Surface Volume Estimation of Digitized Hyperplanes Using Weighted Local Configurations

Abstract

Abstract. We present a method for estimating the surface volume of four-dimensional objects in discrete binary images. A surface volume weight is assigned to each 2 × 2 × 2 × 2 configuration of image elements. The total surface volume of a digital 4D object is given by a summation of the local volume contributions. Optimal volume weights are derived in order to provide an unbiased estimate with minimal variance for randomly oriented digitized planar hypersurfaces. Only 14 out of 64 possible boundary configurations appear on planar hypersurfaces. We use a marching hypercubes tetrahedrization to assign surface volume weights to the non-planar cases. The correctness of the method is verified on fourdimensional balls and cubes digitized in different sizes. The algorithm is appealingly simple; the use of only a local neighbourhood enables efficient implementations in hardware and/or in parallel architectures.