Convergence of map seeking circuits
The map-seeking circuit (MSC) is an explicit biologically-motivated computational mechanism which provides practical solution of problems in object recognition, image registration and stabilization, limb inverse-kinematics and other inverse problems which involve transformation discovery. We formulate this algorithm as discrete dynamical system on a set Delta = Pi(L)(l=1)Delta((l)), where each Delta((l)) is a compact subset of a nonnegative orthant of R-n, and show that for an open and dense set of initial conditions in Delta the corresponding solutions converge to either a vector with unique nonzero element in each Delta((l)) or to a zero vector. The first result implies that the circuit finds a unique best mapping which relates reference pattern to a target pattern; the second result is interpreted as "no match found". These results verify numerically observed behavior in numerous practical applications.
map seeking circuits dynamical systems computer vision lyapunov function