Adaptive reconstruction of bone geometry from serial cross-sections

Abstract

Many biomedical applications, such as the design of customized orthopaedic implants, require accurate mathematical models of bone geometry. The surface geometry is often generated by fitting closed parametric curves, or contours, to the edge points extracted from a sequence of evenly spaced planar images acquired using computed tomography (CT), magnetic resonance imaging (MRI), or ultrasound imaging. The Bernstein basis function (BBF) network described in this paper is a novel neural network approach to performing functional approximation tasks such as curve and surface fitting. In essence, the BBF architecture is a two-layer basis function network that performs a weighted summation of nonlinear Bernstein polynomials. The weight values generated during network training are equivalent to the control points needed to create a smooth closed Bézier curve in a variety of commercially available computer-aided design software. Modifying the number of basis neurons in the architecture is equivalent to changing the degree of the Bernstein polynomials. An increase in the number of neurons will improve the curve fit, however, too many neurons will diminish the network's ability to generate a smooth approximation of the cross-sectional boundary data. Additional constraints are imposed on the learning algorithm in order to ensure positional and tangential continuity for the closed curve. A simulation study and real world experiment are presented to show the effectiveness of this functional approximation method for reverse engineering bone structures from serial medical imagery.