[논문 리뷰] Lifted Disjoint Paths with Application in Multiple Object Tracking

Andrea Horňáková, Roberto Henschel외 2명|arXiv (Cornell University)|2020. 06. 25.

Video Surveillance and Tracking Methods인용 수 84

한 줄 요약

이 연구는 리프팅된 간선을 사용한 분리 경로를 확장하여 MOT의 장거리 시간 상호 작용을 포착하고, 절단면이 포함된 빡빡한 LP 이완을 개발하며, MOT 벤치마크에서 강력한 글로벌 최적화 성능을 보여준다.

ABSTRACT

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.

연구 동기 및 목표

• Extend the disjoint paths framework with lifted edges to encode long-range connectivity priors for MOT.
• Develop a high-quality linear programming relaxation with nontrivial polyhedral inequalities.
• Provide separation routines to efficiently add cutting planes for lifted constraints.
• Apply the approach to multiple object tracking and demonstrate strong performance on MOT benchmarks.
• Offer a tractable two-step graph construction and cost-learning pipeline for practical MOT use.

제안 방법

• Define lifted disjoint paths on a base flow graph and a lifted graph with edges E' encoding v→w connectivity via v→…→w paths in G.
• Derive and tighten linear inequalities (path, path-induced cut, and lifted variants) to obtain a strong LP relaxation.
• Develop efficient separation procedures (Algorithms 1–3) to add violated lifted constraints during solving.
• Solve the ILP with Gurobi using LP-based branch-and-bound on the tightened relaxation.
• Construct graphs over detections and tracklets with a two-step procedure and learn edge costs from visual and motion cues (re-id, DeepMatching, motion, spatio-temporal features).

실험 결과

연구 질문

• RQ1 Can lifted edges express long-range temporal connectivity to improve MOT beyond first-order models?
• RQ2 Do new polyhedral inequalities yield a tighter relaxation than naive liftings for the lifted disjoint paths problem?
• RQ3 Is there a practical global optimization approach that leverages long-range interactions to outperform state-of-the-art MOT trackers?
• RQ4 How does the lifted disjoint paths tracker perform on standard MOT benchmarks compared to prior methods?

주요 결과

• The lifted disjoint paths problem is NP-hard (even with only negative or only positive lifted edges).
• The proposed lifted path and lifted path-induced cut inequalities yield a strictly tighter LP relaxation than their non-lifted counterparts.
• Separation procedures for the lifted constraints run in linear time with respect to the number of active base edges, enabling practical solving.
• The global optimization approach yields near-optimal assignments and significantly improves MOT performance on major benchmarks.