Dynamical models

The remainder of the book aims to establish effective procedures for tracking curves in sequences of images. As with single images, the importance of powerful prior models of shape holds good, but now prior models can be extended to capitalise on the coherence of typical motions through a sequence. Crudely this could mean a repeated application of the regularised curve-fitting of chapter 6, in which the fitted curve in the k — 1th frame of a sequence is used as an initial estimate of curve position and shape for the kth frame. In the probabilistic context of chapter 8 this would involve applying, to each frame, a Gaussian prior distribution with fixed covariance but whose mean was simply the estimated shape from the previous frame. This immediately suggests a more subtle approach. Rather than fixing the form of the prior via one constant covariance for all frames, it seems more natural to take the posterior from frame k — 1 as the prior for frame k. In that way, it would not be merely an estimated shape that would pass from time-step to time-step but an entire probability distribution.