  Automatic facial action unit (AU) recognition has attracted great attention
but still remains a challenging task, as subtle changes of local facial muscles
are difficult to thoroughly capture. Most existing AU recognition approaches
leverage geometry information in a straightforward 2D or 3D manner, which
either ignore 3D manifold information or suffer from high computational costs.
In this paper, we propose a novel geodesic guided convolution (GeoConv) for AU
recognition by embedding 3D manifold information into 2D convolutions.
Specifically, the kernel of GeoConv is weighted by our introduced geodesic
weights, which are negatively correlated to geodesic distances on a coarsely
reconstructed 3D face model. Moreover, based on GeoConv, we further develop an
end-to-end trainable framework named GeoCNN for AU recognition. Extensive
experiments on BP4D and DISFA benchmarks show that our approach significantly
outperforms the state-of-the-art AU recognition methods.
