A system-theoretical view on local motion estimation

The problem of estimating local motion in the presence of noise deserves a thorough system-theoretical analysis. In current textbooks, the predominant procedures are classified into differential (optical flow) approaches and matching (or correlation) methods. From a system-theoretical point of view, both classes can be interpreted as a set of linear filters followed by a simple nonlinear operation. However neither the definition of motion in terms of spatiotemporal gradients nor the minimization of loss functions on two subsequent image patches captures the full essence of what motion, means, ie, the preference direction of a spatiotemporal signal of reduced intrinsic dimensionality embedded in noise. We discuss the elements that influence the possible precision of local motion estimation methods, and describe estimation-theoretic approaches which subsume tradition methods, on one hand, and give perspectives for signal-dependent optimization, on the other hand.