  The premorbid geometry of the mandible is of significant relevance in jaw
reconstructive surgeries and occasionally unknown to the surgical team. In this
paper, an optimization framework is introduced to train deep models for
completion (reconstruction) of the missing segments of the bone based on the
remaining healthy structure. To leverage the contextual information of the
surroundings of the dissected region, the voxel-weighted Dice loss is
introduced. To address the non-deterministic nature of the shape completion
problem, we leverage a weighted multi-target probabilistic solution which is an
extension to the conditional variational autoencoder (CVAE). This approach
considers multiple targets as acceptable reconstructions, each weighted
according to their conformity with the original shape. We quantify the
performance gain of the proposed method against similar algorithms, including
CVAE, where we report statistically significant improvements in both
deterministic and probabilistic paradigms. The probabilistic model is also
evaluated on its ability to generate anatomically relevant variations for the
missing bone. As a unique aspect of this work, the model is tested on real
surgical cases where the clinical relevancy of its reconstructions and their
compliance with surgeon's virtual plan are demonstrated as necessary steps
towards clinical adoption.
