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 necessaril y has a positive value. In this paper, the implication of this constraint f or models of motion detection is examined. The detection of image motion is represented mathematically as a quadratic programming problem in which var iables used to represent image speed are restricted to positive values. Thi s novel representation requires that additional constraints are introduced to stabilize motion computations because quadratic programming problems req uire 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 assumpt ion is shown to account for perceived biases in speed reported for type I p laid patterns [Castet, E. & Morgan, M. (1996). Apparent speed of type-I sym metrical plaids. Vision Research 36, 223-32]. The model suggests that the v isual system uses separate constraints to stabilize motion computations. On e 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 fun ction is one-dimensional and the aperture problem prevails. (C) 2001 Elsevi er Science Ltd. All rights reserved.