On the bijectivity of thinplate splines
(2012) In Analysis for Science, Engineering and Beyond, The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 89, 2008 6. p.93141 Abstract
 The thinplate 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 thinplate spline has a very intuitive
interpretation as well as an elegant mathematical formulation, it has no inherent
restriction to prevent folding, i.e. a nonbijective interpolating function. In this
chapter we discuss some of the properties of the set of parameterizations that form
bijective thinplate splines,... (More)  The thinplate 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 thinplate spline has a very intuitive
interpretation as well as an elegant mathematical formulation, it has no inherent
restriction to prevent folding, i.e. a nonbijective interpolating function. In this
chapter we discuss some of the properties of the set of parameterizations that form
bijective thinplate 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 thinplate spline
deformations, while ensuring bijectivity and (b) groupwise registration of a set of
images, while enforcing bijectivity constraints. (Less)
Please use this url to cite or link to this publication:
http://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
 in
 Analysis for Science, Engineering and Beyond, The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 89, 2008
 editor
 Åström, Karl; Persson, LarsErik and Silvestrov, Sergei
 volume
 6
 pages
 93  141
 publisher
 Springer
 external identifiers

 Scopus:84893550201
 ISBN
 9783642202360
 9783642202353 (print)
 DOI
 10.1007/9783642202360_5
 language
 English
 LU publication?
 yes
 id
 a57fecdaf6bb4a569281091d52684c49 (old id 3437196)
 date added to LUP
 20130906 17:30:29
 date last changed
 20161118 10:05:51
@misc{a57fecdaf6bb4a569281091d52684c49, abstract = {The thinplate 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 thinplate 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 nonbijective interpolating function. In this<br/><br> chapter we discuss some of the properties of the set of parameterizations that form<br/><br> bijective thinplate 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 thinplate spline<br/><br> deformations, while ensuring bijectivity and (b) groupwise registration of a set of<br/><br> images, while enforcing bijectivity constraints.}, author = {Eriksson, Anders P and Åström, Karl}, editor = {Åström, Karl and Persson, LarsErik and Silvestrov, Sergei}, isbn = {9783642202360}, language = {eng}, pages = {93141}, publisher = {ARRAY(0xb865218)}, series = {Analysis for Science, Engineering and Beyond, The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 89, 2008}, title = {On the bijectivity of thinplate splines}, url = {http://dx.doi.org/10.1007/9783642202360_5}, volume = {6}, year = {2012}, }