Relationships between neural fields and computational algorithms

Abstract

The simulations in the last chapter demonstrated that the neural field dynamics organizes percepts that can be interpreted as solutions for different computational problems that are associated with motion perception. Examples are the solution of the motion correspondence problem, the smoothing of the perceived velocity field, or the temporal integration of motion information. In this chapter the relationship between the neural field dynamics and different computational approaches is analyzed in more detail. It will turn out that the neural field dynamics integrates different types of computations that are solved by separate algorithms in computer vision systems. For the derivation of the relationships between the field dynamics and computational methods it is crucial that a Lyapunov functional can be derived for homogeneous neural fields with symmetric interaction function. To give the reader some intuitive ideas about the meaning of Lyapunov functionals first a short introduction in Lyapunov functions for the discrete neural network dynamics is given.