Virtual orthognathic surgical planning involves simulating surgical corrections of jaw deformities on 3D facial bony shape models. Due to the lack of necessary guidance, the planning procedure is highly experience-dependent and the planning results are often suboptimal. A reference facial bony shape model representing normal anatomies can provide an objective guidance to improve planning accuracy. Therefore, we propose a self-supervised deep framework to automatically estimate reference facial

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... ony shape models. Our framework is an end-to-end trainable network, consisting of a simulator and a corrector. In the training stage, the simulator maps jaw deformities of a patient bone to a normal bone to generate a simulated deformed bone. The corrector then restores the simulated deformed bone back to normal. In the inference stage, the trained corrector is applied to generate a patient-specific normal-looking reference bone from a real deformed bone. The proposed framework was evaluated using a clinical dataset and compared with a state-of-the-art method that is based on a supervised point-cloud network. Experimental results show that the estimated shape models given by our approach are clinically acceptable and significantly more accurate than that of the competing method.