[Insight-users] B-spline deformations for image registration? (Vol 63, Issue 31

[Julia A. Schnabel]

insight-users-request at itk.org wrote:
> 
> Date: Mon, 6 Jul 2009 10:33:01 +0200
> From: motes motes <mort.motes at gmail.com>
> Subject: [Insight-users] B-spline deformations for image registration?
> To: insight-users at itk.org
> Message-ID:
> 	<54eca6a70907060133i370210d1x997d97f31ae9884b at mail.gmail.com>
> Content-Type: text/plain; charset="iso-8859-1"
> 
> Most of the B-spline deformations in an image registration procedure I have
> read about typically use uniform B-splines. I have seen that development on
> non-uniform B-splines is in progress in ITK. But what benefits are earned
> from non-uniform B-splines in image registration?
> 
> I have read an article on non-uniform spacing of the control points in
> relation to image registration:
> 
> http://www.springerlink.com/content/0q3bfeunq4avrwdf/
> 
> But to define a non-uniform spacing of the control points one does not
> necessarily need to use non-uniform knot-vectors.
> 
> The purpose of non-uniform knot-vectors as I understand is to have different
> weights for each control point, but to my knowledege no results with this
> approach has been published.

Hello,

yes indeed, you can use regular FFDs, and only allow some control points 
to move, in order to emulate non-uniform FFDs.

Main benefits are: fewer degrees of freedom to optimize = faster; more 
localized deformations (e.g. within brain mask, or automatically in 
regions of high local intensity variance, or steep cost gradient) = 
possibility to focus into relevant regions (especially if used with 
multi-level FFDs or subdivision techniques); regular mesh = easy mesh 
traversal and isotropic optimization parameters

Disadvantage: you still need a big regular mesh even if only few control 
points remain activated. One can however layer smaller B-spline patches 
(over smaller FOVs - e.g. the work by Gustavo Rhode).

I don't know how much of that algorithm has made it into ITK, but simply 
assigning a control point status to each control point, or even to each 
of its 3 degrees of freedom, and querying this status before any 
deformation is applied, should do the trick.

Best regards,
Julia Schnabel

-- 
Julia A. Schnabel, PhD                University Lecturer (Medical Imaging)
University of Oxford                  Fellow, St. Hilda's College
Institute of Biomedical Engineering   http://www.ibme.ox.ac.uk
Department of Engineering Science     Tel: (44) 1865 617687 (voice)
ORCRB, off Roosevelt Drive            Tel: (44) 1865 617675 (Val)
Oxford OX3 7DQ, UK                    Fax: (44) 1865 617671