Shape normalization of 3D cell nuclei using elastic spherical mapping

Topological analysis of cells and subcellular structures on the basis of image data, is one of the major trends in modern quantitative biology. However, due to the dynamic nature of cell biology, the optical appearance of different cells or even time-series of the same cell is undergoing substantial variations in shape and texture, which makes a comparison of shapes and distances across different cells a nontrivial task. In the absence of canonical invariances, a natural approach to the normalization of cells consists of spherical mapping, enabling the analysis of targeted regions in terms of canonical spherical coordinates, that is, radial distances and angles. In this work, we present a physically-based approach to spherical mapping, which has been applied for topological analysis of multichannel confocal laser scanning microscopy images of human fibroblast nuclei. Our experimental results demonstrate that spherical mapping of entire nuclear domains can automatically be obtained by inverting affine and elastic transformations, performed on a spherical finite element template mesh.