Fiber-based materials have an enormous industrial impact. This can be seen in the paper, apparel, and especially in filters, whose market is dominated by automotive applications. In all of these traditional materials cases, as well as emerging advanced materials, such as carbon fiber reinforced polymers (CFRP), the microstructure of the material profoundly impacts the macroscopic properties. By analyzing the microstructure, i.e. abundance, position, length, and orientation of the fibers, investigators can better understand material behavior and be better informed for material design optimization. We describe here our work to elucidate clear microstructural details on materials comprised of constant diameter, non-branching fibers.
Our approach begins by using a Rigaku nano3DX x-ray microscope to derive high-resolution 3D reconstructions of the fibrous materials. Because such materials are subject to fiber crowding and sometimes imaging artifacts that confound extraction of isolated fibers, we established an image processing routine in the Dragonfly data visualization platform that permits us to resolve and isolate individual fibers, which we describe below.
In a heavily cited work on contrast enhancement for vessel analysis in bioimaging, Frangi and coworkers describe an image filtering approach based on evaluating the Hessian--a square matrix of second-order partial derivatives--locally throughout the image to emphasize cylinder-shaped vessels. Local orientation of vessels can be assessed through the Eigenvalue analysis of the Hessian matrix. From this analysis, we derive three Eigenvalues--λ1, λ2, and λ3--which can be combined nonlinearly into three valuable structural descriptors, FiberScore, PlateScore, and BlobScore. The values of each score indicate the structure and how strong the local density is fiber-like, plate-like, or blob-like.
Here, we extend Frangi’s work to non-biological samples, where we apply our methods to track fibers (sometimes non-cylindrical) for the purpose of fiber identification, fiber separation, and fiber direction analysis. In addition to the descriptors FiberScore, PlateScore, and BlobScore, we evaluate new expressions with both the Eigenvalues and the Eigenvectors; the result is a new image that is strongly enhanced for fiber-like density. Additionally, these expressions are interpreted directly in an image segmentation routine which binarizes the fibers. Because the third Eigenvector provides fiber direction, we are able to use that quantity to resolve individual fibers in fiber clusters, which is one of the most challenging image interpretation problems with fiber image analysis.
Fiber contrast enhancement and individual fiber resolution were key to our successful microstructural analyses on multiple fibrous materials. These new filtering and segmentation tools, when combined with Dragonfly’s statistical analysis toolkit, enabled us to easily quantify fiber number, fiber direction, fiber length, and fiber radius, on complicated materials with complex fiber microstructure. Because these methods enable routine interpretation of fiber microstructure, they represent a valuable new tool for materials scientists involved in the material design and optimization for advanced materials.
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