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.

翻译：我们研究了一种利用递归神经网络时空动力学进行图像分割的方法，其中每个单元的状态由复数表示。研究表明，该网络能产生复杂的时空动力学，可根据场景的结构特征有效将图像划分为不同组别。通过利用递归网络动力学的精确解，我们精确描述了该网络中物体分割机制的原理，为网络如何执行此任务提供了清晰的数学解释。随后，我们提出了一种简单的物体分割算法，该算法可泛化至从灰度图像中的简单几何物体到自然图像的各种输入。所有图像中的物体分割均由一个具有固定权重集的单一递归神经网络完成。这证明了当采用融合结构、动力学与计算的数学方法构建递归神经网络时，其具有强大的表达潜力。