  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. Using an exact solution of the recurrent network's dynamics,
we present a precise description of the mechanism underlying object
segmentation in this network, providing a clear mathematical interpretation of
how the network performs this task. We then demonstrate a simple algorithm for
object segmentation that generalizes across inputs ranging from simple
geometric objects in grayscale images to natural images. 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.
