Gradient algorithms for polygonal approximation of convex contours

The subjects of this paper are descent algorithms to optimally approximate a strictly convex contour with a polygon. This classic geometric problem is relevant in interpolation theory and data compression, and has potential applications in robotic sensor networks. We design gradient descent laws for...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 45; no. 2; pp. 510 - 516
Main Authors: Susca, Sara, Bullo, Francesco, Martínez, Sonia
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.02.2009
Elsevier
Subjects:
Applied sciences
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Control theory. Systems
Convex body approximation
Exact sciences and technology
Gradient methods
Interpolation
Motion coordination
Polygonal approximation
Robotics
Software
Gradient methods
Interpolation
Motion coordination
Polygonal approximation
Convex body approximation
Coordination
Data compression
Feedback regulation
Control synthesis
Robotics
Gradient descent
Descent method
Metric
Sensor array
Motion control
Gradient method
Convex polygon
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary:The subjects of this paper are descent algorithms to optimally approximate a strictly convex contour with a polygon. This classic geometric problem is relevant in interpolation theory and data compression, and has potential applications in robotic sensor networks. We design gradient descent laws for intuitive performance metrics such as the area of the inner, outer, and “outer minus inner” approximating polygons. The algorithms position the polygon vertices based on simple feedback ideas and on limited nearest-neighbor interaction.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2008.08.020