Automatic trajectory recognition in Active Target Time Projection Chambers data by means of hierarchical clustering

The automatic reconstruction of three-dimensional particle tracks from Active Target Time Projection Chambers data can be a challenging task, especially in the presence of noise. In this article, we propose a non-parametric algorithm that is based on the idea of clustering point triplets instead of the original points. We define an appropriate distance measure on point triplets and then apply a single-link hierarchical clustering on the triplets. Compared to parametric approaches like RANSAC or the Hough transform, the new algorithm has the advantage of potentially finding trajectories even of shapes that are not known beforehand. This feature is particularly important in low-energy nuclear physics experiments with Active Targets operating inside a magnetic field. The algorithm has been validated using data from experiments performed with the Active Target Time Projection Chamber developed at the National Superconducting Cyclotron Laboratory (NSCL).The results demonstrate the capability of the algorithm to identify and isolate particle tracks that describe non-analytical trajectories. For curved tracks, the vertex detection recall was 86\% and the precision 94\%. For straight tracks, the vertex detection recall was 96\% and the precision 98\%. In the case of a test set containing only straight linear tracks, the algorithm performed better than an iterative Hough transform.