Image Segmentation with Complex Valued Kuramoto Models
Visualization of the phases of a network of locally coupled kuramoto oscillatos, driven by an input image (left), which converge in phase to segment the image into different shapes, with different oscillatory dynamics for each shape.
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 sophis- ticated 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.
Luisa Liboni, Roberto Budzinski, Alexandra Busch, Sindy Lowe, T. Anderson Keller, Max Welling, and Lyle E. Muller
Under Review
ArXiv Preprint: https://arxiv.org/pdf/2311.16943