  The recent performance of facial landmark detection has been significantly
improved by using deep Convolutional Neural Networks (CNNs), especially the
Heatmap Regression Models (HRMs). Although their performance on common
benchmark datasets has reached a high level, the robustness of these models
still remains a challenging problem in the practical use under noisy conditions
of realistic environments. Contrary to most existing work focusing on the
design of new models, we argue that improving the robustness requires
rethinking many other aspects, including the use of datasets, the format of
landmark annotation, the evaluation metric as well as the training and
detection algorithm itself. In this paper, we propose a novel method for robust
facial landmark detection, using a loss function based on the 2D Wasserstein
distance combined with a new landmark coordinate sampling relying on the
barycenter of the individual probability distributions. Our method can be
plugged-and-play on most state-of-the-art HRMs with neither additional
complexity nor structural modifications of the models. Further, with the large
performance increase, we found that current evaluation metrics can no longer
fully reflect the robustness of these models. Therefore, we propose several
improvements to the standard evaluation protocol. Extensive experimental
results on both traditional evaluation metrics and our evaluation metrics
demonstrate that our approach significantly improves the robustness of
state-of-the-art facial landmark detection models.
