Tag Line Tracking

The most intuitively straightforward use of tagged MR images is to view the dark tag lines apparent in Fig. 2 as features to be tracked. For best results, SPAMM pulse sequences with 3 to 7 RF pulses and a total tip angle of 90° are applied. This results in a tag pattern with no net magnetization, f0(p) = 0, wherever gTp = 2mn, m an integer. The set of material points satisfying this condition comprise parallel planes of tissue, called tag planes. In subsequent images, clearly defined lines of minimal brightness— tag lines —correspond to material points within those planes. Thus, if yi is a point along a line of minimal brightness at time t, we know f0(p(y;, t)) = 0.

Then, to translate this knowledge into a motion measurement, we must determine m, which relates the point yi at time t to the specific tag plane on which it was located at time 0. This information provides a 1D measurement of the motion component orthogonal to that tag plane, as illustrated in Fig. 4. Tracking tag lines and measuring this component of motion therefore requires two goals to be met: identifying points of minimal brightness and determining m. Methods for

FIGURE 3 Typical image geometries include stacks of images here showing short axis (SA) images (a) and spoke arrangements (b) that best depict the long axis (LA) of the LV.

true displacement (unknown)

image plane orthogonal component ofdisplacemem (known)

FIGURE 4 Depiction of a point on a tag line. It has been displaced from some unknown reference point that lies on the known initial tag plane. We therefore know the component of the displacement oriented perpendicular to the tag plane.

accomplishing these goals can be divided into template matching [19-21] and active geometry [7,22,23] techniques, both of which we describe here.

Template Matching

In template matching, which is illustrated in Fig. 5, a point on a tag line is found by comparing the image brightness along a strip of pixels to an expected tag pattern template. The location at which the template and the measured brightness best match is assumed to be a point on a tag line. To demonstrate, let s be the 1D position along the strip of pixels, I(s) be the continuous image brightness function along the strip, and g(s) be the centered tag template. Then, the pixels in the strip are samples of I(s) at regularly spaced positions s1;..., sK and the estimated position of the tag line so is found by shifting g(s) until the total squared error between g(s) and I(s1),..., I(sK) is minimized. That is, the tag point estimate is given by

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