Extrapolation of incomplete marker tracks by lower rank approximation

Motion and deformation of an object such as the heart may be measured by tracking optical or radiopaque markers. In the experimental situation markers may fail to be detected due to occlusion or lack of contrast. As a result a continuous marker track is observed in separated parts, which often cannot be directly identified as corresponding to one marker. This paper presents a method of extrapolating a partly known track by using information provided by the known track part and the available complete tracks of other markers. The extrapolations are obtained by iteratively fitting a lower rank matrix to the set of noisy, incomplete marker tracks. The performance is evaluated with computer-simulated data and data obtained in an animal experiment. In both cases 43% of the available complete tracks were made incomplete by removal of track parts varying in length from 3% up to 44%. For the simulated data comparison of the extrapolations with true signal values results in a root mean square (RMS) error about equal to the noise level. For the animal experiment, when comparing the extrapolations with the measured values, in images of 256 x 256 pixels, the RMS error was found to be +/- 0.5 pixel, which is quite small relative to the total excursion of a marker (20 pixels). Estimation of the missing data by applying BMDPAM (BMDP Statistical Software Inc.) to the same data results in RMS errors which are about twice as high.