ContQuat: Continuous quaternion representation for head pose estimation

Recently, head-pose estimation has attracted growing attention due to its inherent value in enhancing the performance of head-related applications. Neural networks often require the handling of various representations of the same rotation space. For instance, Euler angles and standard unit quaternion representations can be employed to represent three-dimensional (3D) rotations. However, these representations suffer from the discontinuity problem (DP). Instead of previous representations, we propose a novel end-to-end landmark-free method that employs a continuous quaternion representation (CQR) based on a symmetric matrix ( A ) for 3D rotations when training deep neural networks. This representation is named ContQuat, which satisfies the continuity property and allows the model to overcome the DP and ambiguity issues encountered in commonly used standard unit quaternion and Euler angle representations, enabling efficient full rotation learning. We also introduce three loss functions appropriate for the proposed method to encapsulate the training loss of the neural network during the optimization process. Furthermore, we present a comprehensive experimental comparison of the proposed method against state-of-the-art approaches on publicly available benchmark datasets. The experimental results and error analysis visualizations demonstrate that the proposed method either outperforms or is highly competitive with the current state-of-the-art techniques. The full code is available at: ( ContQuat ).