On the representation and methodology for wide and short range head pose estimation

Head pose estimation (HPE) is a problem of interest in computer vision to improve the performance of face processing tasks in semi-frontal or profile settings. Recent applications require the analysis of faces in the full 360{\deg} rotation range. Traditional approaches to solve the semi-frontal and profile cases are not directly amenable for the full rotation case. In this paper we analyze the methodology for short- and wide-range HPE and discuss which representations and metrics are adequate for each case. We show that the popular Euler angles representation is a good choice for short-range HPE, but not at extreme rotations. However, the Euler angles' gimbal lock problem prevents them from being used as a valid metric in any setting. We also revisit the current cross-data set evaluation methodology and note that the lack of alignment between the reference systems of the training and test data sets negatively biases the results of all articles in the literature. We introduce a procedure to quantify this misalignment and a new methodology for cross-data set HPE that establishes new, more accurate, SOTA for the 300W-LP|Biwi benchmark. We also propose a generalization of the geodesic angular distance metric that enables the construction of a loss that controls the contribution of each training sample to the optimization of the model. Finally, we introduce a wide range HPE benchmark based on the CMU Panoptic data set.