Image Edge Detection Using FHN-CNN Model Based on Reaction-Diffusion Equations within a Dynamical Systems Framework

Abstract

With the advancement of imaging technology, images present diverse and highly complex characteristics, and the theory of dynamical systems has great potential in image processing due to its unique mathematical properties. Therefore, this study proposes an IPT based on the reaction-diffusion equation. This technique combines cellular neural networks with the reaction-diffusion equation within the framework of dynamical system theory. Specifically, by introducing the Laplacian operator, the membrane potential in the FitzHugh-Nagumo equation is correlated with the spatiotemporal dynamics of the recovery variable. A new type of image processing model is constructed by mapping to the dynamic evolution of locally coupled mesh cells in convolutional neural networks. The theoretical framework of the technology is further improved through the dynamic analysis of the Turing instability of the model and the gradient changes of the reaction-diffusion system. The results showed that in the performance testing of the research model, the Edge Preservation Index (EPI) was 0.89 and the Pratt's Figure of Merit (PFOM) was 0.95, which were higher than the comparison models, indicating excellent model performance. Meanwhile, the time cost for the new model to complete one detection was only 0.9 seconds, and there were only 2 iterations, which was significantly better than other models. Research has shown that the new model has higher computational efficiency and better real-time performance. This study provides new ideas and methods for image processing and helps to promote the development of image processing algorithms towards high efficiency and intelligence.