Partitioning multiple data sets:
                    Multidimensional assignments and Lagrangian
                    relaxation

Poore, Aubrey B.; Rijavec, Nenad

doi:10.1090/dimacs/016/16

Cited by 17 publications

(22 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This development generalizes the various special and example cases in our earlier work [20,21,22]. A reason for this assignment formulation is that it exhibits a rich structure that can be exploited algorithmically [12,20,23,24]. The plan for this section is to begin with a simple description of a model multitarget tracking.…”

Section: Assignment Formulation Of Some General Data Association Probmentioning

confidence: 95%

“…As discussed at the end of the previous section, all the preprocessing that is generally used for multiple hypothesis tracking can be used for other methods for solving the assignment problem (2.16). The particular algorithms that we have developed for obtaining near-optimal solutions of the assignment problem (2.16) [20,23,24] make use of all of these preprocessing techniques, except the explicit pruning of noncompetitive partitions. We do prune tracks of reports from all partitions via the gating techniques discussed at the end of the previous section.…”

Section: Assignment Formulation Of Multiple Hypothesis Tracking For Mmentioning

confidence: 99%

“…The development in Section 2 extracts the salient features and assumptions that occur in a large class of these problems; the concrete examples are given in Sections 3 and 5. Our reason for this specific formulation is the recent development of a class of real-time and near-optimal algorithms [12,20,23,24] for solving these multidimensional assignment prob-lems to the noise level in the problem. Also, the current work differs from our earlier work [20,21,22] in the generality of the formulation, derivation of the cost coefficients, and the allowable dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…We do not discuss algorithms for solving the multidimensional assignment problems such as multiple hypothesis tracking, greedy, branch and bound techniques, and the Lagrangian relaxation methods currently under development [20,24]. We do not discuss the design of a tracking system and the host of associated issues [2,3,7], the use of parallel computation, the various nonlinear estimation techniques for nonlinear dynamics, maneuvering targets characterized by abrupt and unknown changes in the system dynamics, the integration of multisensor data into a multitarget tracking system.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking

Poore

1994

Comput Optim Applic

209

View full text Add to dashboard Cite

Abstract. The ever-increasing demand in surveillance is to produce highly accurate target and track identification and estimation in real-time, even for dense target scenarios and in regions of high track contention. The use of multiple sensors, through more varied information, has the potential to greatly enhance target identification and state estimation. For multitarget tracking, the processing of multiple scans all at once yields high track identification. However, to achieve this accurate state estimation and track identification, one must solve an NP-hard data association problem of partitioning observations into tracks and false alarms in real-time. The primary objective in this work is to formulate a general class of these data association problems as multidimensional assignment problems to which new, fast, near-optimal, Lagrangian relaxation based algorithms are applicable. The dimension of the formulated assignment problem corresponds to the number of data sets being partitioned with the constraints defining such a partition. The linear objective function is developed from Bayesian estimation and is the negative log posterior or likelihood function, so that the optimal solution yields the maximum a posteriori estimate. After formulating this general class of problems, the equivalence between solving data association problems by these multidimensional assignment problems and by the currently most popular method of multiple hypothesis tracking is established. Track initiation and track maintenance using an N-scan sliding window are then used as illustrations. Since multiple hypothesis tracking also permeates multisensor data fusion, two example classes of problems are formulated as multidimensional assignment problems.

show abstract

Section: Assignment Formulation Of Some General Data Association Probmentioning

confidence: 95%

Section: Assignment Formulation Of Multiple Hypothesis Tracking For Mmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking

Poore

1994

Comput Optim Applic

209

View full text Add to dashboard Cite

show abstract

“…The general data association problem has recently received much attention from the radar tracking community who recommend a technique called Lagrangian relaxation for estimating the optimal association [2,11]. Lagrangian relaxation works by first relaxing the uniqueness constraint along all but two of the dimensions so that the problem can be solved, providing a possibly infeasible "dual" solution.…”

Section: Generating 3d Marker Positionsmentioning

confidence: 99%

A Procedure for Automatically Estimating Model Parameters in Optical Motion Capture

Ringer¹,

Lasenby²

2002

Procedings of the British Machine Vision Conference 2002

View full text Add to dashboard Cite

Model-based optical motion capture systems require knowledge of the position of the markers relative to the underlying skeleton, the lengths of the skeleton's limbs, and which limb each marker is attached to. These model parameters are typically assumed and entered into the system manually, although techniques exist for calculating some of them, such as the position of the markers relative to the skeleton's joints.We present a fully automatic procedure for determining these model parameters. It tracks the 2D positions of the markers on the cameras' image planes and determines which markers lie on which limb before calculating the position of the underlying skeleton. The only assumption is that the skeleton is made up of rigid limbs connected with ball joints.The proposed system is demonstrated on a number of real data examples and is shown to calculate good estimates of the model parameters in each.

show abstract

Quadratic Assignment Problem

Pitsoulis

Pardalos

2001

Encyclopedia of Optimization

View full text Add to dashboard Cite

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadratic assignment problem, and discusses the relationship between the QAP and other well known combinatorial optimization problems, e.g. the traveling salesman problem, the graph partitioning problem, etc. The paper will appear in the Handbook of Combinatorial Optimization to be published by Kluwer Academic Publishers, P. Pardalos and D.-Z. Du, eds.

show abstract

Partitioning multiple data sets: Multidimensional assignments and Lagrangian relaxation

Cited by 17 publications

References 0 publications

Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking

Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking

A Procedure for Automatically Estimating Model Parameters in Optical Motion Capture

Quadratic Assignment Problem

Contact Info

Product

Resources

About