Adaptive Morphological Framework for 3d Directional Filtering

Abstract

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.

Microstructural characterisation of 3D printed and injection‐moulded glass fibre‐reinforced polypropylene by image analysis, simulation and experimental methods

“…Here, we therefore follow the new strategy recently suggested by Barisin et al [ 27 ] based on adaptive morphology with line segments. That is, line segments are used as structuring elements for consecutive morphological openings.…”

“…The line segment granulometry suffers from the well‐known problems in discretising the 3D orientation space sufficiently finely if implemented naively. [ 14 ] Barisin's novel adaptive morphology framework [ 27 ] yields, however, a way out by restricting the searched orientations to a conic subset of the full orientation space centred about a roughly estimated preferred orientation. Within this cone, sampling the orientations very finely is affordable.…”

“…Barisin's method [ 27 ] needs the following inputs: The main orientation and the width of the orientation cone about it, the maximal half‐length of the line segments used as structuring elements and a parameter controlling fineness of the discretisation.…”

“…The main orientation is obtained from eigenvalue analysis of the Hessian matrix of second‐order grey value derivatives as described in Wirjadi et al, [ 14 ] with . Due to our goal, the half‐length parameter for the structuring element is large, in particular increased, compared to Barisin et al [ 27 ] The parameters controlling the fineness of discretisation and the width of the orientation cone are kept as suggested in Barisin et al [ 27 ] The latter two result in 368, 201 discrete orientations for the whole orientation space restricted to 7340 falling into the cone.…”

Mathematical morphology on directional data

“…Analysing fibre orientation and quantifying misalignment, for instance by directional filtering [37], may help to optimise the production process and to improve GFRP. We examine a µCT image of GFRP produced and imaged by the Leibniz Institute for Composite Materials (IVW) in Kaiserslautern (Germany) and discussed in [38].…”