Surface area estimation of digitized planes using weighted local configurations

Abstract

We describe a method for estimating surface area of three-dimensional binary objects. The method assigns a surface area weight to each 2x2x2 configuration of voxels. The total surface area is given by a summation of the local area contributions for a digital object. We derive optimal area weights, in order to get an unbiased estimate with minimum variance for randomly oriented planar surfaces. This gives a coefficient of variation (CV) of 1.40% for planar regions. To verify the results and to address the feasibility for area estimation of curved surfaces, the method is tested on convex and non-convex synthetic test objects of increasing size. The algorithm is appealingly simple and uses only a small local neighbourhood. This allows efficient implementations in hardware and/or in parallel architectures. © Springer-Verlag Berlin Heidelberg 2003.