The Butterfly Effect in Primary Visual Cortex

Exploring and establishing artificial neural networks with electrophysiological characteristics and high computational efficiency is a popular topic that has been explored for many years in the fields of pattern recognition and computer vision. Inspired by the working mechanism of the primary visual cortex, pulse-coupled neural networks (PCNNs) can exhibit the characteristics of synchronous oscillation, refractory period, and exponential decay. These characteristics empower the PCNN model to group pixels with similar spatiality and gray values and to process digital images without training. However, electrophysiological evidence shows that the neurons exhibit highly complex nonlinear dynamics when stimulated by external periodic signals. This chaos phenomenon, also known as the ‘butterfly effect,” cannot be explained by all PCNN models. In this work, we analyze the main obstacle preventing PCNN models from imitating a real primary visual cortex. We consider neuronal excitation as a stochastic process. We then propose a novel neural network of the primary visual cortex, called a continuous-coupled neural network (CCNN). Theoretical analysis indicates that the dynamic behavior of the CCNN is distinct from the PCNN. Numerical results show that the CCNN model exhibits periodic behavior under a DC stimulus, and exhibits chaotic behavior under an AC stimulus, which is consistent with the testing results of primary visual cortex neurons. Furthermore, the image and video processing mechanisms of the CCNN model are analyzed. For image processing tasks, this model encodes the pixel intensity as the frequency of output signals so that it can group pixels with similar gray values. This image processing method can reduce the local gray level difference of the image, and compensate for small local discontinuities in the image. For video processing tasks, the CCNN encodes changing pixels as non-periodic chaotic signals, and it encodes static pixels as periodic signals. It thus achieves the purpose of moving target object recognition by distinguishing the dynamic states corresponding to different neuron clusters in the video. Experimental results on image segmentation indicate that the CCNN model has better performance than the state-of-the-art of visual cortex neural network models.