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首页> 外文期刊>Physics in medicine and biology. >APPLICATION OF A NEW DISCREET FORM OF GAUSS THEOREM FOR MEASURING VOLUME
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APPLICATION OF A NEW DISCREET FORM OF GAUSS THEOREM FOR MEASURING VOLUME

机译：高斯定理的新离散形式在体积测量中的应用

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摘要

Volume measurements are useful in many branches of science and medicine. They are usually accomplished by acquiring a sequence of cross sectional images through the object using an appropriate scanning modality, for example x-ray computed tomography (CT), magnetic resonance (MR) or ultrasound (US). In the cases of CT and MR, a dividing cubes algorithm can be used to describe the surface as a triangle mesh. However, such algorithms are not suitable for US data, especially when the image sequence is multiplanar (as it usually is). This problem may be overcome by manually tracing regions of interest (ROIs) on the registered multiplanar images and connecting the points into a trianglar mesh. In this paper we describe and evaluate a new discreet form of Gauss' theorem which enables the calculation of the volume of any enclosed surface described by a triangular mesh. The volume is calculated by summing the vector product of the centroid, area and normal of each surface triangle. The algorithm was tested on computer-generated objects, US-scanned balloons, livers and kidneys and CT-scanned clay rocks. The results, expressed as the mean percentage difference +/- one standard deviation were 1.2 +/- 2.3, 5.5 +/- 4.7, 3.0 +/- 3.2 and -1.2 +/- 3.2% for balloons, livers, kidneys and rocks respectively. The results compare favourably with other volume estimation methods such as planimetry and tetrahedral decomposition. [References: 18]
机译：体积测量在科学和医学的许多分支中都是有用的。通常通过使用适当的扫描方式（例如X射线计算机断层扫描（CT），磁共振（MR）或超声（US））获取通过物体的一系列横截面图像来实现。在CT和MR的情况下，可以使用除法算法将曲面描述为三角形网格。但是，此类算法不适用于美国数据，尤其是当图像序列是多平面的（通常如此）时。通过手动跟踪已注册的多平面图像上的感兴趣区域（ROI）并将这些点连接到三角形网格中，可以解决此问题。在本文中，我们描述并评估了高斯定理的一种新的离散形式，它可以计算由三角形网格描述的任何封闭表面的体积。通过将每个曲面三角形的质心，面积和法线的矢量积相加来计算体积。该算法已在计算机生成的物体，美国扫描的气球，肝脏和肾脏以及CT扫描的粘土岩石上进行了测试。结果表示为气球，肝脏，肾脏和岩石的平均百分比差+/-一个标准偏差分别为1.2 +/- 2.3、5.5 +/- 4.7、3.0 +/- 3.2和-1.2 +/- 3.2％ 。结果与其他体积估计方法（如平面法和四面体分解）相比具有优势。 [参考：18]

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