-------- Original Message --------
Subject: RE: TPS 3D negative bending energy
Date: Fri, 4 Feb 2011 11:39:16 -0500
From: F. James Rohlf <[email protected]>
Reply-To: [email protected]
Organization: Stony Brook University
To: [email protected]
Not really "negative bending energy".
U = -|r| is the kernel for 3D data and it results in a correct
positive-semidefinite bending energy matrix.
I don’t know what U = |r| corresponds to.
----------------------
F. James Rohlf, John S. Toll Professor
Dept. Ecology and Evolution, Stony Brook University, NY 11794-5245
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-----Original Message-----
From: morphmet [mailto:[email protected]]
Sent: Thursday, February 03, 2011 12:29 PM
To: morphmet
Subject: Re: TPS 3D negative bending energy
-------- 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
>
