Snakes and splines for tracking non-rigid heart motion

Abstract

MRI is unique in its ability to non-invasively and selectively alter tissue magnetization, and create tagged patterns within a deforming body such as the heart muscle. The resulting patterns (radial or SPAMM patterns) define a time-varying curvilinear coordinate system on the tissue, which we track with B-snakes and coupled B-snake grids. The B-snakes are optimized by a dynamic programming algorithm operating on B-spline control points in discrete pixel space. Coupled B-snake optimization based on an extension of dynamic programming to two dimensions, and gradient descent are proposed. Novel spline warps are also proposed which can warp an area in the plane such that two embedded snake grids obtained from two SPAMM frames are brought into registration, interpolating a dense displacement vector field. The reconstructed vector field adheres to the known displacement information at the intersections, forces corresponding snakes to be warped into one another, and for all other points in the plane, where no information is available, a second order continuous vector field is interpolated.