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.