Hierarchical contour matching in medical images

A hierarchical finite difference method to match analogous contours is presented. Our approach has been inspired by the method due to Duncan, who proposed a scheme for matching two contours based on the minimization of a quadratic fitting criterion. This criterion consists of a curvature dependent bending energy term and a smoothness term. Cohen improved this method by ensuring that the resulting displacement vectors actually map points belonging to the two contours. Building on this method, the innovation of our work is in the introduction of a number of modifications and extensions, which promise to considerably improve its already proven performance. First, a new smoothness term in the matching cost function has been derived, supported by a revealing analysis of the discretization process. As a result, the computational complexity is reduced and the equation corresponding to the minimization of the fitting criterion has a simple interpretation. To solve the resulting nonlinear system of equations, a new method is derived based on a two-step predictor-corrector scheme, for which we present a detailed analytical convergence analysis. Unlike previous algorithms, which relied on (semi-)implicit problem formulations, this explicit scheme has a clear advantage in terms of convergence rate. Finally, the algorithm is extended with a new multi-smoothing scheme which not only increases the convergence speed, but even more importantly, makes the method more robust and less dependent on a good initialization value to guarantee convergence to a global optimum. Experimental validation is carried out on three medical applications: (i) Matching of left ventricular contours in successive images of a time sequence of spin echo cardiac magnetic resonance (MR) images; (ii) matching of brain object contours in consecutive slices of a digital brain atlas; (iii) matching of brain object contours in segmented MR images to the outlines of the corresponding brain objects in a digital anatomical atlas.