A reaction–diffusion based level set method for image segmentation in three dimensions

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.