Adaptive Morphological Framework for 3D Directional Filtering

Abstract

Engineering materials often feature lower dimensional and directed structures such as cracks, fibers, or closed facets in foams. The characterization of such structures in 3D is of particular interest in various applications in materials science. In image processing, knowledge of the local structure orientation can be used for structure enhancement, directional filtering, segmentation, or separation of interacting structures. The idea of using banks of directed structuring elements or filters parameterized by a discrete subset of the orientation space is proven to be effective for these tasks in 2D. However, this class of methods is prohibitive in 3D due to the high computational 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 inspired by the idea of adaptive refinement in discretized settings. Furthermore, an operator for distinction between isotropic and anisotropic structures is defined based on our method. This operator utilizes orientation information to successfully preserve structures with one or two dominant dimensions. Finally, feasibility and effectiveness of the method are demonstrated on 3D micro-computed tomography images in three use cases: detection of a misaligned region in a fiber-reinforced polymer, segmentation of cracks in concrete, and separation of facets and strut system in partially closed foams.

Keywords

• adaptive directional filtering
• computed tomography
• crack detection
• filter banks
• local fiber orientation
• local surface normal orientation
• orientation estimation