  This paper proposes to use the three vectors in a rotation matrix as the
representation in head pose estimation and develops a new neural network based
on the characteristic of such representation. We address two potential issues
existed in current head pose estimation works: 1. Public datasets for head pose
estimation use either Euler angles or quaternions to annotate data samples.
However, both of these annotations have the issue of discontinuity and thus
could result in some performance issues in neural network training. 2. Most
research works report Mean Absolute Error (MAE) of Euler angles as the
measurement of performance. We show that MAE may not reflect the actual
behavior especially for the cases of profile views. To solve these two
problems, we propose a new annotation method which uses three vectors to
describe head poses and a new measurement Mean Absolute Error of Vectors (MAEV)
to assess the performance. We also train a new neural network to predict the
three vectors with the constraints of orthogonality. Our proposed method
achieves state-of-the-art results on both AFLW2000 and BIWI datasets.
Experiments show our vector-based annotation method can effectively reduce
prediction errors for large pose angles.
