research-article

On Simulated Annealing and the Construction of Linear Spline Approximations for Scattered Data

Authors:

Oliver Kreylos,

Bernd HamannAuthors Info & Claims

IEEE Transactions on Visualization and Computer Graphics, Volume 7, Issue 1

Pages 17 - 31

https://doi.org/10.1109/2945.910818

Published: 01 January 2001 Publication History

Abstract

We describe a method to create optimal linear spline approximations to arbitrary functions of one or two variables, given as scattered data without known connectivity. We start with an initial approximation consisting of a fixed number of vertices and improve this approximation by choosing different vertices, governed by a simulated annealing algorithm. In the case of one variable, the approximation is defined by line segments; in the case of two variables, the vertices are connected to define a Delaunay triangulation of the selected subset of sites in the plane. In a second version of this algorithm, specifically designed for the bivariate case, we choose vertex sets and also change the triangulation to achieve both optimal vertex placement and optimal triangulation. We then create a hierarchy of linear spline approximations, each one being a superset of all lower-resolution ones.

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https://dl.acm.org/doi/10.1007/s11042-023-15558-9
Zhu HCao JXiao YChen ZZhong ZZhang Y(2022)TCB-spline-based Image VectorizationACM Transactions on Graphics10.1145/351313241:3(1-17)Online publication date: 14-Jun-2022
https://dl.acm.org/doi/10.1145/3513132
Llanas BSáinz F(2010)Uniform tree approximation by global optimization techniquesComputing and Visualization in Science10.5555/3113219.311353613:2(83-97)Online publication date: 1-Feb-2010
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Index Terms

On Simulated Annealing and the Construction of Linear Spline Approximations for Scattered Data
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
      1. Approximation
    2. Numerical analysis
      1. Computations on polynomials
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

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cover image IEEE Transactions on Visualization and Computer Graphics

IEEE Transactions on Visualization and Computer Graphics Volume 7, Issue 1

January 2001

96 pages

ISSN:1077-2626

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Copyright © Copyright © 2001 IEEE. All Rights Reserved.

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IEEE Educational Activities Department

United States

Publication History

Published: 01 January 2001

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Cited By

Gong WFan X(2024)Image adaptive sampling using reinforcement learningMultimedia Tools and Applications10.1007/s11042-023-15558-983:2(5511-5530)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s11042-023-15558-9
Zhu HCao JXiao YChen ZZhong ZZhang Y(2022)TCB-spline-based Image VectorizationACM Transactions on Graphics10.1145/351313241:3(1-17)Online publication date: 14-Jun-2022
https://dl.acm.org/doi/10.1145/3513132
Llanas BSáinz F(2010)Uniform tree approximation by global optimization techniquesComputing and Visualization in Science10.5555/3113219.311353613:2(83-97)Online publication date: 1-Feb-2010
https://dl.acm.org/doi/10.5555/3113219.3113536
Kolingerová IKohout JRulf MUher V(2010)A proper choice of vertices for triangulation representation of digital imagesProceedings of the 2010 international conference on Computer vision and graphics: Part II10.5555/1894615.1894622(41-48)Online publication date: 20-Sep-2010
https://dl.acm.org/doi/10.5555/1894615.1894622
erveňanský MTóth ZStarinský JFerko AŠrámek M(2010)Technical SectionComputers and Graphics10.1016/j.cag.2010.01.00134:2(125-135)Online publication date: 1-Apr-2010
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Courchesne OGuibault FDompierre JCheriet F(2007)Adaptive mesh generation of MRI images for 3D reconstruction of human trunkProceedings of the 4th international conference on Image Analysis and Recognition10.5555/2394970.2395074(1040-1051)Online publication date: 22-Aug-2007
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Kohout J(2007)On digital image representation by the delaunay triangulationProceedings of the 2nd Pacific Rim conference on Advances in image and video technology10.5555/1782074.1782151(826-840)Online publication date: 17-Dec-2007
https://dl.acm.org/doi/10.5555/1782074.1782151
Kohout J(2007)On Digital Image Representation by the Delaunay TriangulationAdvances in Image and Video Technology10.1007/978-3-540-77129-6_70(826-840)Online publication date: 17-Dec-2007
https://dl.acm.org/doi/10.1007/978-3-540-77129-6_70
Doherty LPister KRamchandran KSztipanovits JHou JPappas T(2004)Scattered data selection for dense sensor networksProceedings of the 3rd international symposium on Information processing in sensor networks10.1145/984622.984676(369-378)Online publication date: 26-Apr-2004
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Battiato SGallo GMessina GPasko A(2004)SVG rendering of real images using data dependent triangulationProceedings of the 20th Spring Conference on Computer Graphics10.1145/1037210.1037238(185-192)Online publication date: 22-Apr-2004
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