Note that one does not really have to program the spline "from scratch". Bookstein (1991) gives straight-forward FORTRAN code on pages 374-375 for the 1, 2, and 3 dimensional cases. The only thing one has to add are some standard subroutines for linear equation solving and plotting routines.
In addition, the file valsain.exe (listed under thin plate spline software on the Stony Brook Morphometrics web site) contains MATLAB code written by Les Marcus. It includes code for a 2D analysis of relative warps. They can be easily modified for 3D computations. One thing that is not obvious for the 3D case is that the upper left p by p block of the inverse of the L matrix must be multiplied by -1 to yield the bending energy matrix for the 3D case. As mentioned by Dennis, the real challenge is in creating nice looking visualizations of the spline for 3D data. ----------------------- F. James Rohlf State University of New York, Stony Brook, NY 11794-5245 > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] Behalf Of [EMAIL PROTECTED] > Sent: Wednesday, October 01, 2003 8:43 AM > To: [EMAIL PROTECTED] > Subject: Re: 3D Thin Plane Spline > > > The relevant formulae are in Bookstein (1991) Morphometric Tools for > Landmark Data: Geometry and Biology. Cambridge University Press (and > other places). The only difference for 3D is U(r) = |r| and obvious > adjustments to matrix sizes, etc. The more difficult problem is > generating effective visualizations in 2D of volumetric transformations. > > -ds > > On Wed, 2003-10-01 at 08:16, [EMAIL PROTECTED] wrote: > > Dear Morphometricians: > > I need to program a 3D Thin Plane Spline analysis routine. > > I would like information on this algorithm to program it from scratch. > > Best regards > > > > == > > Replies will be sent to list. > > For more information see > http://life.bio.sunysb.edu/morph/morphmet.html. > -- > Dennis E. Slice, Ph.D. > Department of Biomedical Engineering > Wake Forest University School of Medicine > Winston-Salem, North Carolina, USA > 27157-1022 > Phone: 336-716-5384 > Fax: 336-716-2870 > =========================================================== > This message is coming to you from [EMAIL PROTECTED] > that serves both as the administrative account for morphmet > and the support account for the Morpheus et al. software. > > For more information on how to use this mailing list see... > http://life.bio.sunysb.edu/morph/morphmet.html > > For more information on Morpheus et al. visit... > http://life.bio.sunysb.edu/morph/morpheus > > The Stony Brook morphmetrics site is a wealth of > morphometric resources... > http://life.bio.sunysb.edu/morph > =========================================================== > == > Replies will be sent to list. > For more information see http://life.bio.sunysb.edu/morph/morphmet.html == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
