In this paper, we describe an efficient method for 3D image segmentation. The method uses a PDE model - the so called generalized subjective surface equation which is an equation of advection-diffusion type. The main goal is to develop an efficient and stable numerical method for solving this problem. The numerical solution is based on semi-implicit time discretization and flux-based level set finite volume space discretization. The space discretization is discussed in details and we introduce three possible alternatives of the so called diamond cell finite volume scheme for this type of 3D nonlinear diffusion equation. We test the performance of the method and all its variants introduced in the paper by determining the experimental order of convergence. Finally we show a couple of practical applications of the method.