Image Segmentation Model Of Partial Differential Equation On Graph

In recent years,many researchers have studied partial differential equations on the graph in many aspects,and have been widely used in image processing.In this paper,the?-heat equation with discrete Sobolev gradient flow has similar properties to the solution of the?-heat equation,such as the average value,maximum principal,asymptotic behaviour and so on.Then,the numerical simulation was carried out on a specific graph.Through numerical experiments,it was found that when the weight parameter? increased,the time step?t could also select a larger value and maintain the stability of the numerical algorithm.In this way,the solution of the ?-heat equation with discrete Sobolev gradient flow had faster convergence speed and calculation time.Finally,numerical experiments were carried out on the existing image segmentation algorithm based on Sobolev gradient flow.When the weight parameter? is set to 2 and the parameter ? and the time step?t both increased,the number of iterations decreased significantly and the extraction effect of significant features remained unchanged.The main content of this article is arranged as follows:The first chapter briefly introduces the background and development status of image segmentation models,and summarizes the main content of this article.The second chapter briefly introduces the basic concepts of calculus on the graph and the lemma required for its proof.The third chapter proves the properties of the?-heat equation solution with discrete Sobolev gradient flow based on the principle of maximum value and gradient descent,and compares the properties of the solution with the?-heat equation.Numerical simulations were performed.The fourth chapter briefly describes the variational model in this paper,and detects the target image.According to the experimental results,it is concluded that the model in this paper can get the target more quickly and significantly reduce the number of iterations.The fifth chapter summarizes the research content of this article.