APPLICATION OF A NEW DISCREET FORM OF GAUSS THEOREM FOR MEASURING VOLUME

Volume measurements are useful in many branches of science and medicin e. They are usually accomplished by acquiring a sequence of cross sect ional 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 algori thm can be used to describe the surface as a triangle mesh. However, s uch algorithms are not suitable for US data, especially when the image sequence is multiplanar (as it usually is). This problem may be overc ome by manually tracing regions of interest (ROIs) on the registered m ultiplanar images and connecting the points into a trianglar mesh. In this paper we describe and evaluate a new discreet form of Gauss' theo rem which enables the calculation of the volume of any enclosed surfac e described by a triangular mesh. The volume is calculated by summing the vector product of the centroid, area and normal of each surface tr iangle. The algorithm was tested on computer-generated objects, US-sca nned balloons, livers and kidneys and CT-scanned clay rocks. The resul ts, expressed as the mean percentage difference +/- one standard devia tion 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.