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In this contribution, we propose a novel approach to the segmentation of tomographic image data considering topological properties of binarized image components expressed in terms of the Minkowski Functionals in 3D. Electron tomography is a non-invasive method for three-dimensional (3D) reconstruction of cellular sub-structures from a series of projection images (i.e. from a tilt series) recorded with a transmission electron microscope. Data obtained by electron tomography provide a rich source of quantitative information concerning the structural composition and organization of cellular components. It allows to obtain 3D information on structural cellular arrangements at a significantly higher resolution than any other of the currently available imaging modalities. A major challenge, in this context, is the segmentation of the image data with respect to the identification macro-molecular structures such as the actin-cytoskeleton or cell organelles. We introduce a morphological filtering algorithm based on the Minkowski Functionals in 3D for segmentation of macromolecular structures in intact eukaryotic cells depicted by cryo-electron tomography. In mathematical topology, multi-dimensional convex objects can be characterized with respect to shape, structure, and the connectivity of their components using a set of morphological descriptors known as the Minkowski functionals. In a 3D-Euclidian space, these correspond to volume, surface area, mean integral curvature, and the Euler-Poincare characteristic. The morphological filtering procedure is applied to a 3D image data of an intact, ice-embedded Dictyostelium cell obtained by low dose transmission electron microscopy using a tilt series of -50° to +41.5° with an increment of 1.5°. Our method allows to separate cellular components with predefined textural properties, e.g. filamentary or globular structures, from the image data, which may then be studied and interpreted further.
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