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On the Bijectivity of Thin-plate Splines

Eriksson, Anders P LU and Åström, Karl LU (2005) Swedish Symposium on Image Analysis (SSBA) 2005
Abstract
The thin-plate spline (TPS) has been widely used in a number of areas such as image warping, shape analysis and scattered data interpolation. Introduced by Bookstein[1], it is a natural interpolating function in two dimensions, parameterized by a finite numb er of landmarks. However, even though the thin-plate spline has a very elegant intuitive interpretation as well as mathematical formulation it has no inherent restriction to prevent folding, i.e.
a non-bijective interpolating function. In this paper we discuss some of the properties of the set of parameterizations that form bijective thin-plate
splines, such as convexity and boundness. Methods for finding sufficient as well as necessary conditions for bijectivity are also... (More)
The thin-plate spline (TPS) has been widely used in a number of areas such as image warping, shape analysis and scattered data interpolation. Introduced by Bookstein[1], it is a natural interpolating function in two dimensions, parameterized by a finite numb er of landmarks. However, even though the thin-plate spline has a very elegant intuitive interpretation as well as mathematical formulation it has no inherent restriction to prevent folding, i.e.
a non-bijective interpolating function. In this paper we discuss some of the properties of the set of parameterizations that form bijective thin-plate
splines, such as convexity and boundness. Methods for finding sufficient as well as necessary conditions for bijectivity are also presented. (Less)
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Contribution to conference
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published
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pages
4 pages
conference name
Swedish Symposium on Image Analysis (SSBA) 2005
language
English
LU publication?
yes
id
ea48ab82-0bb9-4861-afd8-1446f4c69db6 (old id 787247)
alternative location
http://www.maths.lth.se/vision/publdb/reports/pdf/eriksson-ssia-05.pdf
date added to LUP
2008-01-04 13:05:40
date last changed
2016-11-18 10:05:51
@misc{ea48ab82-0bb9-4861-afd8-1446f4c69db6,
  abstract     = {The thin-plate spline (TPS) has been widely used in a number of areas such as image warping, shape analysis and scattered data interpolation. Introduced by Bookstein[1], it is a natural interpolating function in two dimensions, parameterized by a finite numb er of landmarks. However, even though the thin-plate spline has a very elegant intuitive interpretation as well as mathematical formulation it has no inherent restriction to prevent folding, i.e.<br/>a non-bijective interpolating function. In this paper we discuss some of the properties of the set of parameterizations that form bijective thin-plate<br/>splines, such as convexity and boundness. Methods for finding sufficient as well as necessary conditions for bijectivity are also presented.},
  author       = {Eriksson, Anders P and Åström, Karl},
  language     = {eng},
  pages        = {4},
  title        = {On the Bijectivity of Thin-plate Splines},
  year         = {2005},
}