On the Bijectivity of Thin-plate Splines
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/787247
- author
- Eriksson, Anders P LU and Åström, Karl LU
- organization
- publishing date
- 2005
- type
- Contribution to conference
- publication status
- published
- subject
- pages
- 4 pages
- conference name
- Swedish Symposium on Image Analysis (SSBA) 2005
- conference location
- Malmö, Sweden
- conference dates
- 2005-03-10 - 2005-03-11
- 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
- 2016-04-04 14:33:16
- date last changed
- 2020-12-22 02:16:00
@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}}, title = {{On the Bijectivity of Thin-plate Splines}}, url = {{http://www.maths.lth.se/vision/publdb/reports/pdf/eriksson-ssia-05.pdf}}, year = {{2005}}, }