Visual processing has often been divided into three stages—early, intermediate, and high level vision, which roughly correspond to the sensation, perception, and cognition of the visual world. In this paper, we present a network-based model of intermediate-level vision that focuses on how surfaces might be represented in visual cortex. We propose a mechanism for representing surfaces through the establishment of “ownership”—a selective binding of contours and regions. The representation of ownership provides a central locus for visual integration. Our simulations show the ability to segment real and illusory images in a manner consistent with human perception. In addition, through ownership, other processes such as depth, transparency, and surface completion can interact with one another to organize an image into a perceptual scene.