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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Vydáno v:	Automatica (Oxford) Ročník 45; číslo 2; s. 510 - 516
Hlavní autoři:	Susca, Sara, Bullo, Francesco, Martínez, Sonia
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Kidlington Elsevier Ltd 01.02.2009 Elsevier
Témata:	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
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Abstract	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.
AbstractList	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.
Author	Martínez, Sonia Susca, Sara Bullo, Francesco
Author_xml	– sequence: 1 givenname: Sara surname: Susca fullname: Susca, Sara email: sara@ece.ucsb.edu organization: Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, 93106-5070, USA – sequence: 2 givenname: Francesco surname: Bullo fullname: Bullo, Francesco email: bullo@engineering.ucsb.edu organization: Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, 93106-5070, USA – sequence: 3 givenname: Sonia surname: Martínez fullname: Martínez, Sonia email: soniamd@ucsd.edu organization: Mechanical and Aerospace Engineering Department, University of California at San Diego, 9500 Gilman Dr, La Jolla, CA, 92093-0411, USA
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Keywords	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
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SubjectTerms	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
Title	Gradient algorithms for polygonal approximation of convex contours
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