Statistical deformable bone models for robust 3D surface extrapolation from sparse data

A majority of pre-operative planning and navigational guidance during computer assisted orthopaedic surgery routinely uses three-dimensional models of patient anatomy. These models enhance the surgeon's capability to decrease the invasiveness of surgical procedures and increase their accuracy and safety. A common approach for this is to use computed tomography (CT) or magnetic resonance imaging (MRI). These have the disadvantages that they are expensive and/or induce radiation to the patient. In this paper we propose a novel method to construct a patient-specific three-dimensional model that provides an appropriate intra-operative visualization without the need for a pre or intra-operative imaging. The 3D model is reconstructed by fitting a statistical deformable model to minimal sparse 3D data consisting of digitized landmarks and surface points that are obtained intra-operatively. The statistical model is constructed using Principal Component Analysis from training objects. Our deformation scheme efficiently and accurately computes a Mahalanobis distance weighted least square fit of the deformable model to the 3D data. Relaxing the Mahalanobis distance term as additional points are incorporated enables our method to handle small and large sets of digitized points efficiently. Formalizing the problem as a linear equation system helps us to provide real-time updates to the surgeons. Incorporation of M-estimator based weighting of the digitized points enables us to effectively reject outliers and compute stable models. We present here our evaluation results using leave-one-out experiments and extended validation of our method on nine dry cadaver bones.