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Publication# Tracking Interacting Objects Using Intertwined Flows

Abstract

In this paper, we show that tracking different kinds of interacting objects can be formulated as a network-flow Mixed Integer Program. This is made possible by tracking all objects simultaneously using intertwined flow variables and expressing the fact that one object can appear or disappear at locations where another is in terms of linear flow constraints. Our proposed method is able to track invisible objects whose only evidence is the presence of other objects that contain them. Furthermore, our tracklet-based implementation yields real-time tracking performance. We demonstrate the power of our approach on scenes involving cars and pedestrians, bags being carried and dropped by people, and balls being passed from one player to the next in team sports. In particular, we show that by estimating jointly and globally the trajectories of different types of objects, the presence of the ones which were not initially detected based solely on image evidence can be inferred from the detections of the others.

Official source

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Related concepts (7)

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Linear programming

Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.

Max-flow min-cut theorem

In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink is equal to the total weight of the edges in a minimum cut, i.e., the smallest total weight of the edges which if removed would disconnect the source from the sink. This is a special case of the duality theorem for linear programs and can be used to derive Menger's theorem and the Kőnig–Egerváry theorem.

Integer programming

An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.

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2023