| This thesis presents a cost and time effective computational method for generating a three-dimensional bone shape from multiple x-ray images. Starting with a predefined three-dimensional template bone shape, whose shape is clinically normal and scaled to an average size, our method scales, and deforms the template shape until the deformed shape gives an image similar to an input x-ray image when projected onto a two-dimensional plane. We use hierarchical free form deformation to scale and deform the template bone, and a deformation in each deformation layer is controlled by eight variables. The problem of finding the three-dimensional shape of the bone is thus reduced to a sequence of optimization problems with eight design variables; our objective is to minimize the error, or the difference between the input x-ray image and the projected image of the deformed template shape. We use sequential quadratic programming (SQP) to solve this multidimensional optimization problem. The proposed x-ray image based shape reconstruction is more computationally efficient, cost effective, and portable compared to standard three-dimensional sensor based methods, such as computerized tomography (CT) and magnetic resonance imaging (MRI). Although the final three-dimensional shape of our method can be less accurate than using CT and MRI, because of our minimum input of x-ray images, our method creates a three-dimensional shape accurate enough for many applications such as: (1) making a three-dimensional physical mockup for training, and (2) importing into and using in a computer aided planning system for orthopedic surgery, including bone distraction and open/closed wedge osteotomy. |
