发表机构
Dept. of Computer Eng., METU（中东技术大学计算机工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对密集人群多目标跟踪中匈牙利算法效率低的问题，提出增量分配算法，利用成本矩阵块稀疏结构，每次添加一人进行增量计算，避免全矩阵扫描，在现实人群基准测试中比匈牙利算法有显著加速，适用于大规模人群场景。
AI 中文摘要
在密集人群中的多目标跟踪需要在每个视频帧解决检测与轨迹之间的二分分配问题。经典匈牙利算法以\(O(N^3)\)时间复杂度解决此问题，对于有数百人的大场景成为瓶颈。我们提出一种增量分配算法，利用人群跟踪成本矩阵的块稀疏结构。我们计算与匈牙利算法相同的最优\(N\times N\)分配，但通过增量策略，每次添加一人，利用在步骤\(n - 1\)后对偶势对于\((n - 1)\times(n - 1)\)子问题是精确最优的这一事实。每个新步骤仅需从经认证的最优起始点进行一次增广路径搜索。这避免了重复的全矩阵扫描，同时保证相同的全局最优结果。对角重排序不变量保持数据结构紧凑且利于缓存。在有\(N\in[200,5000]\)人组成密集簇的现实人群基准测试中，我们的算法比匈牙利基线实现了\(3.7 - 6.5\)倍加速，同时产生与匈牙利算法相同的可证明最优匹配。加速随\(N\)增长且在\(N = 3000\)之后保持稳定，使该方法对体育场出口和大型公共活动等大规模人群场景特别有吸引力。
英文摘要
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.
