A Moving Window Based Approach to Multi-scan Multi-Target Tracking

Multi-target state estimation refers to estimating the number of targets and their trajectories in a surveillance area using measurements contaminated with noise and clutter. In the Bayesian paradigm, the most common approach to multi-target estimation is by recursively propagating the multi-target filtering density, updating it with current measurements set at each timestep. In comparison, multi-target smoothing uses all measurements up to current timestep and recursively propagates the entire history of multi-target state using the multi-target posterior density. The recent Generalized Labeled Multi-Bernoulli (GLMB) smoother is an analytic recursion that propagate the labeled multi-object posterior by recursively updating labels to measurement association maps from the beginning to current timestep. In this paper, we propose a moving window based solution for multi-target tracking using the GLMB smoother, so that only those association maps in a window (consisting of latest maps) get updated, resulting in an efficient approximate solution suitable for practical implementations

Biological cell tracking and lineage inference via random finite sets

Automatic cell tracking has long been a challenging problem due to the uncertainty of cell dynamic and observation process, where detection probability and clutter rate are unknown and time-varying. This is compounded when cell lineages are also to be inferred. In this paper, we propose a novel biological cell tracking method based on the Labeled Random Finite Set (RFS) approach to study cell migration patterns. Our method tracks cells with lineage by using a Generalised Label Multi-Bernoulli (GLMB) filter with objects spawning, and a robust Cardinalised Probability Hypothesis Density (CPHD) to address unknown and time-varying detection probability and clutter rate. The proposed method is capable of quantifying the certainty level of the tracking solutions. The capability of the algorithm on population dynamic inference is demonstrated on a migration sequence of breast cancer cells

Linear Complexity Gibbs Sampling for Generalized Labeled Multi-Bernoulli Filtering

Generalized Labeled Multi-Bernoulli (GLMB) densities arise in a host of multi-object system applications analogous to Gaussians in single-object filtering. However, computing the GLMB filtering density requires solving NP-hard problems. To alleviate this computational bottleneck, we develop a linear complexity Gibbs sampling framework for GLMB density computation. Specifically, we propose a tempered Gibbs sampler that exploits the structure of the GLMB filtering density to achieve an $\mathcal{O}(T(P+M))$ complexity, where $T$ is the number of iterations of the algorithm, $P$ and $M$ are the number hypothesized objects and measurements. This innovation enables an $\mathcal{O}(T(P+M+\log(T))+PM)$ complexity implementation of the GLMB filter. Convergence of the proposed Gibbs sampler is established and numerical studies are presented to validate the proposed GLMB filter implementation

Label Space Partition Selection for Multi-Object Tracking Using Two-Layer Partitioning

Estimating the trajectories of multi-objects poses a significant challenge due to data association ambiguity, which leads to a substantial increase in computational requirements. To address such problems, a divide-and-conquer manner has been employed with parallel computation. In this strategy, distinguished objects that have unique labels are grouped based on their statistical dependencies, the intersection of predicted measurements. Several geometry approaches have been used for label grouping since finding all intersected label pairs is clearly infeasible for large-scale tracking problems. This paper proposes an efficient implementation of label grouping for label-partitioned generalized labeled multi-Bernoulli filter framework using a secondary partitioning technique. This allows for parallel computation in the label graph indexing step, avoiding generating and eliminating duplicate comparisons. Additionally, we compare the performance of the proposed technique with several efficient spatial searching algorithms. The results demonstrate the superior performance of the proposed approach on large-scale data sets, enabling scalable trajectory estimation.Comment: 6 pages, 4 figure