We present an extension to the disjoint paths problem in which additional \emph{lifted} edges are introduced to provide path connectivity priors. We call the resulting optimization problem the lifted disjoint paths problem. We show that this problem is NP-hard by reduction from integer multicommodity flow and 3-SAT. To enable practical global optimization, we propose several classes of linear inequalities that produce a high-quality LP-relaxation. Additionally, we propose efficient cutting plane algorithms for separating the proposed linear inequalities. The lifted disjoint path problem is a natural model for multiple object tracking and allows an elegant mathematical formulation for long range temporal interactions. Lifted edges help to prevent id switches and to re-identify persons. Our lifted disjoint paths tracker achieves nearly optimal assignments with respect to input detections. As a consequence, it leads on all three main benchmarks of the MOT challenge, improving significantly over state-of-the-art.

中文翻译：

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提升不相交路径在多目标跟踪中的应用

我们提出了不相交路径问题的扩展，其中引入了额外的 \emph{lifted} 边以提供路径连接先验。我们将由此产生的优化问题称为提升不相交路径问题。我们通过减少整数多商品流和 3-SAT 来证明这个问题是 NP-hard 问题。为了实现实际的全局优化，我们提出了几类产生高质量 LP 松弛的线性不等式。此外，我们提出了有效的切割平面算法来分离所提出的线性不等式。提升的不相交路径问题是多对象跟踪的自然模型，并允许为长距离时间交互提供优雅的数学公式。凸起的边缘有助于防止身份转换和重新识别人员。我们提升的不相交路径跟踪器在输入检测方面实现了近乎最佳的分配。因此，它在 MOT 挑战的所有三个主要基准上都处于领先地位，比最先进的技术有了显着改进。