Shape analysis of 3D nanoscale reconstructions of brain cell nuclear envelopes by implicit and explicit parametric representations

Marco Agus, Maria Veloz Castillo, Javier F. Garnica Molina, Enrico Gobbetti, Heikki Lehväslaiho, Alex Morales Tapia, Pierre J. Magistretti, Markus Hadwiger, Corrado Cali

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Shape analysis of cell nuclei is becoming increasingly important in biology and medicine. Recent results have identified that large 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, but are mostly performed in 2D. Methods for 3D shape analysis, made possible by emerging acquisition methods capable to provide nanometric-scale 3D reconstructions, are 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 two parametric representations: the first one customizes the implicit hyperquadricsformulation and it is particularly suited for convex shapes, while the latter considers a spherical harmonics decomposition of the explicit radial representation. Point clouds of nuclear envelopes, extracted from image data, are fitted to the parameterized models which are then used for performing statistical analysis and shape comparisons. We report on the analysis of a collection of 121 nuclei of brain cells obtained from the somatosensory cortex of a juvenile rat.
Original languageEnglish (US)
Pages (from-to)100004
JournalComputers & Graphics: X
StatePublished - Jun 6 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): CRG grant no. 2313
Acknowledgements: This work was supported by the CRG grant no. 2313 from King Abdullah University of Science and Technology KAUST-EPFL Alliance for Integrative Modeling of Brain Energy Metabolism. We also acknowledge the contribution of Sardinian Regional Authorities under project VIGECLAB. We finally thank Helmut Pottmann (King Abdullah University of Science and Technology) for useful comments and suggestions.


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