Abstract
PURPOSE: Accurate estimation of reference bony shape models is fundamental for orthognathic surgical planning. Existing methods to derive this model are of two types: one determines the reference model by estimating the deformation field to correct the patient's deformed jaw, often introducing distortions in the predicted reference model; The other derives the reference model using a linear combination of their landmarks/vertices but overlooks the intricate nonlinear relationship between the subjects, compromising the model's precision and quality. METHODS: We have created a self-supervised learning framework to estimate the reference model. The core of this framework is a deep query network, which estimates the similarity scores between the patient's midface and those of the normal subjects in a high-dimensional space. Subsequently, it aggregates high-dimensional features of these subjects and projects these features back to 3D structures, ultimately achieving a patient-specific reference model. RESULTS: Our approach was trained using a dataset of 51 normal subjects and tested on 30 patient subjects to estimate their reference models. Performance assessment against the actual post-operative bone revealed a mean Chamfer distance error of 2.25 mm and an average surface distance error of 2.30 mm across the patient subjects. CONCLUSION: Our proposed method emphasizes the correlation between the patients and the normal subjects in a high-dimensional space, facilitating the generation of the patient-specific reference model. Both qualitative and quantitative results demonstrate its superiority over current state-of-the-art methods in reference model estimation.