Fan Wang, Huidong Liu, Dimitris Samaras and Chao Chen
European Conference on Computer Vision (ECCV), 2020, (Oral, acceptance rate 2.1%)

Most existing generative adversarial networks (GANs) focus on generating realistic images with regard to CNN-based image features, but fail to preserve the structural properties of real images. This can be fatal in applications where the underlying structure (e.g., neurons, vessels, membranes, road networks) of the image carries crucial semantic meaning. In this paper, we propose a novel GAN model that learns the topology of the real images, i.e., connectedness and loopy-ness. In particular, we introduce a new loss that bridges the gap between synthetic image distribution and real image distribution in the topological feature space. By optimizing this loss, the generator produces images with the same structural topology as real images. We also propose new GAN evaluation metrics that measure the topological realism of the synthetic images. We show in experiments that our method generates synthetic images with realistic topology. We also highlight the increased performance that our method brings to downstream tasks such as segmentation.

In the topological feature space, the topological GAN loss compares the real and synthetic persistence diagrams. We find a pairwise matching between two sets of persistence diagrams with optimal transport. We define the loss as the summation of the distances between all matched persistence diagrams. We minimize this loss by forcing the persistence diagrams of synthetic images to be alike those of real images. In this way, the generator produces synthetic images similar to the real images [in]* terms of the topology. Prior work from our group uses topological information to define a loss at the instance-level while TopoGAN compares topology at the distribution-level.