Robust quasi-uniform surface meshing of neuronal morphology using line skeleton-based progressive convolution approximation - Zhu, Xiaoqiang; Liu, Xiaomei; Liu, Sihu; Shen, Yalan; You, Lihua; Wang, Yimin (Frontiers in Neuroinformatics, 2022)
Creating high-quality membrane surfaces of neural cell morphology for both visualization and numerical simulation is always a challenging task. In this paper, we developed a novel approach of reconstructing water-light 3D neural membrane surfaces from abstract point-and-diameter data. The membrane shapes of the neurons are reconstructed by progressively deforming an initial sphere, and it can be taken as a digital sculpting process. In the dynamic sculpting, the embedded skeleton with radii can serve as a guidance for surface mesh evolution. In order to efficiently deform the surface, a local mapping is adopted to simulate the animation skinning. Therefore, only the vertices within the ROI of the current skeletal position have to be updated. The actual region of influence (ROI) can be determined based on the adopted finite-support convolution kernel, which is convolved with the neural line skeleton to generate a potential field. The progressive convolution potential field guides the mesh evolution to smooth the overall surface regardless of the dendrites or the neural arborizations. On the other hand, the mesh quality during the whole evolution is always guaranteed by the quasi-uniform rules, which splits too long edges, collapses too short ones and moves the vertices within the tangent plane to get regular triangles. Finally, the vertices density on the iso-surface is adaptively distributed according to the neural radii and the surface curvatures.