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

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 parameterization 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.