*4.2. Application to Cell Microscopy*

In this experiment, we attempt to track biological cells from a sequence of images containing 90 frames by using the proposed tracker. A snapshot of the sequence is shown in Figure 15. In this application, we use the constant turn rate for the dynamic model as in Section 4.1.2 and the standard observation model as in Section 4.1.1. We also implement the measurement driven model as described in Reference [20]. For the first time step, the birth rate is set to a very high value (≈1) to initialize objects. Subsequently, the birth rate is capped at 10−7. The standard deviation of the turn rate noise is *π*/90 rad/s, and the standard deviation of the velocity noise is 5 pixels/frame. The number of hypotheses is capped at 10,000. The detection rate is set to 0.88, and the surviving rate and the spawning rate are 0.999 and 0.035, respectively. The clutter rate is set to 0.05. The cell spawning model is the same as described in Reference [57] with the covariance of the spawning model given as *QT* = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 40 0 0 0 0 0500 0 0 0 40 0 0 0005 0 0000 *π*/90 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ and the smoothing interval set to the entire image sequence. In this

application, we set the track pruning threshold of the estimator to 3 time steps.

**Figure 14.** Percentage of smoothing time over filtering time.

**Figure 15.** Snapshot of biological cell sequence.

From the tracking results, significant improvement is observed as the proposed tracker is able to eliminate incorrect spawned tracks. While the OSPA error in Figure 16 shows similar performance for the GLMB filter and the proposed tracker, the improvement is clearly reflected in the OSPA<sup>2</sup> cardinality error plots in Figure 17. From the cardinality plot in Figure 18, the estimated cardinality from our tracker is much closer to the true values as fewer incorrect spawned tracks are estimated. In this

experiment, there is not much difference between the GLMB filter and the proposed tracker estimates localization error due to the mismatch between the dynamic model and actual motion of the cells. Finally, in Figure 19, we illustrate the improved tracking results in terms of tracking sequence for several time steps at a selected region where the cell splitting process occurs.

**Figure 16.** OSPA error for tracking biological cells.

**Figure 17.** OSPA2 error for tracking biological cells.

**Figure 18.** Estimated cardinality for tracking biological cells.

**Figure 19.** The tracked image sequences of biological cells with blue asterisks denoting points detection. Top row: Generalized Labeled Multi-Bernoulli (GLMB) filter tracking results. Bottom: Proposed tracker tracking results.
