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Med Phys. 1994 Jun;21(6):741-52.

Evaluation of new algorithms for the interactive measurement of surface area and volume.

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  • 1Department of Radiology, University of Texas Health Science Center at San Antonio 78284-6240.


The maximum unit normal component (MUNC) method used for surface area measurement and the divergence theorem algorithm (DTA) used for volume measurement were evaluated. The accuracy and precision of these methods were investigated at varying signal-to-noise ratios (SNRs), sampling, spatial averaging, and orientation. The accuracy of the MUNC measured surface area, as indicated by the mean error, was 2.0% for seven spherical samples, with SNRs ranging from 5:1 to 39:1. The precision, as indicated by the percent coefficient of variation (% CV) for these samples, was less than 3.0%. Likewise, the accuracy and precision of the DTA measured volume for these samples were both less than 1.0%. MUNC surface area measurement from 23 samples of a computed tomography (CT) image of a wooden sphere (51.44-mm diameter) with x,y voxel size ranging from 1 to 10 mm and z voxel size ranging from 2 to 14 mm yielded an accuracy of 1.3% and a precision of 2.2%. The DTA volume measurements from 18 samples of the wooden sphere with x,y vowel size ranging from 1 to 8 mm and z size ranging from 2 to 14 mm provided an accuracy of 1.2% and a precision of 1.8%. Measurement of surface area for a cylindrical rod scanned by CT in five different orientations, ranging from along each axis to between all three axes, yielded an accuracy of 3.7% and a precision of 2.0%. The volume of the cylindrical rod measured by the DTA method for these orientations produced an accuracy of 4.0% and a precision of 3.7%. The volume measured by DTA compared well with the volume measured by a modified voxel counting method. The MUNC surface area method was superior to counting surface voxels. The accuracy and precision for five interactive surface area and volume measurements, using paired cut planes to select subsets of a computer-generated sphere with radius 25 pixels, were both less than 1.0%.

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