Local topology preservation for vascular centerline matching using a hybrid mixture model

Non-rigid registration is essential for a wide range of clinical applications, such as intraoperative image-guidance and postoperative follow-up assessment, and longitudinal image analysis for disease diagnosis and monitoring. Vascular structures are a rich descriptor of the organ deformation, since it permeates through all organs within body. As vasculature differs in size, shape and topology, following surgical intervention/treatment or due to disease progression, non-rigid vessel matching remains a challenging task. Recently, hybrid mixture models (HdMM) have been applied to tackle this challenge, and demonstrate significant improvements in terms of accuracy and robustness relative to the state-of-the-art. However, the smoothness constraint enforced on the deformation field with this approach only accounts for the global topology of the vasculature, resulting in a reduced capacity to accurately match localized changes to vascular structures, and preserve local topology. In this work, we proposed a modified version of HdMM by formulating an adaptive kernel, to enforce a local smoothness constraint on the deformation field, henceforth referred to as HdMMad. The proposed HdMMad framework is evaluated with cerebral and pulmonary vasculature, acquired retrospectively. The registration results for both data sets demonstrate that the proposed approach outperforms registration algorithms also designed to preserve local topology. Using HdMMad, around 80% of the initial registration error was reduced, for both data sets.