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In order to optimize the acoustic properties of a stacked fiber nonwoven, the microstructure of the non-woven is modeled by a macroscopically homogeneous random system of straight cylinders (tubes). That is, the fibers are modeled by a spatially stationary random system of lines (Poisson line process), dilated by a sphere. Pressing the non-woven causes anisotropy. In our model, this anisotropy is described by a one parametric distribution of the direction of the fibers. In the present application, the anisotropy parameter has to be estimated from 2d reflected light microscopic images of microsections of the non-woven.After fitting the model, the flow is computed in digitized realizations of the stochastic geometric model using the lattice Boltzmann method. Based on the flow resistivity, the formulas of Delany and Bazley predict the frequency-dependent acoustic absorption of the non-woven in the impedance tube.Using the geometric model, the description of a non-woven with improved acoustic absorption properties is obtained in the following way: First, the fiber thicknesses, porosity and anisotropy of the fiber system are modified. Then the flow and acoustics simulations are performed in the new sample. These two steps are repeatedc for various sets of parameters. Finally, the set of parameters for the geometric model leading to the best acoustic absorption is chosen.

SummaryNanoporous materials play an important role in modern batteries as well as fuel cells. The materials microstructure needs to be analyzed as it determines the electrochemical properties. However, the microstructure is too fine to be resolved by microcomputed tomography. The method of choice to analyze the microstructure is focused ion beam nanotomography (FIB-SEM). However, the reconstruction of the porous 3D microstructure from FIB-SEM image data in general has been an unsolved problem so far. In this paper, we present a new method using morphological operations. First, features are extracted from the data. Subsequently, these features are combined to an initial segmentation, that is then refined by a constrained watershed transformation. We evaluate our method with synthetic data, generated by a simulation of the FIB-SEM imaging process. We compare the ground truth in the simulated data to the segmentation result. The new method is found to produce a much smaller error than existing techniques.

SummaryIn this paper, the field of quantitative microcomputed tomography arising from the combination of microcomputed tomography and quantitative 3D image analysis, is summarized with focus on materials science applications. Opportunities and limitations as well as typical application scenarios are discussed. Selected examples provide an insight into commonly used as well as recent methods from mathematical morphology and stochastic geometry.

SummaryWe studied the point processes of intramembranous particles of mitochondrial membranes from HeLa cells using the freeze fracture technique. Three groups -under normal conditions, after exposition with rotenone, and after exposition with sodium acid -were compared. First, we used several summary statistics in order to study the two-dimensional point patterns of intramembranous particles within each group. Then, we compared the patterns in different groups by bootstrap tests using the K -function and the nearest neighbour distance function G ( r ). Estimation of the G -function provided significant results but no significant differences between groups were found using the classical K -function; estimation of G ( r ) should therefore not be omitted when studying observed planar point patterns.

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This paper introduces methods for the detection of anisotropies which are caused by compression of regular 3D point patterns. Isotropy tests based on directional summary statistics and estimators for the compression factor are developed. Using simulated data, the dependence of the power of these methods on the intensity, the degree of regularity, and the compression strength is studied. Finally, our methods are applied to the point patterns of centers of air pores extracted from tomographic images of ice cores. This way the presence of anisotropies in the ice caused by the compression of the ice sheet and an increase of their strength with increasing depth are shown

Fibre reinforced composites constitute a relevant class of materials used chiefly in lightweight constructions for example in fuselages or car bodies. The spatial arrangement of the fibres and in particular their direction distribution have huge impact on macroscopic properties and, thus, its determination is an important topic of material characterisation. The fibre direction distribution is defined on the unit sphere, and it is therefore preferable to work with fully three-dimensional images of the microstructure as obtained, e.g., by computed micro-tomography. A number of recent image analysis algorithms exploit local grey value variations to estimate a preferred direction in each fibre point. Averaging these local results leads estimates of the volume-weighted fibre direction distribution. We show how the thus derived fibre direction distribution is related to quantities commonly used in engineering applications. Furthermore, we discuss four algorithms for local orientation analysis, namely those based on the response of anisotropic Gaussian filters, moments and axes of inertia derived from directed distance transforms, the structure tensor, or the Hessian matrix. Finally, the feasibility of these algorithms is demonstrated for application examples and some advantages and disadvantages of the underlying methods are pointed out.