  The one-to-one mapping is necessary for many bidirectional image-to-image
translation applications, such as MRI image synthesis as MRI images are unique
to the patient. State-of-the-art approaches for image synthesis from domain X
to domain Y learn a convolutional neural network that meticulously maps between
the domains. A different network is typically implemented to map along the
opposite direction, from Y to X. In this paper, we explore the possibility of
only wielding one network for bi-directional image synthesis. In other words,
such an autonomous learning network implements a self-inverse function. A
self-inverse network shares several distinct advantages: only one network
instead of two, better generalization and more restricted parameter space. Most
importantly, a self-inverse function guarantees a one-to-one mapping, a
property that cannot be guaranteed by earlier approaches that are not
self-inverse. The experiments on three datasets show that, compared with the
baseline approaches that use two separate models for the image synthesis along
two directions, our self-inverse network achieves better synthesis results in
terms of standard metrics. Finally, our sensitivity analysis confirms the
feasibility of learning a self-inverse function for the bidirectional image
translation.
