Learning the anatomical topology consistency driven by Wasserstein distance for weakly supervised 3D pancreas registration in multi-phase CT images

Accurate and automatic registration of the pancreas between contrast-enhanced CT (CECT) and non-contrast CT (NCCT) images is crucial for diagnosing and treating pancreatic cancer. However, existing deep learning-based methods remain limited due to inherent intensity differences between modalities, which impair intensity-based similarity metrics, and the pancreas's small size, vague boundaries, and complex surroundings, which trap segmentation-based metrics in local optima. To address these challenges, we propose a weakly supervised registration framework incorporating a novel mixed loss function. This loss leverages Wasserstein distance to enforce anatomical topology consistency in 3D pancreas registration between CECT and NCCT. We employ distance transforms to build the small, uncertain and complex anatomical topology distribution of the pancreas. Unlike conventional voxel-wise<i>L</i>₁or<i>L</i>₂loss, the Wasserstein distance directly measures the similarity between warped and fixed anatomical topologies of pancreas. Experiments on a dataset of 975 paired CECT-NCCT images from patients with seven pancreatic tumor types (PDAC, IPMN, MCN, SCN, SPT, CP, PNET), demonstrate that our method outperforms state-of-the-art weakly supervised approaches, achieving improvements of 3.2% in Dice score, reductions of 28.54% in false positive segmentation rate with 0.89% in Hausdorff distance. The source code will be made publicly available athttps://github.com/ZouLiwen-1999/WSMorph.