Hyperquadrics for shape analysis of 3D nanoscale reconstructions of brain cell nuclear envelopes

Shape analysis of cell nuclei is becoming increasingly important in biology and medicine. Recent results have identified that the significant variability in shape and size of nuclei has an important impact on many biological processes. Current analysis techniques involve automatic methods for detection and segmentation of histology and microscopy images, and are mostly performed in 2D. Methods for 3D shape analysis, made possible by emerging acquisition methods capable to provide nanometric-scale 3D reconstructions, are, however, still at an early stage, and often assume a simple spherical shape. We introduce here a framework for analyzing 3D nanoscale reconstructions of nuclei of brain cells (mostly neurons), obtained by semiautomatic segmentation of electron micrographs. Our method considers an implicit parametric representation customizing the hyperquadrics formulation of convex shapes. Point clouds of nuclear envelopes, extracted from image data, are fitted to our parametrized model, which is then used for performing statistical analysis and shape comparisons. We report on the preliminary analysis of a collection of 92 nuclei of brain cells obtained from a sample of the somatosensory cortex of a juvenile rat.