hep-exMar 24, 2026

Contrastive Metric Learning for Point Cloud Segmentation in Highly Granular Detectors

Authors: Max Marriott-Clarke, Lazar Novakovic, Elizabeth Ratzer, Robert J. Bainbridge, Loukas Gouskos, Benedikt Maier

Organizations: Blackett Laboratory, Imperial College London, UK · Department of Physics & Astronomy, Brown University, USA · Brown Center for Theoretical Physics and Innovation (BCTPI), Brown University, USA

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Abstract

We propose a novel clustering approach for point-cloud segmentation based on supervised contrastive metric learning (CML). Rather than predicting cluster assignments or object-centric variables, the method learns a latent representation in which points belonging to the same object are embedded nearby while unrelated points are separated. Clusters are then reconstructed using a density-based readout in the learned metric space, decoupling representation learning from cluster formation and enabling flexible inference. The approach is evaluated on simulated data from a highly granular calorimeter, where the task is to separate highly overlapping particle showers represented as sets of calorimeter hits. A direct comparison with object condensation (OC) is performed using identical graph neural network backbones and equal latent dimensionality, isolating the effect of the learning objective. The CML method produces a more stable and separable embedding geometry for both electromagnetic and hadronic particle showers, leading to improved local neighbourhood consistency, a more reliable separation of overlapping showers, and better generalization when extrapolating to unseen multiplicities and energies. This translates directly into higher reconstruction efficiency and purity, particularly in high-multiplicity regimes, as well as improved energy resolution. In mixed-particle environments, CML maintains strong performance, suggesting robust learning of the shower topology, while OC exhibits significant degradation. These results demonstrate that similarity-based representation learning combined with density-based aggregation is a promising alternative to object-centric approaches for point cloud segmentation in highly granular detectors.

Figures & tables

ModelMethodδagg\delta_{\mathrm{agg}}tβt_{\beta}tdt_{d}
EMCML80.40.45
OC6.750.10.25
HADCML100.40.45
OC110.10.35
MixedCML9.50.40.45
OC7.50.10.3
Table 1: Clustering thresholds. The parameter δagg\delta_{\mathrm{agg}} denotes the agglomerative clustering distance threshold, while tβt_{\beta} and tdt_{d} correspond to thresholds used in both the density-based readout and object condensation inference.
DatasetNparticlesN_{\rm particles}R@1R@1R@10R@10C@10C@10⟨Nhits⟩\langle N_{\rm hits}\rangle
EM20.9800.9960.0222 180
150.7840.9530.24615 406
300.7110.9240.33426 493
HAD20.9420.9920.0723 148
150.6290.9100.42624 461
300.5090.8460.54943 661
Table 2: Spatial overlap metrics and average hit counts computed in detector coordinate space (x,y,z)(x,y,z) at representative multiplicities. Metrics are defined in Section IV.1 and applied directly to the hit positions without any learned transformation. The large point-cloud sizes and high contamination values at N=30N=30 illustrate the intrinsic difficulty of the segmentation task.
Figure 1: Event-level embedding-geometry distributions for EM and HAD showers at increasing generated particle multiplicity ( NparticlesN_{\mathrm{particles}} ). Top: median inter-shower separation dintermediand_{\mathrm{inter}}^{\mathrm{median}} . Middle: intra-shower distance tail dintraQ99d_{\mathrm{intra}}^{\mathrm{Q99}} . Bottom: separation margin Δ=dintermedian−dintraQ99\Delta=d_{\mathrm{inter}}^{\mathrm{median}}-d_{\mathrm{intra}}^{\mathrm{Q99}} . Narrow positive or near-zero margins indicate a well-defined clustering scale, while broad or negative margins indicate increasing ambiguity between showers.
DatasetNparticlesN_{\rm particles}MethodR@kR@kC@10C@10AUC
   111010  
EM2CML0.9410.9920.0670.956
OC0.9350.9890.0720.944
15CML0.6910.9320.3390.950
OC0.6670.9200.3630.923
30CML0.5720.8860.4670.945
Table 3: Embedding-geometry metrics for EM and HAD showers at representative multiplicities. CML consistently achieves higher Recall@ kk , lower contamination@10, and higher AUC than OC, with the performance gap increasing as multiplicity increases.
Figure 2: Reconstruction efficiency (top) and purity (bottom) as functions of primary particle energy for electromagnetic (EM) and hadronic (HAD) showers. Columns show models trained on EM, trained on HAD, and a mixed-trained model evaluated separately on EM and HAD showers. The vertical dashed line indicates the upper boundary of the training energy range. The dominant differences are largely independent of energy, indicating that performance is controlled primarily by the learned representation rather than by the absolute shower energy.
Figure 3: Reconstruction efficiency (top), purity (middle), and number ratio (bottom) as functions of particle multiplicity NN for electromagnetic (EM) and hadronic (HAD) showers. Columns show models trained on EM, trained on HAD, and a mixed-trained model evaluated separately on EM and HAD showers. The vertical dashed line indicates the upper boundary of the training multiplicity range. The performance gap between CML and OC increases strongly with multiplicity, showing that clustering stability in dense environments is determined by the underlying embedding geometry.
Figure 4: Energy resolution as a function of primary particle energy for electromagnetic (EM) and hadronic (HAD) showers. Panels show models trained on EM, a mixed-trained model evaluated on EM, trained on HAD, and a mixed-trained model evaluated on HAD. The vertical dashed line marks the upper boundary of the training energy range. The black dashed curve denotes the ideal pattern-recognition limit, defined as the resolution obtained by a perfect clustering algorithm with no merging or splitting, and represents a lower bound on the achievable resolution given the detector response. Improvements in CML resolution follow directly from its improved clustering purity and reduced merging. Results are averaged over the full test dataset spanning multiplicities from 1 to 30 particles per event.
Figure 5: Reconstruction efficiency (top) and purity (bottom) for the HAD model as functions of primary particle energy under three systematic variations: 1.2×1.2\times hadronic interaction length scaling, QGSP_BERT physics list, and 5%5\% random hit masking. The nominal performance is shown for reference. Neither method shows significant degradation, and the performance gap between CML and OC is preserved under all variations.
ModelDimensionClusteringPurityEfficiency
CML16Agglomerative0.7220.932
16Density0.7100.945
4Agglomerative0.6900.887
4Density0.6370.905
OC16Agglomerative0.4690.849
16Density0.5200.838
Table 4: Mean reconstruction purity and efficiency for the mixed-trained model evaluated on the combined EM and HAD test sample for 16- and 4-dimensional embeddings. The relative ordering between methods is unchanged when the embedding dimensionality is reduced, showing that the CML advantage is not driven by latent-space size alone.
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