A Multiscale Approach to the Representation of 3d Images, With Application to Polymer Solar Cells

Abstract

A multiscale approach to the description of geometrically complex 3D image data is proposed which distinguishes between morphological features on a 'macro-scale' and a 'micro-scale'. Since our method is mainly tailored to nanostructures observed in composite materials consisting of two different phases, an appropriate binarization of grayscale images is required first. Then, a morphological smoothing is applied to extract the structural information from binarized image data on the 'macro-scale'. A stochastic algorithm is developed for the morphologically smoothed images whose goal is to find a suitable representation of the macro-scale structure by unions of overlapping spheres. Such representations can be interpreted as marked point patterns. They lead to an enormous reduction of data and allow the application of well-known tools from point-process theory for their analysis and structural modeling. All those voxels which have been 'misspecified' by the morphological smoothing and subsequent representation by unions of overlapping spheres are interpreted as 'micro-scale' structure. The exemplary data sets considered in this paper are 3D grayscale images of photoactive layers in hybrid solar cells gained by electron tomography. These composite materials consist of two phases: a polymer phase and a zinc oxide phase. The macro-scale structure of the latter is represented by unions of overlapping spheres.

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