  Unsupervised domain mapping aims to learn a function to translate domain X to
Y by a function GXY in the absence of paired examples. Finding the optimal GXY
without paired data is an ill-posed problem, so appropriate constraints are
required to obtain reasonable solutions. One of the most prominent constraints
is cycle consistency, which enforces the translated image by GXY to be
translated back to the input image by an inverse mapping GYX. While cycle
consistency requires the simultaneous training of GXY and GY X, recent studies
have shown that one-sided domain mapping can be achieved by preserving pairwise
distances between images. Although cycle consistency and distance preservation
successfully constrain the solution space, they overlook the special properties
that simple geometric transformations do not change the semantic structure of
images. Based on this special property, we develop a geometry-consistent
generative adversarial network (GcGAN), which enables one-sided unsupervised
domain mapping. GcGAN takes the original image and its counterpart image
transformed by a predefined geometric transformation as inputs and generates
two images in the new domain coupled with the corresponding
geometry-consistency constraint. The geometry-consistency constraint reduces
the space of possible solutions while keep the correct solutions in the search
space. Quantitative and qualitative comparisons with the baseline (GAN alone)
and the state-of-the-art methods including CycleGAN and DistanceGAN demonstrate
the effectiveness of our method.
