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Estimating Volumes of Near-spherical Molded Artifacts



David E. Gilsinn, Bruce R. Borchardt, Amelia Tebbe


The Food and Drug Administration (FDA) is conducting research on developing reference lung cancer cancer lesions, called phantoms, to test computed tomography (CT) scanners and their software. FDA loaned two semi-spherical phantoms to the National Institute of Standards and Technology (NIST), called Green and Pink, and asked to have the phantoms' volumes estimated. This report describes in detail both the metrology and computational methods used to estimate the phantoms' volumes. Three sets of CMM measured data were produced. One set of data involved reference surface data measurements of a known calibrated metal sphere. The other two sets were measurements of the two FDA phantoms at two densities, called the coarse set and the dense set. Two computational approaches were applied to the data. In the first approach spherical models were fit to the calibrated sphere data and to the phantom data. The second approach was to model the data points on the boundaries of the spheres with surface B-splines and then use the Divergence Theorem to estimate the volumes. Fitting a spherical model to the calibrated sphere data was done as a reference check on the algorithm performance. It gave assurance that the volumes estimated for the phantoms would be meaningful. The results for the coarse and dense data sets tended to predict the volumes as expected and the results did show that the Green phantom was very near spherical. This was confirmed by both computational methods. The spherical model did not fit the Pink phantom as well and the B-spline approach provided a better estimate of the volume in that case.
Journal of Research (NIST JRES) -


B-splines, computed tomography, coordinate measuring machine, divergence theorem, lung cancer, lung cancer phantoms, nonlinear least squares


Gilsinn, D. , Borchardt, B. and Tebbe, A. (2010), Estimating Volumes of Near-spherical Molded Artifacts, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed May 25, 2024)


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Created May 3, 2010, Updated February 19, 2017