On the representation and methodology for wide and short range head pose
  estimation
Alejandro Cobo Roberto Valle José M. Buenaposada Luis Baumela
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.