A comparative study of transformation functions for nonrigid image registration. Zagorchev, L. and Goshtasby, A. Image Processing, IEEE Transactions on, 15(3):529--538, March, 2006.
doi  abstract   bibtex   
Transformation functions play a major role in nonrigid image registration. In this paper, the characteristics of thin-plate spline (TPS), multiquadric (MQ), piecewise linear (PL), and weighted mean (WM) transformations are explored and their performances in nonrigid image registration are compared. TPS and MQ are found to be most suitable when the set of control-point correspondences is not large (fewer than a thousand) and variation in spacing between the control points is not large. When spacing between the control points varies greatly, PL is found to produce a more accurate registration than TPS and MQ. When a very large set of control points is given and the control points contain positional inaccuracies, WM is preferred over TPS, MQ, and PL because it uses an averaging process that smoothes the noise and does not require the solution of a very large system of equations. Use of transformation functions in the detection of incorrect correspondences is also discussed.
@Article{Zagorchev2006,
  author =    {Zagorchev, L. and Goshtasby, A.},
  title =     {{A comparative study of transformation functions for nonrigid image registration}},
  journal =   {Image Processing, IEEE Transactions on},
  year =      {2006},
  volume =    {15},
  number =    {3},
  pages =     {529--538},
  month =     mar,
  abstract =  {Transformation functions play a major role in nonrigid image registration. In this paper, the characteristics of thin-plate spline (TPS), multiquadric (MQ), piecewise linear (PL), and weighted mean (WM) transformations are explored and their performances in nonrigid image registration are compared. TPS and MQ are found to be most suitable when the set of control-point correspondences is not large (fewer than a thousand) and variation in spacing between the control points is not large. When spacing between the control points varies greatly, PL is found to produce a more accurate registration than TPS and MQ. When a very large set of control points is given and the control points contain positional inaccuracies, WM is preferred over TPS, MQ, and PL because it uses an averaging process that smoothes the noise and does not require the solution of a very large system of equations. Use of transformation functions in the detection of incorrect correspondences is also discussed.},
  doi =       {10.1109/TIP.2005.863114},
  issn =      {1057-7149},
  keywords =  {image registration; piecewise linear techniques; splines (mathematics)control points domain; multiquadric transformation; nonrigid image registration; piecewise linear transformation; thin-plate spline transformation; transformation functions; weighted mean transformation},
  owner =     {imagenes2},
  timestamp = {2009.02.11}
}
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