Title: Minimal Geometry-Distortion Constraint for Unsupervised Image-to-Image Translation. Abstract: Unsupervised image-to-image (I2I) translation, which aims to learn a domain mapping function without paired data, is very challenging because the function is highly under-constrained. Despite the significant progress in constraining the mapping function, current methods suffer from the \textit{geometry distortion} problem: the geometry structure of the translated image is inconsistent with the input source image, which may cause the undesired distortions in the translated images.  To remedy this issue, we propose a novel I2I translation constraint,  called \textit{Minimal Geometry-Distortion Constraint} (MGC), which promotes the consistency of geometry structures and reduce the unwanted distortions in translation by reducing the randomness of color transformation in the translation process. To facilitate estimation and maximization of MGC, we propose an approximate representation of mutual information called relative Squared-loss Mutual Information (rSMI) that can be efficiently estimated analytically. We demonstrate the effectiveness of our MGC by providing quantitative and qualitative comparisons with the state-of-the-art methods on several benchmark datasets.
