  The unsupervised image-to-image translation aims at finding a mapping between
the source ($A$) and target ($B$) image domains, where in many applications
aligned image pairs are not available at training. This is an ill-posed
learning problem since it requires inferring the joint probability distribution
from marginals. Joint learning of coupled mappings $F_{AB}: A \rightarrow B$
and $F_{BA}: B \rightarrow A$ is commonly used by the state-of-the-art methods,
like CycleGAN [Zhu et al., 2017], to learn this translation by introducing
cycle consistency requirement to the learning problem, i.e. $F_{AB}(F_{BA}(B))
\approx B$ and $F_{BA}(F_{AB}(A)) \approx A$. Cycle consistency enforces the
preservation of the mutual information between input and translated images.
However, it does not explicitly enforce $F_{BA}$ to be an inverse operation to
$F_{AB}$. We propose a new deep architecture that we call invertible
autoencoder (InvAuto) to explicitly enforce this relation. This is done by
forcing an encoder to be an inverted version of the decoder, where
corresponding layers perform opposite mappings and share parameters. The
mappings are constrained to be orthonormal. The resulting architecture leads to
the reduction of the number of trainable parameters (up to $2$ times). We
present image translation results on benchmark data sets and demonstrate
state-of-the art performance of our approach. Finally, we test the proposed
domain adaptation method on the task of road video conversion. We demonstrate
that the videos converted with InvAuto have high quality and show that the
NVIDIA neural-network-based end-to-end learning system for autonomous driving,
known as PilotNet, trained on real road videos performs well when tested on the
converted ones.
