Image Segmentation with Traveling Waves in an Exactly Solvable Recurrent Neural Network

We study image segmentation using spatiotemporal dynamics in a recurrent neural network where the state of each unit is given by a complex number. We show that this network generates sophisticated spatiotemporal dynamics that can effectively divide an image into groups according to a scene's structural characteristics. We then demonstrate a simple algorithm for object segmentation that generalizes across inputs ranging from simple geometric objects in grayscale images to natural images. Using an exact solution of the recurrent network's dynamics, we present a precise description of the mechanism underlying object segmentation in the network dynamics, providing a clear mathematical interpretation of how the algorithm performs this task. Object segmentation across all images is accomplished with one recurrent neural network that has a single, fixed set of weights. This demonstrates the expressive potential of recurrent neural networks when constructed using a mathematical approach that brings together their structure, dynamics, and computation.