Application to particle velocimetry

In this section, application of the proposed tracking algorithm is demonstrated. Particles in a blood flow were tracked with the purpose of measuring their velocities. In particle velocimetry [8], a velocity field should be computed to adequately represent motion in all parts of flow. There are hundreds of particles in a sequence. Due to varying visibility, they often disappear and appear again. Entries and exits are also frequent. Partial trajectories can only be tracked, which is sufficient to obtain a velocity field. Here, the proper merit of tracking performance is the link-based one, as discussed in section 5.2.

From table 1, it is obvious that the tracking algorithms SJ87 and RS91 are unsuitable for this task, since they cannot handle flow across image border. SS90 cannot handle occlusions, which is of no particular importance, as partial trajectories are sufficient. However, SS90 cannot be applied to such a large number of points because of the prohibitive computational cost of this iterative algorithm. Therefore, HW89 and IP97 remain the only two candidates for this velocimetry application.

Blood flow tracking results by IP97 (left) and HW89 (right).

Blood flow is coherent motion, in which spatially close particles are likely to have similar velocity vectors. To enhance the velocity estimation, coherence based post-processing was applied to the tracking results of the two selected algorithms. The post-processing discards those velocity vectors whose orientation is incompatible with the dominant orientation of the surrounding vectors. The dominant orientation is the median in a window centered on the origin of the vector being considered. Incompatible outliers are detected as falling outside the limits specified by the median and the double variance.

The figure below shows the results of the coherence filtering of the original trajectories displayed in the previous figure. The image size is $512 \times 512$, the window size $100 \times 100$ pixels. After coherence filtering, very short trajectories (less than 3 frames) were discarded. The IPAN Tracker yields more trajectories, and these are more coherent than those obtained by HW89. The latter provides longer connected trajectories, since this algorithm can cope with longer occlusions than IP97.

Enhanced results by IP97 (left) and HW89 (right) after coherence filtering.