Zonohedral Approximation of Spherical Structuring Element for Volumetric Morphology

Performing dilation and erosion using large structuring elements can be computationally slow – a problem especially pronounced when processing volumetric data. To reduce the computational complexity of dilation/erosion using spherical structuring elements, we propose a method for approximating a sphere with a zonohedron. Since zonohedra can be created via successive dilations/erosions of line segments, this allows morphological operations to be performed in constant time per voxel. As the complexity of commonly used methods typically scales with the size of the structuring element, our method significantly improves the run time. We use the proposed approximation to detect large spherical objects in volumetric data. Results are compared with other image analysis frameworks demonstrating constant run time and significant performance gains.