Snakes and splines for tracking non-rigid heart motion

Measurement of 3D motion of myocardial material points from explicit B-surface reconstruction of tagged MRI data

“…B-splines are suitable for representing a variety of industrial and anatomical shapes [1,7,8]. The advantages of B-spline representations are: (1) They are smooth, continuous parametric curves which can represent open or closed curves.…”

“…Two remarks should be made regarding the sequence of control points: a) The number of control points is much fewer in number than a sampling of the curve a(u) on a pixel grid, and b) Pi rarely reside on the actual curve. To localize a tag line based on B-snakes, an external energy can be defined and optimized in order to locate feature points on individual image slices [1,10]. Given a spatial stack of m curves on m image slices, each represented by n control points, a matrix of control points is constructed as follows:…”

“…The approach of Guttman, Prince, and McVeigh [5] for analysis of radial tagged images is to use a graph-search technique that determines the optimal inner and outer boundaries of the myocardium as well as tag lines by finding points one after the other in a sequence, using initial search starting points on the determined LV boundaries. In Amini, Curwen, and Gore [1,2], tag lines are tracked with Dynamic Programming B-snakes and coupled B-snake grids. Spline warps then warp an area in the plane such that snake grids obtained from two SPAMM frames are brought into registration, interpolating a dense displacement vector field.…”

Dense 2D displacement reconstruction from SPAMM-MRI with constrained elastic splines: Implementation and validation

“…In [2], the method was further extended to that of constrained thin-plate reconstruction of the displacement field from points and lines based on a variational solution (for related work, also please see [11].) In this paper, we improve on the reconstruction paradigm in [2] and present extensive validation of the methodologies.…”

“…In [2], the method was further extended to that of constrained thin-plate reconstruction of the displacement field from points and lines based on a variational solution (for related work, also please see [11].) In this paper, we improve on the reconstruction paradigm in [2] and present extensive validation of the methodologies. One advantage of this line of work is that it allows for reconstruction of dense deformations between 2 arbitrary frames in a sequence of tagged images, as dense motion reconstruction methods generally produce displacement vector fields relative to undeformed tags in the initial frame.…”