Robust quasi-uniform surface meshing of neuronal morphology using line skeleton-based progressive convolution approximation

Xiaoqiang Zhu; Xiaomei Liu; Sihu Liu; Yalan Shen; Lihua You; Yimin Wang

doi:10.3389/fninf.2022.953930

Robust quasi-uniform surface meshing of neuronal morphology using line skeleton-based progressive convolution approximation

Front Neuroinform. 2022 Oct 27:16:953930. doi: 10.3389/fninf.2022.953930. eCollection 2022.

Authors

Xiaoqiang Zhu¹, Xiaomei Liu¹, Sihu Liu¹, Yalan Shen^{2

3}, Lihua You⁴, Yimin Wang^{2

3}

Affiliations

¹ School of Communication and Information Engineering, Shanghai University, Shanghai, China.
² Guangdong Institute of Intelligence Science and Technology, Hengqin, China.
³ School of Computer Engineering and Science, Shanghai University, Shanghai, China.
⁴ National Center for Computer Animation, Bournemouth University, Bournemouth, United Kingdom.

Abstract

Creating high-quality polygonal meshes which represent the membrane surface of neurons for both visualization and numerical simulation purposes is an important yet nontrivial task, due to their irregular and complicated structures. In this paper, we develop a novel approach of constructing a watertight 3D mesh from the abstract point-and-diameter representation of the given neuronal morphology. The membrane shape of the neuron is reconstructed by progressively deforming an initial sphere with the guidance of the neuronal skeleton, which can be regarded as a digital sculpting process. To efficiently deform the surface, a local mapping is adopted to simulate the animation skinning. As a result, only the vertices within the region of influence (ROI) of the current skeletal position need to be updated. The ROI is determined based on the finite-support convolution kernel, which is convolved along the line skeleton of the neuron to generate a potential field that further smooths the overall surface at both unidirectional and bifurcating regions. Meanwhile, the mesh quality during the entire evolution is always guaranteed by a set of quasi-uniform rules, which split excessively long edges, collapse undersized ones, and adjust vertices within the tangent plane to produce regular triangles. Additionally, the local vertices density on the result mesh is decided by the radius and curvature of neurites to achieve adaptiveness.

Keywords: dynamic sculpting; finite-support convolution kernel; geometry-based techniques; local mapping query; multiresolution techniques; neuronal morphology; quasi-uniform mesh.