自适应骨几何重建从连续横截面

George K. Knopf, Rasha Al-Naji
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引用次数: 24

摘要

许多生物医学应用,如定制骨科植入物的设计,需要精确的骨几何数学模型。表面几何形状通常是通过拟合闭合参数曲线或轮廓来生成的,这些曲线或轮廓是从计算机断层扫描(CT)、磁共振成像(MRI)或超声成像获得的一系列均匀间隔的平面图像中提取的边缘点。本文所描述的Bernstein基函数(BBF)网络是一种新的神经网络方法,用于执行函数逼近任务,如曲线和曲面拟合。本质上,BBF架构是一个两层基函数网络,执行非线性伯恩斯坦多项式的加权求和。在网络训练过程中产生的权值相当于在各种市售计算机辅助设计软件中创建光滑封闭bsamzier曲线所需的控制点。修改结构中基神经元的数量相当于改变Bernstein多项式的度。神经元数量的增加将改善曲线拟合,然而,过多的神经元将降低网络生成横截面边界数据的平滑近似的能力。为了保证闭合曲线的位置和切向连续性,对学习算法施加了额外的约束。仿真研究和现实世界的实验表明,该函数逼近方法的有效性,从序列医学图像逆向工程骨结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Adaptive reconstruction of bone geometry from serial cross-sections

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.

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