  Automatically detecting the positions of key-points (e.g., facial key-points
or finger key-points) in an image is an essential problem in many applications,
such as driver's gaze detection and drowsiness detection in automated driving
systems. With the recent advances of Deep Neural Networks (DNNs), Key-Points
detection DNNs (KP-DNNs) have been increasingly employed for that purpose.
Nevertheless, KP-DNN testing and validation have remained a challenging problem
because KP-DNNs predict many independent key-points at the same time -- where
each individual key-point may be critical in the targeted application -- and
images can vary a great deal according to many factors.
  In this paper, we present an approach to automatically generate test data for
KP-DNNs using many-objective search. In our experiments, focused on facial
key-points detection DNNs developed for an industrial automotive application,
we show that our approach can generate test suites to severely mispredict, on
average, more than 93% of all key-points. In comparison, random search-based
test data generation can only severely mispredict 41% of them. Many of these
mispredictions, however, are not avoidable and should not therefore be
considered failures. We also empirically compare state-of-the-art,
many-objective search algorithms and their variants, tailored for test suite
generation. Furthermore, we investigate and demonstrate how to learn specific
conditions, based on image characteristics (e.g., head posture and skin color),
that lead to severe mispredictions. Such conditions serve as a basis for risk
analysis or DNN retraining.
