# Multi-cell 3D tracking with adaptive acceptance gates

## Project Info

Title |
Multi-Cell 3D Tracking with Adaptive Acceptance Gates |

Goal |
To provide a routine to automatically detect and track cells in a 3D space |

Paper |
M. Landau, E. Koltsova, K. Ley and S.T. Acton, “Multi-cell 3D tracking with adaptive acceptance gates,” *Proc. IEEE SW Symposium on Image Analysis and Interpretation,* Austin, Texas, May 23-25, 2010. [.pdf] |

## Purpose

Develop a routine to automatically detect and track dendritic cells (DCs) and T cells in a locally dense 3D target space, and collect statistics on their characteristics of motion and interaction durations. A novel method to extend the track longevity is presented, where an adaptive acceptance gate (AAG) is computed based on the local target density.
Discussion

Manually tracking a collection of hundreds of cells in a 3-Dimensional space can prove to be an arduous and tedious task. Therefore a method to automate the detection and tracking of these cells was devised to precipitate the extraction of pertinent information regarding the motion and interaction sequences. In a medium containing dendritic cells (DCs) and T cells, this information includes statistics on the change in speed, direction of movement, tortuosity, confinement ratio, motility, and interaction durations.

In highly dense target spaces, the task of tracking each cell becomes increasingly difficult. These difficulties include tracks swapping to different cells or losing the cell altogether. Moreover, even in lowly dense target spaces, tracks on volatile cells may be lost. Therefore, we present an approach to take the local track density estimate, computed separately for each track, to compute an adaptive measurement association gate.

An adaptive measurement association gate implies that as the track travels to areas with varying local target densities, the Chi-squared measurement gate-threshold will change accordingly to an optimal size, as opposed to using a fixed Chi-squared threshold. The track's measurement covariance can be thought of as a search region to determine the target that most likely belongs to the track, i.e. when the residual between the track and measurement is near zero. The target density can be computed in a variety of ways, including a geometric based estimate or universal density estimate including information taken from the entire target space. However, a desired estimator for the target density should be very localized because, generally speaking, target density is not spatially-invariant nor homogeneous in the entire target space. Spatial-invariance is a term used to describe a consistent separation between each target during its existence. Ideally, a density estimate can be computed separately in the neighborhood of each track. This implies that little information about neighboring tracks should be known in order to compute a local normalized density.

We implement a method to compute the density based on a specified number of nearest neighboring tracks, including just the first nearest neighbor. By normalizing this density with the covariance of the residual, a new Chi-squared measurement gate-threshold can be computed to accept more measurements in lesser dense regions, and fewer measurements in higher dense regions. Below are demonstrations when the AAG extension is either employed or not employed for two targets approaching each other, where the tracks are propagated and updated. In each simulation, since the targets are traveling at a constant velocity, when the tracks are updated the measurement covariances (green ellipses) shrink because the tracks are being smoothed. Note however when the AAG extension is included, when the tracks are further apart the Chi-squared thresholds are larger, but when the tracks approach each other the Chi-squared thresholds shrink thereby shrinking the ellipse.

**Fig 1.** Two simulated targets approaching each other. Top graph, the fixed Chi-squared threshold maintains a nearly constant measurement covariance ellipse. Bottom graph, the AAG extension manages the Chi-squared measurement gate-threshold depending on the first nearest neighbor distance.

**Fig 2.** Dendritic cells (green track trails) and T cells (red track trails) traveling in a non-dense 3-dimensional cellular space.

**Fig 3.** T cells traveling in a dense 3-dimensional cellular space.