Surface area estimation of digitized 3D objects using weighted local configurations

We present a method for estimating surface area of three-dimensional objects in discrete binary images. A surface area weight is assigned to each 2×2×2 configuration of voxels. The total surface area of a digital object is given by a summation of the local area contributions. Optimal area weights are derived in order to provide an unbiased estimate with minimum variance for randomly oriented digitized planar surfaces. Due to co-appearance of certain voxel combinations, the optimal solution is not uniquely defined for planar surfaces. A Monte Carlo-based optimization of the estimator performance on the distribution of digitized balls of increasing radii is performed in order to uniquely determine the optimal surface area weights. The method is further evaluated on various objects in a range of sizes. A significant reduction of the error for small objects is observed. The algorithm is appealingly simple; the use of only a small local neighborhood enables efficient implementations in hardware and/or in parallel architectures.