Joint modeling of the intensity of facial action units
(AUs) from face images is challenging due to the large number
of AUs (30+) and their intensity levels (6). This is in
part due to the lack of suitable models that can efficiently
handle such a large number of outputs/classes simultaneously,
but also due to the lack of labelled target data. For
this reason, majority of the methods proposed so far resort
to independent classifiers for the AU intensity. This is suboptimal
for at least two reasons: the facial appearance of
some AUs changes depending on the intensity of other AUs,
and some AUs co-occur more often than others. Encoding
this is expected to improve the estimation of target AU
intensities, especially in the case of noisy image features,
head-pose variations and imbalanced training data. To this
end, we introduce a novel modeling framework, Copula Ordinal
Regression (COR), that leverages the power of copula
functions and CRFs, to detangle the probabilistic modeling
of AU dependencies from the marginal modeling of
the AU intensity. Consequently, the COR model achieves
the joint learning and inference of intensities of multiple
AUs, while being computationally tractable. We show on
two challenging datasets of naturalistic facial expressions
that the proposed approach consistently outperforms (i) independent
modeling of AU intensities, and (ii) the state-ofthe-art
approach for the target task.