TopoSinGAN: Learning a Topology-Aware Generative Model from a Single Image

Abstract

Generative adversarial networks (GANs) have significantly advanced synthetic image generation, yet ensuring topological coherence remains a challenge. This paper introduces TopoSinGAN, a topology-aware extension of the SinGAN framework, designed to enhance the topological accuracy of generated images. TopoSinGAN incorporates a novel, differentiable topology loss function that minimizes terminal node counts along predicted segmentation boundaries, thereby addressing topological anomalies not captured by traditional losses. We evaluate TopoSinGAN using agricultural and dendrological case studies, demonstrating its capability to maintain boundary continuity and reduce undesired loop openness. A novel evaluation metric, Node Topology Clustering (NTC), is proposed to assess topological attributes independently of geometric variations. TopoSinGAN significantly improves topological accuracy, reducing NTC index values from 15.15 to 3.94 for agriculture and 14.55 to 2.44 for dendrology, compared to the baseline SinGAN. Modified FID evaluations also show improved realism, with lower FID scores: 0.1914 for agricultural fields compared to 0.2485 for SinGAN, and 0.0013 versus 0.0014 for dendrology. The topology loss enables end-to-end training with direct topological feedback. This new framework advances the generation of topologically accurate synthetic images, with applications in fields requiring precise structural representations, such as geographic information systems (GIS) and medical imaging.