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Abstract
Craniofacial fractures are very frequent in the present society, the major causes being gunshotwounds, motor vehicle accidents and sports related injuries. The surgical reconstructionis challenging because the surgeons have to accurately register the broken fragments withina limited amount of time. Detection of the fractures, the other integral component of anysurgical process, often becomes difficult because of the fracture pattern, intensity inhomogeneity,and noise.In this thesis we explore the reconstruction and detection of craniofacial fracturesusing computer vision. Within the broad class of craniofacial fractures, our emphasis is onmandibular fractures. A typical input for us is a sequence of Computed Tomography (CT)images of a fractured human mandible. In chapter 1, we discuss in detail the overall significanceof our work and the lay-out of this thesis. Chapter 2 is devoted to different aspectsof virtual single fracture reconstruction, including the use of bipartite graph matching forestablishment of correspondence in the Iterative Closest Point (ICP) algorithm, variousmeans of improving the registration error from the ICP algorithm, exploration of anatomicalsymmetry and biomechanical stability of the human mandible in the reconstruction process,etc. In Chapter 3, the problem of virtual multi-fracture reconstruction, which resembles theassembly of a 3D jigsaw puzzle, is shown to have an worst case exponential time complexity.The problem is modeled as one of maximum weight graph matching, which even in the worstcase, runs in polynomial time.Chapter 4 discusses the hairline/minor fracture detection and target pattern generationin a hierarchical Bayesian restoration framework. We use the Markov Random Field (MRF)-Maximum A Posteriori (MAP) approach of Geman and Geman and model the fracture as alocal stochastic degradation of an hypothetical intact mandible. The MAP estimate correspondsto the target pattern (reconstructed jaw) and the differences in intensity between theinput data and MAP estimate at specific pixel locations mark the occurrence of a fracture. InChapter 5, we apply traditional scale-space theory for corner detection, followed by Kalmanfilter within a Bayesian inference paradigm to identify well-displaced/major fracture points.Bayesian credible sets are constructed to establish a spatial consistency check among the2D corners/fracture points, already identified using the scale space theory. In chapter 6, afracture is modeled as a minimum cut in an appropriate weighted network. Ford-Fulkersonsalgorithm is employed to obtain the minimum cut and the magnitude of the flow is usedas an approximate estimate of the extent of the fracture. Chapter 7 summarizes our overallcontributions and discusses directions for future research.