Multi-object tracking has been recently approached with the min-cost network flow optimization techniques. Such methods simultaneously resolve multiple object tracks in a video and enable modeling of dependencies among tracks. Min-cost network flow methods also fit well within the "tracking-by-detection" paradigm where object trajectories are obtained by connecting per-frame outputs of an object detector. Object detectors, however, often fail due to occlusions and clutter in the video. To cope with such situations, we propose to add pairwise costs to the min-cost network flow framework. While integer solutions to such a problem become NP-hard, we design a convex relaxation solution with an efficient rounding heuristic which empirically gives certificates of small suboptimality. We evaluate two particular types of pairwise costs and demonstrate improvements over recent tracking methods in real-world video sequences.
We propose an algorithm that incorporates quadratic pairwise costs into the traditional min-cost flow network. Unlike previous methods @cite_23 @cite_14 , which either build on top of min-cost flow solutions @cite_22 or change the network structure @cite_24 , we propose a modification to the standard optimization algorithm. Such quadratic costs can represent several useful properties like similar motion of people in a rally, co-occurrence of tracks for different parts of the same object instance and others.
@cite_24 @cite_14 @cite_22 @cite_23
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Multi-object tracking has been recently approached with the min-cost network flow optimization techniques. Such methods simultaneously resolve multiple object tracks in a video and enable modeling of dependencies among tracks. Min-cost network flow methods also fit well within the “tracking-by-detection” paradigm where object trajectories are obtained by connecting per-frame outputs of an object detector. Object detectors, however, often fail due to occlusions and clutter in the video. To cope with such situations, we propose to add pairwise costs to the min-cost network flow framework. While integer solutions to such a problem become NP-hard, we design a convex relaxation solution with an efficient rounding heuristic which empirically gives certificates of small suboptimality. We evaluate two particular types of pairwise costs and demonstrate improvements over recent tracking methods in real-world video sequences. We propose a method for global multi-target tracking that can incorporate higher-order track smoothness constraints such as constant velocity. Our problem formulation readily lends itself to path estimation in a trellis graph, but unlike previous methods, each node in our network represents a candidate pair of matching observations between consecutive frames. Extra constraints on binary flow variables in the graph result in a problem that can no longer be solved by min-cost network flow. We therefore propose an iterative solution method that relaxes these extra constraints using Lagrangian relaxation, resulting in a series of problems that ARE solvable by min-cost flow, and that progressively improve towards a high-quality solution to our original optimization problem. We present experimental results showing that our method outperforms the standard network-flow formulation as well as other recent algorithms that attempt to incorporate higher-order smoothness constraints. We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of l∞-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when the groups are disjoint or embedded in a specific hierarchical structure, we address here the case of general overlapping groups. To this end, we show that the corresponding optimization problem is related to network flow optimization. More precisely, the proximal problem associated with the norm we consider is dual to a quadratic min-cost flow problem. We propose an efficient procedure which computes its solution exactly in polynomial time. Our algorithm scales up to millions of variables, and opens up a whole new range of applications for structured sparse models. We present several experiments on image and video data, demonstrating the applicability and scalability of our approach for various problems. We propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. In particular, when both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty, we propose a robust integer programming problem of moderately larger size that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation. When only the cost coefficients are subject to uncertainty and the problem is a 0−1 discrete optimization problem on n variables, then we solve the robust counterpart by solving at most n+1 instances of the original problem. Thus, the robust counterpart of a polynomially solvable 0−1 discrete optimization problem remains polynomially solvable. In particular, robust matching, spanning tree, shortest path, matroid intersection, etc. are polynomially solvable. We also show that the robust counterpart of an NP-hard α-approximable 0−1 discrete optimization problem, remains α-approximable. Finally, we propose an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network.