Image Segmentation Models Based On Partial Differential Equation And Fast Algorithm Design

Image segmentation is the basis of digital image processing.Partial differential equation models of image segmentation have advantages that traditional image segmentation models and deep learning-based image segmentation models do not have.With the deepening of image segmentation in actual production and life,how to improve the accuracy and real-time performance of image segmentation has become a research hotspot in recent years.This dissertation studies the accuracy and speed of image segmentation of partial differential equations from two aspects: model and algorithm.The main tasks are:(1)we put forward an idea of indirect diffusion and further develope an indirect diffusion-based level set model for image segmentation.This model is based on the dynamic process of diffusion that is posed indirectly on level set function by way of auxiliary function,coupled with a transition region-based force that exhibits the desired sign-changing property.It is formulated as a coupled system of two evolution equations,in which the first equation drives the motion of zero level set toward the object edges and makes it possible to set a termination criterion on the algorithm,while the second equation(indirect diffusion)smoothens the auxiliary function and keeps the auxiliary function as close to the level set function as possible.The derived model can effectively be solved purely by the simplest explicit finite difference.Experimental results show that the pro-posed model not only has the strong capability of noise immunity,but it also can much better conduce to extraction of deeply concave edges and preservation of sharp corners,compared with the direct diffusion-based counterpart.(2)Variational method and gradient descent flow are usually used to minimize the energy functional of evolution curve in active contour model based on variational level set methods.The gradient descent method has poor convergence and is sensitive to local minimum.An improved Nesterov's Accelerated Gradient(NAG)algorithm is proposed to replace the gradient descent algorithm in the distant regularized level set evolution(DRLSE)model,and then obtains a fast image segmentation algorithm based on NAGalgorithm.Experimental results show that the proposed algorithm is simple and can effectively improve segmentation speed of DRLSE model,which can be applied to segment infrared images and medical images stricted with real-time requirements.