Tracking markers with missing data by lower rank approximation

Motion and deformation of an object may be quantified by following attached markers in video or cine frame sequences. When recording cardiac motion by video (256 × 256 pixels, 50 Hz), generally no more than approximately 20 markers can be followed due to difficulties in proper identification of marker images. In the present study we developed the lower rank (LR) tracking method which can automatically follow considerably more than 20 markers. The performance of the method was evaluated in computer simulations of naturally moving myocardial markers observed in a sequence of 60 video frames. White noise was added to the marker coordinates. Realistic loss of data due to detection failure was simulated by deleting a generated marker image when the distance to another marker image was below a given minimum value. In a test, realistic values were substituted for the noise level σ (0.5 pixel) and the minimum marker distance d m (4 pixels). For numbers of markers ranging from 50 to 100, 95-90% of the detected marker images was correctly tracked. Less than 0.7% was part of a false track, i.e. a track containing images of different markers. Under less favourable conditions (σ = 1 pixel; d m = 8 pixels) the method was robust: for 75 markers with 40% of the marker images missing, still 70% of the detected images was correctly tracked, while the fraction in false tracks did not increase. The LR tracking method appears reliable for automatic tracking of large amounts of moving markers in a sequence of video or cine frames.