Pde-based Study On Some Dynamical Behavior Of Neural Networks With Time Delays And Multiscale Method In Image Processing

Part 1:PDE-based Study on Some Dynamical Behavior of Reaction-diffusion Neural Networks with Time Delays:1. The author discussed the existence of the equilibrium point and its global exponential stability of reaction-diffusion recurrent neural networks with S-type distributed signal transmission delays by means of the topological degree theory and differential inequlity technique. The sufficient conditions on global exponential stability established, which are easily verifiable, have a wider adaptive range.2. Based on study of exponential stability of reaction-diffusion recurrent neural networks with S-type distributed signal transmission delays, the author made further developments on exponential stability of reaction-diffusion high-order recurrent neural networks with S-type distributed signal transmission delays, and obtained some new results.3. Some criteria for global stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters are presented. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality(LMI) approach is developed to establish some easy-to-test criteria of global exponential stability in the mean square for the stochastic neural networks.4. Stuied global stochastic exponential stability of the delayed reaction-diffusion high-order recurrent neural networks with Marovian jumping parameters and gave some new results which have not reported.Part 2:PDE-based Study on Multiscale Method in Image Processing:1. the author propose a novel method for the retinal vessel segmentation using multiscale hierarchical decomposition on the pixel's response image enhanced by matched filter (MF) with multiwavelet kernels. The MF with multiwavelet kernels (MFMK) are able to enhance vessels and edges, to relatively lower the noise, as well as to distinguish the vessels and non-vessel edges. The method is resilient to distracting artifacts like big bright lesions. So they are very good to preprocess an image. Then the noise removal and vessel extraction can be readily achieved by the multiscale hierarchical decomposition on the normalized MFMK response image. By gradually varying the scaling parameter of the multiscale, more and more blood vessels can be accumulatively segmented. A necessary condition of the optimal decomposition stopping time is presented to help us obtain the optimal retinal blood vessel segmentation. Finally, the binary vessel segmentation is obained by a locally adaptive method, which generates a threshold surface using accurate edge information created through MFMK and multiscale decomposition. Experimental results on two standard retinal databases are given and good performance is demonstrated in comparison with a few existing retinal vessel segmentation methods.2. The aim of this paper is to introduce a new type of multiscale model for cancer invasion by accounting the macroscopic dynamics of the densities of cancer cells and of the surrounding ECM that is taking place on a macroscopic domain whose boundary is permanently transformed and moved by a MMP-micro-dynamics developed on its microscopic-scale spatial-neighbouring bundle.