How to Analyze the Neurodynamic Characteristics of Pulse-Coupled Neural Networks? A Theoretical Analysis and Case Study of Intersecting Cortical Model

The intersecting cortical model (ICM), initially designed for image processing, is a special case of the biologically inspired pulse-coupled neural-network (PCNN) models. Although the ICM has been widely used, few studies concern the internal activities and firing conditions of the neuron, which may lead to an invalid model in the application. Furthermore, the lack of theoretical analysis has led to inappropriate parameter settings and consequent limitations on ICM applications. To address this deficiency, we first study the continuous firing condition of ICM neurons to determine the restrictions that exist between network parameters and the input signal. Second, we investigate the neuron pulse period to understand the neural firing mechanism. Third, we derive the relationship between the continuous firing condition and the neural pulse period, and the relationship can prove the validity of the continuous firing condition and the neural pulse period as well. A solid understanding of the neural firing mechanism is helpful in setting appropriate parameters and in providing a theoretical basis for widespread applications to use the ICM model effectively. Extensive experiments of numerical tests with a common image reveal the rationality of our theoretical results.