Robust geometric drift correction and identity reconstruction for biological 3D time-lapse point clouds

Structural time-lapse microscopy experiments aim to follow cells or subcellular structures over time, typically by detecting objects in each frame and linking them into trajectories. In practice, this process yields sequences of spatial coordinates derived from segmentation, while identity information across time is often absent or unreliable. In addition, the observed coordinates may be affected by systematic geometric drift. As a result, two coupled inference problems arise: geometric drift must be corrected, and object identities must be reconstructed from unlabeled point clouds.

Here, we formulate both drift correction and identity reconstruction within a unified point-cloud framework and evaluate them jointly using controlled synthetic benchmarks and biological datasets. For drift correction, we compare rigid, local, and nonparametric models across spatially varying and non-rigid drift regimes. For identity reconstruction, we analyze a family of Hungarian assignment methods with constant-velocity refinement and different gating strategies, including innovation-based normalization.

Across benchmarks, we find that increased model flexibility does not necessarily improve drift correction. A simple rigid stepwise model provides the most robust performance across a wide range of conditions, with a local community model as a competitive alternative under structured spatial heterogeneity. On the association side, innovation-based gating emerges as the key determinant of performance. Hungarian constant-velocity assignment with normalized innovation gating consistently outperforms coordinate-space variants, particularly under heterogeneous motion scales, birth and death processes, and density-induced ambiguity.

Application to biological datasets confirms that the combined pipeline improves trajectory consistency and restores interpretable motion statistics, while highlighting the role of proxy references when ground truth is unavailable. Together, these results establish a practical and robust workflow for post hoc trajectory analysis in point-cloud-based time-lapse data, and clarify the methodological trade-offs between model expressivity and robustness in both drift correction and identity reconstruction.

Author Summary

Time-lapse microscopy is widely used to study how cells and subcellular structures move and change over time. A common analysis goal is to track these objects by detecting them in each frame and linking them into trajectories. In practice, however, this process often produces only their spatial coordinates, while consistent identity information across time is missing or unreliable. In addition, the entire field of view may shift or rotate during imaging, a problem known as drift.

We developed and systematically evaluated a computational framework that addresses both challenges using coordinate-based data alone. By combining controlled synthetic benchmarks with real biological datasets, we show that simple and robust approaches often outperform more complex ones. In particular, a rigid drift correction model remains effective even when drift varies across space, and trajectory reconstruction improves substantially when candidate matches are evaluated relative to their uncertainty rather than by fixed distance thresholds.

Our results provide practical guidance for analyzing time-lapse data when only coordinates are available. More broadly, they show that accounting for uncertainty and prioritizing robustness over model complexity leads to more reliable trajectory reconstruction in noisy and heterogeneous biological systems.