The image segmentation of computed tomography data for three-dimensional biological structures remains challenging because of the limitations of existing numerical techniques and computer resources. The work represents the structures as the zero-level contour of a level set function whose value is constrained to a narrow band ranging. A cost functional composed of fitting energy for extracting the local intensity and diffusion energy for regularization is minimized within a framework of optimization. To avoid the re-initialization procedure and accelerate the convergence when updating the level set function, a reaction–diffusion technique is developed to replace the upwind algorithm by finite element analysis. Numerical examples demonstrate elegant biological structures with clear and smooth interfaces can be generated within a few iteration steps because the time step 100-fold larger than the allowable value of Courant–Friedrichs–Lewy stability condition can be applied in the proposed method.

由于现有数值技术和计算机资源的局限性，用于三维生物结构的计算机断层扫描数据的图像分割仍然具有挑战性。作品将结构表示为水平集函数的零水平轮廓，其值被限制在窄带范围内。在优化框架内，最小化由拟合能量（用于提取局部强度）和扩散能量（用于正则化）组成的成本函数。为了避免重新初始化过程并在更新水平集函数时加快收敛速度​​，开发了一种反应扩散技术，以有限元分析代替逆风算法。