53 research outputs found
Local search heuristics for multi-index assignment problems with decomposable costs.
The multi-index assignment problem (MIAP) with decomposable costs is a natural generalization of the well-known assignment problem. Applications of the MIAP arise for instance in the field of multi-target multi-sensor tracking. We describe an (exponentially sized) neighborhood for a solution of the MIAP with decomposable costs, and show that one can find a best solution in this neighborhood in polynomial time. Based on this neighborhood, we propose a local search algorithm. We empirically test the performance of published constructive heuristics and the local search algorithm on random instances; a straightforward tabu search is also tested. Finally, we compute lower bounds to our problem, which enable us to assess the quality of the solutions found.Assignment; Costs; Heuristics; Problems; Applications; Performance;
A Multi-Scan Labeled Random Finite Set Model for Multi-object State Estimation
State space models in which the system state is a finite set--called the
multi-object state--have generated considerable interest in recent years.
Smoothing for state space models provides better estimation performance than
filtering by using the full posterior rather than the filtering density. In
multi-object state estimation, the Bayes multi-object filtering recursion
admits an analytic solution known as the Generalized Labeled Multi-Bernoulli
(GLMB) filter. In this work, we extend the analytic GLMB recursion to propagate
the multi-object posterior. We also propose an implementation of this so-called
multi-scan GLMB posterior recursion using a similar approach to the GLMB filter
implementation
Marginal multi-Bernoulli filters: RFS derivation of MHT, JIPDA and association-based MeMBer
Recent developments in random finite sets (RFSs) have yielded a variety of
tracking methods that avoid data association. This paper derives a form of the
full Bayes RFS filter and observes that data association is implicitly present,
in a data structure similar to MHT. Subsequently, algorithms are obtained by
approximating the distribution of associations. Two algorithms result: one
nearly identical to JIPDA, and another related to the MeMBer filter. Both
improve performance in challenging environments.Comment: Journal version at http://ieeexplore.ieee.org/document/7272821.
Matlab code of simple implementation included with ancillary file
New Auction Algorithms for the Assignment Problem and Extensions
We consider the classical linear assignment problem, and we introduce new
auction algorithms for its optimal and suboptimal solution. The algorithms are
founded on duality theory, and are related to ideas of competitive bidding by
persons for objects and the attendant market equilibrium, which underlie
real-life auction processes. We distinguish between two fundamentally different
types of bidding mechanisms: aggressive and cooperative. Mathematically,
aggressive bidding relies on a notion of approximate coordinate descent in dual
space, an epsilon-complementary slackness condition to regulate the amount of
descent approximation, and the idea of epsilon-scaling to resolve efficiently
the price wars that occur naturally as multiple bidders compete for a smaller
number of valuable objects. Cooperative bidding avoids price wars through
detection and cooperative resolution of any competitive impasse that involves a
group of persons.
We discuss the relations between the aggressive and the cooperative bidding
approaches, we derive new algorithms and variations that combine ideas from
both of them, and we also make connections with other primal-dual methods,
including the Hungarian method. Furthermore, our discussion points the way to
algorithmic extensions that apply more broadly to network optimization,
including shortest path, max-flow, transportation, and minimum cost flow
problems with both linear and convex cost functions
Comparison of two 3D tracking paradigms for freely flying insects
In this paper, we discuss and compare state-of-the-art 3D tracking paradigms for flying insects such as Drosophila melanogaster. If two cameras are employed to estimate the trajectories of these identical appearing objects, calculating stereo and temporal correspondences leads to an NP-hard assignment problem. Currently, there are two different types of approaches discussed in the literature: probabilistic approaches and global correspondence selection approaches. Both have advantages and limitations in terms of accuracy and complexity. Here, we present algorithms for both paradigms. The probabilistic approach utilizes the Kalman filter for temporal tracking. The correspondence selection approach calculates the trajectories based on an overall cost function. Limitations of both approaches are addressed by integrating a third camera to verify consistency of the stereo pairings and to reduce the complexity of the global selection. Furthermore, a novel greedy optimization scheme is introduced for the correspondence selection approach. We compare both paradigms based on synthetic data with ground truth availability. Results show that the global selection is more accurate, while the previously proposed tracking-by-matching (probabilistic) approach is causal and feasible for longer tracking periods and very high target densities. We further demonstrate that our extended global selection scheme outperforms current correspondence selection approaches in tracking accuracy and tracking time
- …