Ricci curvature discretizations for head pose estimation from a single image

Head pose estimation (HPE) is crucial in various real-world applications, like human–computer interaction and biometric framework enhancement. This research aims to leverage network curvature to predict head pose from a single image. In networks, certain groups of nodes fulfill significant functional roles. This study focuses on the interactions of facial landmarks, considered as vertices in a weighted graph. The experiments demonstrate that the underlying graph geometry and topology enable the detection of similarities among various head poses. Two independent notions of discrete Ricci curvature for graphs, namely Ollivier–Ricci and Forman–Ricci curvatures, are investigated. These two types of Ricci curvature, each reflecting distinct geometric properties of the network, serve as inputs to the regression model. The results from the BIWI, AFLW2000, and Pointing‘04 datasets reveal that the two discretizations of Ricci’s curvature are closely related and outperform state-of-the-art methods, including both landmark-based and image-only approaches. This demonstrates the effectiveness and promise of using network curvature for HPE in diverse applications. • The topology of the underlying graph can identify similarities across head poses. • Analyzes the performance differences between Ollivier and Forman Ricci curvatures. • Ollivier–Ricci-based method shows competitive results on three different datasets. • The Forman–Ricci-based method offers a computationally efficient alternative.