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On the Bijectivity of Thin-plate Splines

På svenska

Author

Summary, in English

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.

Publishing year

2005

Language

English

Document type

Conference paper

Topic

  • Mathematics

Conference name

Swedish Symposium on Image Analysis (SSBA) 2005

Conference date

2005-03-10 - 2005-03-11

Conference place

Malmö, Sweden

Status

Published