Figure 5.

Revise the x,y coordinates of a material point, given the z-axis coordinate. In the apical and basal planes, find the centroids of all tag points on the same contour as that of the material point. Connect these with a straight line. The intersections of this line with the images give the local origins. About these origins, define local polar coordinates for the tag point (●) on each short-axis image that has the same tag segment and heart contour as those of the material point. Fit their radii and angles as functions of z by using cubic splines. Use the estimated z value to find the material point vector. Add this to an origin that is also on the intercentroid line to find the new x,y coordinates of the material point (■).