On the bijectivity of thin-plate splines
Eriksson, Anders P LU and Åström, Karl LU
(2012)
6.
p.93-141
- 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 (IEEE Trans. Pattern Anal. Mach. Intell. 11(6):567–585 1989), it is a
natural interpolating function in two dimensions, parameterized by a finite number
of landmarks. However, even though the thin-plate spline has a very intuitive
interpretation as well as an elegant mathematical formulation, it has no inherent
restriction to prevent folding, i.e. a non-bijective interpolating function. In this
chapter we discuss some of the properties of the set of parameterizations that form
bijective thin-plate splines,... (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 (IEEE Trans. Pattern Anal. Mach. Intell. 11(6):567–585 1989), it is a
natural interpolating function in two dimensions, parameterized by a finite number
of landmarks. However, even though the thin-plate spline has a very intuitive
interpretation as well as an elegant mathematical formulation, it has no inherent
restriction to prevent folding, i.e. a non-bijective interpolating function. In this
chapter 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. The
methods are used in two settings (a) to register two images using thin-plate spline
deformations, while ensuring bijectivity and (b) group-wise registration of a set of
images, while enforcing bijectivity constraints. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3437196
- author
- Eriksson, Anders P
LU
and Åström, Karl
LU
- organization
- publishing date
- 2012
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Analysis for Science, Engineering and Beyond, The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 8-9, 2008
- editor
- Åström, Karl ; Persson, Lars-Erik and Silvestrov, Sergei
- volume
- 6
- pages
- 93 - 141
- publisher
- Springer
- external identifiers
-
- scopus:84893550201
- ISBN
- 978-3-642-20236-0
- 978-3-642-20235-3 (print)
- DOI
- 10.1007/978-3-642-20236-0_5
- language
- English
- LU publication?
- yes
- id
- a57fecda-f6bb-4a56-9281-091d52684c49 (old id 3437196)
- date added to LUP
- 2016-04-04 10:39:09
- date last changed
- 2022-02-21 03:28:30
@inbook{a57fecda-f6bb-4a56-9281-091d52684c49,
abstract = {{The thin-plate spline (TPS) has been widely used in a number of areas<br/><br>
such as image warping, shape analysis and scattered data interpolation. Introduced<br/><br>
by Bookstein (IEEE Trans. Pattern Anal. Mach. Intell. 11(6):567–585 1989), it is a<br/><br>
natural interpolating function in two dimensions, parameterized by a finite number<br/><br>
of landmarks. However, even though the thin-plate spline has a very intuitive<br/><br>
interpretation as well as an elegant mathematical formulation, it has no inherent<br/><br>
restriction to prevent folding, i.e. a non-bijective interpolating function. In this<br/><br>
chapter we discuss some of the properties of the set of parameterizations that form<br/><br>
bijective thin-plate splines, such as convexity and boundness. Methods for finding<br/><br>
sufficient as well as necessary conditions for bijectivity are also presented. The<br/><br>
methods are used in two settings (a) to register two images using thin-plate spline<br/><br>
deformations, while ensuring bijectivity and (b) group-wise registration of a set of<br/><br>
images, while enforcing bijectivity constraints.}},
author = {{Eriksson, Anders P and Åström, Karl}},
booktitle = {{Analysis for Science, Engineering and Beyond, The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 8-9, 2008}},
editor = {{Åström, Karl and Persson, Lars-Erik and Silvestrov, Sergei}},
isbn = {{978-3-642-20236-0}},
language = {{eng}},
pages = {{93--141}},
publisher = {{Springer}},
title = {{On the bijectivity of thin-plate splines}},
url = {{http://dx.doi.org/10.1007/978-3-642-20236-0_5}},
doi = {{10.1007/978-3-642-20236-0_5}},
volume = {{6}},
year = {{2012}},
}