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WISH: efficient 3D biological shape classification through Willmore flow and Spherical Harmonics decomposition

Marco Agus, Enrico Gobbetti, Giovanni Pintore, Corrado Calì, and Jens Schneider

June 2020

Abstract

Shape analysis of cell nuclei, enabled by the recent advances in nano-scale digital imaging and reconstruction methods, is emerging as a very important tool to understand low-level biological processes. Current analysis techniques, however, are performed on 2D slices or assume very simple 3D shape approximations , limiting their discrimination capabilities. In this work, we introduce a compact rotation-invariant frequency-based representation of genus-0 3D shapes represented by manifold triangle meshes, that we apply to cell nuclei envelopes reconstructed from electron micrographs. The representation is robustly obtained through Spherical Harmonics coefficients over a spherical parame- terization of the input mesh obtained through Willmore flow. Our results show how our method significantly improves the state-of-the-art in the classification of nuclear envelopes of rodent brain samples. Moreover, while our method is motivated by the analysis of specific biological shapes, the framework is of general use for the compact frequency encoding of any genus-0 surface.

Reference and download information

Marco Agus, Enrico Gobbetti, Giovanni Pintore, Corrado Calì, and Jens Schneider. WISH: efficient 3D biological shape classification through Willmore flow and Spherical Harmonics decomposition. In Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW). Pages 4184-4194, June 2020. DOI: 10.1109/CVPRW50498.2020.00494.

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Bibtex citation record

@inproceedings{Agus:2020:WE3,
    author = {Marco Agus and Enrico Gobbetti and Giovanni Pintore and Corrado Cal\`i and Jens Schneider},
    title = {{WISH}: efficient {3D} biological shape classification through {Willmore} flow and {Spherical Harmonics} decomposition},
    booktitle = {Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)},
    pages = {4184--4194},
    month = {June},
    year = {2020},
    abstract = { Shape analysis of cell nuclei, enabled by the recent advances in nano-scale digital imaging and reconstruction methods, is emerging as a very important tool to understand low-level biological processes. Current analysis techniques, however, are performed on 2D slices or assume very simple 3D shape approximations , limiting their discrimination capabilities. In this work, we introduce a compact rotation-invariant frequency-based representation of genus-0 3D shapes represented by manifold triangle meshes, that we apply to cell nuclei envelopes reconstructed from electron micrographs. The representation is robustly obtained through Spherical Harmonics coefficients over a spherical parame- terization of the input mesh obtained through Willmore flow. Our results show how our method significantly improves the state-of-the-art in the classification of nuclear envelopes of rodent brain samples. Moreover, while our method is motivated by the analysis of specific biological shapes, the framework is of general use for the compact frequency encoding of any genus-0 surface. },
    doi = {10.1109/CVPRW50498.2020.00494},
    url = {http://vic.crs4.it/vic/cgi-bin/bib-page.cgi?id='Agus:2020:WE3'},
}