-------- Original Message -------- Subject: Re: TPS 3D negative bending energy Date: Thu, 3 Feb 2011 04:10:46 -0500 From: Stefan Schlager <[email protected]> To: [email protected] Dear all, Note to my earlier question: I noticed that the negative version of U creates a negative Version of the bending energy matrix - resulting in a positve-semidefinite matrix (it was late yesterday...) But I'm still curious about the explanation of negative bending energy. Stefan Stefan Schlager M.A. Anthropologie Medizinische Fakultät der der Albert Ludwigs- Universität Freiburg Hebelstr. 29 79104 Freiburg Anthropology Faculty of Medicine, Albert-Ludwigs-University Freiburg Hebelstr. 29 D- 79104 Freiburg phone +49 (0)761 203-5522 fax +49 (0)761 203-6898 On 02/02/11 22:00, Stefan Schlager wrote:
Dear morphometricans, I'm currently programming on calculations of principal and relative warps in R ( programming the functions helps me grasping the maths behind). Everything works great in 2D - I'm getting the exact same results as Bookstein (although the erroneous coefficients in the paper of 1989 stole me a day) and Dryden in their papers/books. Now in the 3D case I observed negative eigenvalues of the bending energy matrix - getting energy from bending doesn't make sense. I happened to see that Dryden uses the negative 3d kernel function (U(r)=-|r| instead of U(r)=|r|) to calculate the bending energy matrix . For me, all other applications however work perfect with the "normal" kernel. Are there any papers out there on this problem/solution, dealing with the maths? Thanks Stefan
