Surface area estimation of digitized planes

A method for estimating surface area is developed for three-dimensional binary objects. This method is based on assigning surface area weights to the surface volume-elements (voxels) of a binary object. Surface voxels are defined as object voxels which are six-connected to one or more background voxels. Of the many types of surface voxel configurations, three basic types dominate the surface of relatively smooth, solid objects. These basic types are surface voxels with one, two or three adjacent sides exposed to the background. In planar regions, only these three types exist. By assigning weights to the various surface voxel configurations, total surface area can be estimated by summing the area contributed by all surface voxels of an object. Since this method estimates an object's true surface area, the weights selected should be optimized to give unbiased results with minimum mean-square-error. Formulae to calculate bias and mean-square-error are developed for this surface model when applied to randomly oriented and positioned planar regions. Optimal weights computed from these formulae for surface voxels with one, two or three adjacent sides are W1 ≈ 0.8940, W2 ≈ 1.3409 and W3 ≈ 1.5879, respectively, in sample-grid units squared, with a coefficient of variation (CV = σ/μ) of 2.33%. To address the feasibility for area estimation of curved surfaces, e.g. surfaces of objects extracted from biological or medical 3D images, this method is applied to binary spheres. Furthermore, previously published methods for estimating surface area are compared with the method presented.