Weakly Supervised Learning of Piecewise Rigid Transformation for Orthognathic Surgical Reconstruction of Dentofacial Deformity

We propose a data-driven surgical reconstruction algorithm under observation that the volumetric deformation of pre- and post-op dentofacial deformity volumes can be explained by a collection of rigidly movable pieces of the mandible and the maxilla. The disentanglement of the deformable registration into piecewise rigid transformations regarding underlying hard pieces relaxes the supervision of dense voxel-wise correspondence with sparse annotation of binary masks of movable pieces. We design a novel piecewise rigid transformation constraint to enforce the semantic and meaningful correspondence of maxillofacial structures, avoiding bony structural distortion. The interpretable voxel-wise displacement fields account for morphology variations caused by orthognathic surgery and enable the prediction of the post-op craniofacial shapes. The experimental results showcase the effectiveness of the proposed approach on the clinically obtained cone-beam computed tomography dataset with dentofacial deformity.