Visual information processing in the brain goes from global to local. A large volume of experimental studies has suggested that among global features, the brain perceives the topological information of an image first. Here, we propose a neural network model to elucidate the underlying computational mechanism. The model consists of two parts. The first part is a neural network in which neurons are coupled through gap junctions, mimicking the neural circuit formed by alpha ganglion cells in the retina. Gap junction plays a key role in the model, which, on one hand, facilitates the synchronized firing of a neuron group covering a connected region of an image, and on the other hand, staggers the firing moments of different neuron groups covering disconnected regions of the image. These two properties endow the network with the capacity of detecting the connectivity and closure of images. The second part of the model is a read-out neuron, which reads out the topological information that has been converted into the number of synchronized firings in the retina network. Our model provides a simple yet effective mechanism for the neural system to detect the topological information of images in ultra-speed.

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