A constrained analytic solution for tracking non-rigid motion of the left ventricle

The problem of tracking left-ventricular (LV) endocardial motion from medical images is addressed. This approach accounts for information over two spatial dimensions and time in formulating a displacement flow field of the LV wall viewed as a deformable contour. A two-stage approach consisting of shape-based matching followed by smoothing of the resultant vectors over pairs of successive contours is described. Using least squares analysis, the authors derive an analytic solution to the smoothing stage, while still constraining displacement vectors to the contour definitions. The resulting formulation is considerably faster than previous methods and provides a vehicle for multistage development.