Virtual Multiple-Fracture Mandibular Reconstruction
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From a surgical perspective, the craniofacial reconstruction problem assumes even greater complexity when faced with multiple fractures since the operating surgeon has to identify the opposable fracture surfaces before physically registering them. Very often, the cost of surgery becomes prohibitive with the increased operative time necessary to complete the entire reconstruction process. Moreover, the increased operative time also poses increased operative trauma and an increased risk of postoperative complications to the patient. In this chapter, the problem of virtual craniofacial reconstruction in the presence of multiple fractures is shown to resemble that of automated assembly of a 3D jigsaw puzzle and to have a worst-case exponential-time complexity when formulated as the Traveling Salesperson Problem (TSP). In an alternative formulation, the problem of virtual craniofacial reconstruction is modeled as one of maximum-weight graph matching which, in contrast, is shown to have a polynomial-time complexity in the worst case. The surface matching algorithms described in the previous chapter are used to achieve pairwise registration of the fracture surfaces. The global shape of the mandible is monitored at the end of each pairwise surface registration step by computing the Tanimoto coefficient between the partially reconstructed mandible and an intact reference mandible.
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