  Recognizing facial action units (AUs) during spontaneous facial displays is a
challenging problem. Most recently, Convolutional Neural Networks (CNNs) have
shown promise for facial AU recognition, where predefined and fixed convolution
filter sizes are employed. In order to achieve the best performance, the
optimal filter size is often empirically found by conducting extensive
experimental validation. Such a training process suffers from expensive
training cost, especially as the network becomes deeper.
  This paper proposes a novel Optimized Filter Size CNN (OFS-CNN), where the
filter sizes and weights of all convolutional layers are learned simultaneously
from the training data along with learning convolution filters. Specifically,
the filter size is defined as a continuous variable, which is optimized by
minimizing the training loss. Experimental results on two AU-coded spontaneous
databases have shown that the proposed OFS-CNN is capable of estimating optimal
filter size for varying image resolution and outperforms traditional CNNs with
the best filter size obtained by exhaustive search. The OFS-CNN also beats the
CNN using multiple filter sizes and more importantly, is much more efficient
during testing with the proposed forward-backward propagation algorithm.
