups of nodes that are well connected to each other with significant functional roles. Similarly, the interactions of facial landmarks can be represented as complex dynamic systems modeled by weighted graphs. The functionality of such a system is therefore intrinsically linked to the topology and geometry of the underlying graph. In this work, using the geometric notion of Ollivier-Ricci curvature (ORC) on weighted graphs as input to the XGBoost regression model, we show that the intrinsic geometric basis of ORC offers a natural approach to discovering underlying common structure within a pool of poses. Experiments on the BIWI, AFLW2000 and Pointing '04 datasets show that the ORC_XGB method performs well compared to state-of-the-art methods, both landmark-based and image-only.