Network model of shape-from-shading: neural function arises from both receptive and projective fields.

It is not known how the visual system is organized to extract information about shape from the continuous gradations of light and dark found on shaded surfaces of three-dimensional objects. To investigate this question, we used a learning algorithm to construct a neural network model which determines surface curvatures from images of simple geometrical surfaces. The receptive fields developed by units in the network were surprisingly similar to the actual receptive fields of neurons observed in the visual cortex which are commonly believed to be 'edge' or 'bar' detectors, but have never previously been associated with shading. Thus, our study illustrates the difficulty of trying to deduce neuronal function solely from determination of their receptive fields. It is also important to consider the connections a neuron makes with other neurons in subsequent stages of processing, which we call its 'projective field'.