TDPSR-Net: Topographic Distance Priors and a Spatial Regularization Network for Enhanced PET Segmentation

Positron emission tomography (PET) provides functional information by capturing tracer uptake and is widely used for disease assessment. Accurate segmentation of regions of interest is essential for quantitative analysis and clinical decision-making. However, PET images often exhibit low spatial resolution, high noise, and blurred boundaries due to partial volume effects, which hampers precise delineation. To address this, we propose TDPSR-Net, a PET image segmentation network that integrates topographic distance priors (TDP) and spatial regularization techniques. Our method automatically generates marker points for computing topographic distances, and the network jointly extracts features from both PET images and the resulting TDP maps. To enhance spatial coherence and boundary consistency, we introduce a Soft Threshold Dynamics of Sigmoid (STD-Sigmoid) layer that imposes spatial regularization on the network output, and we further establish a theoretical connection between the proposed formulation and a Potts-type model. We evaluate TDPSR-Net on multiple datasets, including liver, hippocampus, and lung cancer tumor segmentation, and the results demonstrate consistently high accuracy and robustness across diverse datasets, highlighting the potential of TDPSR-Net for a wide range of clinical applications.