Optimization by neural networks application of motion estimation

The authors´ purpose is to develop a method of estimation of the field of vectors velocity to evaluate motion in a sequence of images. This method is based on the application of a neural network to optical flow estimation. The network is discrete, deterministic and locally connected. It contains redundant neurons for representing w_{(i,j/x) and w}sub (i,j/y) the components of the velocity vector at point (i,j). The authors formulate the motion estimation problem as one of minimizing an error function of two terms. The first term is a least-squares penalty expression which coerce the flow field, the second, a smoothness constraint used for obtaining a smooth optical flow. The model consists of 4*L*M Hopfield sub-networks for an image of size L*M. Results provide a good coherence between the homogeneous area cartography of motion and textured regions present in the image. The authors used synthetic images and the algorithm was tested on echocardiographic images