Regularization in a neural model of motion perception

Neurons in sensory systems encode and transmit information about attributes of the environment. Much of the information transmitted by spiking neurons appears to be encoded in the rate at which they fire. This rate necessarily has a positive value. In this paper, the implication of this constraint for models of motion detection is examined. The detection of image motion is represented mathematically as a quadratic programming problem in which variables used to represent image speed are restricted to positive values. This novel representation requires that additional constraints are introduced to stabilize motion computations because quadratic programming problems require a surplus of unknowns to code for image speed. Two further constraints are introduced into the model to take into account possible cases of image degeneracy. They are based upon (i) an a priori preference for small image speeds, and (ii) the assumption that image motion parallel to contours of constant intensity for a one-dimensional signal is zero. The latter assumption is shown to account for perceived biases in speed reported for type I plaid patterns [Castet, E. & Morgan, M. (1996). Apparent speed of type-I symmetrical plaids. Vision Research 36, 223-32]. The model suggests that the visual system uses separate constraints to stabilize motion computations. One set of constraints arises from the nature of the motion detection process itself, while another two constraints take into account possible cases of degeneracy where image contrast is low or near zero and where the image function is one-dimensional and the aperture problem prevails.