Optical flow determination using topology preserving mappings

Determining the optical flow is an ill-posed problem, and requires the inclusion of a regularization term for solution. We show that ordered maps produced through self-organization reflect the topological relationships of the input, and can thus inherently supply the constraints required in obtaining the optical flow. Our computational procedure is thus based on training a self-organizing feature map with features from the first frame of an image sequence, and observing the displacement weights in the weights when, the network is subsequently trained with features drawn from the second frame. We show through four simulations (three single object, and one multiple object) that the weight displacements provide an accurate representation of the optical flow.