Adaptive Morphological Framework for 3D Directional Filtering

Engineering materials often feature lower dimensional and directed structures such as cracks, fibers, or closedfacets in foams. The characterization of such structures in 3D is of particular interest in various applications inmaterials science. In image processing, knowledge of the local structure orientation can be used for structureenhancement, directional filtering, segmentation, or separation of interacting structures. The idea of usingbanks of directed structuring elements or filters parameterized by a discrete subset of the orientation space isproven to be effective for these tasks in 2D. However, this class of methods is prohibitive in 3D due to the highcomputational burden of filtering on a sufficiently fine discretization of the unit sphere.This paper introduces a method for 3D pixel-wise orientation estimation and directional filtering inspiredby the idea of adaptive refinement in discretized settings. Furthermore, an operator for distinction betweenisotropic and anisotropic structures is defined based on our method. This operator utilizes orientationinformation to successfully preserve structures with one or two dominant dimensions. Finally, feasibilityand effectiveness of the method are demonstrated on 3D micro-computed tomography images in three usecases: detection of a misaligned region in a fiber-reinforced material, crack detection in concrete, and facetdetection in partially closed foams.