Abstract: Humans perceive the world through global structures such as parts, branches, and their spatial arrangement. Most deep learning models, however, operate mainly at the pixel level. This disconnect between local and global understanding limits interpretability and control. In this thesis, we explore topology as a mathematical framework for bridging local predictions and global structure in dense prediction and generation tasks. We first incorporate topological constraints into semantic segmentation to preserve anatomical relationships and improve multi-class consistency. We next develop structure-level uncertainty estimation, producing more interpretable and actionable measures of model error over branches and connections rather than isolated pixels. Then, we introduce a topology-guided diffusion framework for controllable image generation using structural attributes such as object count and connectivity. Finally, we extend image generation to the longitudinal task, where we aim to capture structural changes across timepoints. All these contributions together establish topology as a unifying interface for building dense prediction models that are structurally aware, interpretable, and controllable.

Speaker: Saumya Gupta

Location: NCS 220

Zoom: https://stonybrook.zoom.us/j/97950688136?pwd=NCa3XOsgIaMIsTVlQBQJ11n27NzL8s.1
Meeting ID: 979 5068 8136
Passcode: 941798