On gray scale image measurements. II. Surface area and volume

We introduce methods for approximating area of a surface and volume of a region whose boundary is a closed surface where the data are taken from a 3-dimensional lattice of gray scale values. The methods require construction of unit normal vectors for the sampled surface points. The volume can be approximated by using these normal vectors in the divergence theorem from calculus. Two major advantages for this new method are that no geometric ordering of data points is required and that the algorithms are easily implemented. We compare the method to standard algorithms for measuring surface area and volume, using both artificially created data and actual data obtained from a computed tomography scanner.