Separating figure from ground with a parallel network

The differentiation of figure from ground plays an important role in the perceptual organization of visual stimuli. The rapidity with which we can discriminate the inside from the outside of a figure suggests that at least this step in the process may be performed in visual cortex by a large number of neurons in several different areas working together in parallel. We have attempted to simulate this collective computation by designing a network of simple processing units that receives two types of information: bottom-up input from the image containing the outlines of a figure, which may be incomplete, and a top-down attentional input that biases one part of the image to be the inside of the figure. No presegmentation of the image was assumed. Two methods for performing the computation were explored: gradient descent, which seeks locally optimal states, and simulated annealing, which attempts to find globally optimal states by introducing noise into the computation. For complete outlines, gradient descent was faster, but the range of input parameters leading to successful performance was very narrow. In contrast, simulated annealing was more robust: it worked over a wider range of attention parameters and a wider range of outlines, including incomplete ones. Our network model is too simplified to serve as a model of human performance, but it does demonstrate that one global property of outlines can be computed through local interactions in a parallel network. Some features of the model, such as the role of noise in escaping from nonglobal optima, may generalize to more realistic models.