State-of-the-art methods for optical flow estimation rely on deep learning,
which require complex sequential training schemes to reach optimal performances
on real-world data. In this work, we introduce the COMBO deep network that
explicitly exploits the brightness constancy (BC) model used in traditional
methods. Since BC is an approximate physical model violated in several
situations, we propose to train a physically-constrained network complemented
with a data-driven network. We introduce a unique and meaningful flow
decomposition between the physical prior and the data-driven complement,
including an uncertainty quantification of the BC model. We derive a joint
training scheme for learning the different components of the decomposition
ensuring an optimal cooperation, in a supervised but also in a semi-supervised
context. Experiments show that COMBO can improve performances over
state-of-the-art supervised networks, e.g. RAFT, reaching state-of-the-art
results on several benchmarks. We highlight how COMBO can leverage the BC model
and adapt to its limitations. Finally, we show that our semi-supervised method
can significantly simplify the training procedure