Patient-specific three-dimensional (3-D) bone models are useful for a number of clinical applications such as surgery planning, postoperative evaluation, as well as implant and prosthesis design. Two-dimensional-to-3-D (2-D/3-D) reconstruction, also known as model-to-modality or atlas-based 2-D/3-D registration, provides a means of obtaining a 3-D model of a patient's bones from their 2-D radiographs when 3-D imaging modalities are not available. The preferred approach for estimating both shape and density information (that would be present in a patient's computed tomography data) for 2-D/3-D reconstruction makes use of digitally reconstructed radiographs and deformable models in an iterative, non-rigid, intensity-based approach. Based on a large number of state-of-the-art 2-D/3-D bone reconstruction methods, a unified mathematical formulation of the problem is proposed in a common conceptual framework, using unambiguous terminology. In addition, shortcomings, recent adaptations, and persisting challenges are discussed along with insights for future research.
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