arXiv:2607.21368cs.CVcs.DS2026-07

提出增量匹配算法,让人群追踪速度提升6倍以上。

Incremental Optimal Assignment for Real-Time Crowd Tracking

  • 按人逐次加入,利用前一步的最优对偶势能加速计算
  • 在200到5000人场景下实现3.7至6.5倍加速
  • 适合大规模人群追踪,如体育场出口等高密度场景

密集人群中的多目标追踪需在每帧视频中求解检测与轨迹间的二分图匹配问题。经典匈牙利算法时间复杂度为$O(N^3)$,在数百人以上的场景中成为瓶颈。本文提出一种增量式匹配算法,利用人群追踪代价矩阵的块稀疏结构——同一群组内稠密,群组间近零。该算法在保持与匈牙利算法完全相同的最优$N \times N$匹配结果前提下,采用逐人添加策略:第$ n-1 $步后,对偶势能已对$(n-1)\times(n-1)$子问题精确最优(强于匈牙利算法的中间可行性)。因此每一步仅需从一个经验证的最优起点进行一次增广路径搜索,避免重复全矩阵扫描,同时保证全局最优。对角重排不变性使数据结构紧凑且缓存友好。在真实人群基准测试中($N \in [200, 5000]$),本方法相比匈牙利基线获得3.7–6.5×加速,且加速随$N$增大而提升,在$N>3000$时仍稳定,特别适用于体育场出口、大型公共活动等大规模人群场景。

原文摘要 · Abstract (English)

Multi-object tracking in dense crowds requires solving a bipartite assignment problem between detections and trajectories at every video frame. The classical Hungarian algorithm solves this in $O(N^3)$ time, which becomes a bottleneck for large scenes with hundreds of people. We propose an \emph{incremental} assignment algorithm that exploits the block-sparse structure of crowd tracking cost matrices --- dense within each crowd cluster, near-zero between clusters. We compute the exact same optimal $N \times N$ assignment as the Hungarian algorithm, but via an incremental strategy: we add one person at a time, exploiting the fact that after step $n-1$ the dual potentials are \emph{exactly optimal} for the $(n-1)\times(n-1)$ subproblem --- a strictly stronger condition than the intermediate feasibility maintained by the Hungarian algorithm during its $N$ outer iterations. Each new step therefore requires only a single augmenting path search from a certified optimal starting point. This avoids repeated full-matrix scans while guaranteeing an identical globally optimal result. A diagonal-reordering invariant keeps the data structure compact and cache-friendly. On realistic crowd benchmarks with $N \in [200, 5000]$ people organised into dense clusters, our algorithm achieves \textbf{3.7--6.5$\times$ speedup} over the Hungarian baseline while producing provably optimal matchings identical to those of Hungarian. The speedup grows with $N$ and remains stable beyond $N=3000$, making the method especially attractive for large-scale crowd scenes such as stadium exits and mass public events.

人群追踪增量算法最优匹配实时系统

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