Topologically-enhanced deep learning for spatial image processing and generation

Abstract

This dissertation explores the integration of topological awareness into deep learning frameworks for spatial image segmentation and generation. Addressing the critical need for topological consistency, the research develops novel methods to enhance the accuracy and reliability of segmentation outputs in geospatial and dendrological contexts. Key contributions include the introduction of TopoSinGAN, a topology-aware generative adversarial network, and TopoSegNet, a scalable segmentation model that incorporates topology-preserving loss functions. These models are evaluated across diverse datasets, including ultra-high-resolution tree-ring images and agricultural field boundaries. Building on the individual contributions of TopoSinGAN and TopoSegNet, the dissertation implements a comprehensive workflow that combines these models. TopoSinGAN is used to generate topologically consistent synthetic datasets, which are then employed to improve the training and accuracy of TopoSegNet. This integrated approach demonstrates significant advancements in segmentation performance, emphasizing the synergy between synthetic data generation and topological enhancement. The dissertation's findings establish a robust foundation for applying topological principles in deep learning, with implications for geospatial analysis, dendrochronology, and other domains requiring precise spatial delineation. By leveraging topology-aware techniques, this work advances the state-of-the-art in deep learning for image analysis, ensuring both geometric and structural fidelity in challenging applications.