Computational-geometric methods for polygonal approximations of a curve

Mixed integer optimal compensation deals with optimization problems with integer-and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls could lead to intractability in problems of large dimensions. To address this challenge, we introduce a decomposition method which turns the original n-dimensional optimization problem into n independent scalar problems of lot sizing form. Each of these problems can be viewed as a two-player zero-sum game, which introduces some element of conservatism. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon, a step that mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent system problem, where each agent seeks to compensate a combination of an exogenous signal and the local state average. We discuss a large population mean-field type Communicated by

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“…More details on this conversion can be found in [12, p. 98] and [13,14]. The underlying idea is summarized in Fig.…”

Section: Highlights Of the Main Results And Relationship With The Relmentioning

confidence: 99%

Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems

Bauso

Zhu

Başar

2016

J Optim Theory Appl

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“…In our technique, we simplify centerline curves to generate a coarse representation of the vessel tree to infer the large-scale behavior of the cut surfaces. As an old problem from computational geometry, it was already investigated by Imai and Iri [13,14] for polygonal curves in the late 80s. The most commonly used algorithm was developed by Ramer [31] and Douglas and Peucker [9].…”

Section: Related Workmentioning

confidence: 99%

Vessel Visualization using Curved Surface Reformation

Auzinger

Mistelbauer

Baclija

et al. 2013

IEEE Trans. Visual. Comput. Graphics

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To analyze the lumen of arbitrarily oriented vessels, Centerline Reformation (CR) has been proposed. Both methods project the vascular structures into 2D image space in order to reconstruct the vessel lumen. In this paper, we propose Curved Surface Reformation (CSR), a technique that computes the vessel lumen fully in 3D. This offers high-quality interactive visualizations of vessel lumina and does not suffer from problems of earlier methods such as ambiguous visibility cues or premature discretization of centerline data. Our method maintains exact visibility information until the final query of the 3D lumina data. We also present feedback from several domain experts.

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“…The found numbers of segments {M k (1) } are restricted to the range [a k , b k ], and they can provide only local minimum of the approximation error E(P 1 , …, P K , M). To find the global optimal allocation of the resource {M k While we iterate the algorithm to find the optimal distribution of the segments number M k , we simultaneously optimize the location of the approximation vertices {q k,m } for the current number of segments M k .…”

Section: Iterative Reduced Search Algorithmmentioning

confidence: 99%

“…Optimal approximation of a single polygonal curve can be solved by methods from graph theory [1][2][3][4][5], dynamic programming [6][7][8][9][10][11][12], or A*-search [13,14] in O(N 2 )-O(N 3 ) time where N is the number of vertices in the input curve.…”

Section: Introductionmentioning

confidence: 99%