Point proposal network for reconstructing 3D particle endpoints with subpixel precision in liquid argon time projection chambers

Liquid argon time projection chambers (LArTPCs) are particle imaging detectors recording 2D or 3D images of trajectories of charged particles. Identifying points of interest in these images, namely, the initial and terminal points of track-like particle trajectories such as muons and protons, and the initial points of electromagnetic shower-like particle trajectories such as electrons and gamma rays, is a crucial step in identifying and analyzing these particles and impacts the inference of physics signals such as neutrino interaction. The Point Proposal Network is designed to discover these specific points of interest. The algorithm predicts with a subvoxel precision their spatial location, and also determines the category of the identified points of interest. Using as a benchmark the PILArNet public LArTPC data sample in which the voxel resolution is $3\mathrm{mm}/\mathrm{voxel}$, our algorithm successfully predicts 96.8% and 97.8% of 3D points within a distance of 3 and 10 voxels from the provided true point locations, respectively. For the predicted 3D points within 3 voxels of the closest true point locations, the median distance is found to be 0.25 voxels, achieving subvoxel-level precision. In addition, we report our analysis of the mistakes where our algorithm prediction differs from the provided true point positions by more than 10 voxels. Among the mistakes we visually scanned 50 events: 25 were due to the definition of true position location, 15 were legitimate mistakes where a physicist cannot visually disagree with the algorithm’s prediction, and 10 were genuine mistakes that we wish to improve in the future. Further, using these predicted points, we demonstrate a simple algorithm to cluster 3D voxels into individual track-like particle trajectories with a clustering efficiency, purity, and adjusted Rand index of 96%, 93%, and 91%, respectively.

Figure 1

U-ResNet architecture for semantic segmentation. In this example we say that the U-ResNet has a depth of 3 since we perform three down-samplings. Turquoise boxes represent convolutions with stride 2 that increase the number of filters. Dark blue boxes are transpose convolutions with stride 2 that decrease the number of filters. Purple boxes are convolutions with stride 1 that decrease the number of filters. Blue boxes (“add labels @ train”) represent the inclusion of true voxels in the mask of positive voxels, and only apply during training. The gold boxes are a score thresholding ($>0.5$) operation on the softmax of predicted scores. The spatial size of the data tensor is constant across the horizontal dimension.

Figure 2

Simulated LArTPC event from our data set. The left picture (network input) shows energy deposits from charged particle trajectories, whose color corresponds to an energy scale. In the right image (labels), each voxel is assigned one of five colors: HIPs in purple, MIPs in dark blue, electromagnetic showers in light blue, delta rays in green, and Michel electrons in orange.

Figure 3

Example of predictions by $\mathrm{U}\text{−}\mathrm{ResNet}+\mathrm{PPN}$. The voxels’ color corresponds to their semantic class as predicted by U-ResNet. The dots are proposed by PPN, and the dots’ color represents the point type predicted by PPN. See Fig. 2 for the color legend.

Figure 4

Distance from true points to the closest predicted points, and from predicted points to the closest true points. Both the true and predicted points of delta-ray type are excluded in this plot. 97.8% of the points are contained in the $x$ axis range for both histograms.

Figure 5

Correlation between the distance from a predicted point to the closest true point, and the distance from a predicted point to the voxel center of the corresponding true point. We selected predicted points that are within 3 voxels of a true point. About 3.6% of these predicted points are associated with true points that PILArNet locates exactly at the center of a voxel. They are not pictured here.

Figure 6

Confusion matrix for U-ResNet. Each cell contains the fraction of voxels in percent belonging to a certain true semantic type on the vertical axis that have been predicted as the semantic type shown on the horizontal axis. Each row sums to 100%.

Figure 7

Looking at the distance between predicted points of Michel electron or delta-ray type (i.e., with a corresponding semantic type score $>0.5$) and the closest voxel with the true semantic type of MIP.

Figure 8

This histogram shows the distance from a predicted point before post-processing with a type HIP, MIP, or EM shower (i.e., type score $>0.5$) to the closest voxel of the same type as predicted by U-ResNet. 1024 events are used in this histogram.

Figure 9

This picture shows the semantic and point predictions of U-ResNet and PPN. Predicted EM shower voxels are in cyan, MIP in dark blue, and HIP in purple. The yellow points are true points. The red points are predicted by PPN. The shower fragment on the left belongs to the EM shower coming from the right, and PILArNet only provides a single initial point for the whole shower (the yellow dot at the shower start on the right, where PPN correctly predicted another EM shower point).

Figure 10

Example of a short trajectory (purple voxels) that is lacking true points due to small total energy deposit. The red points are predicted by PPN.

Figure 11

Example of a kink along a HIP trajectory (purple voxels) causing a legitimate mistake by PPN. The yellow points are true points. The red points are predicted by PPN.

Figure 12

Example of shower trajectory exiting the volume. All the cyan (true shower) points were mistakenly classified as MIP by U-ResNet. The yellow points are true points. The red points are PPN predictions with high MIP score.

Figure 13

Example of MIP trajectory exiting and briefly re-entering the volume. The yellow points are label points. The red points are PPN prediction.

Figure 14

An example issue of a true point that appears to be mistakenly shifted. The yellow points are true label points. The red points are PPN predictions.

Figure 15

Track clustering. Top left: $\mathrm{U}\text{−}\mathrm{ResNet}+\mathrm{PPN}$ predictions. Top right: selecting U-ResNet track predictions only and removing voxels around PPN predictions. A radius of 10 voxels is used to make the gaps visible in this figure, but the clustering algorithms use a radius of 7 voxels. Bottom left: true track particle clusters. Bottom right: predicted track particle clusters.