Lecture notes in computer science vol:3216 pages:639-646
7th international conference on medical image computing and computer-assisted intervention - MICCAI 2004 location:Saint-Malo, France date:26-29 September 2004
Voxel-based nonrigid image registration can be formulated as an optimisation problem whose goal is to minimise a cost function, consisting of a first term that characterises the similarity between both images and a second term that regularises the transformation and/or penalties improbable or impossible deformations. Within this paper, we extend previous works on nonrigid image registration by the introduction of a new penalty term that expresses the local rigidity of the deformation. A necessary and sufficient condition for the transformation to be locally rigid at a particular location is that its Jacobian matrix J(T) at this location is orthogonal, satisfying the orthogonality condition J(T)J(T)(T) = 1. So we define the penalty term as the weighted integral of the Frobenius norm of J(T)J(T)(T)-1 integrated over the overlap of the images to be registered. We fit the implementation of the penalty term in a multidimensional, continuous and differentiable B-spline deformation framework and analytically determine the derivative of the similarity criterion and the penalty term with respect to the deformation parameters. We show results of the impact of the proposed rigidity constraint on artificial and clinical images demonstrating local shape preservation with the proposed constraint.
Loeckx D., Maes F., Vandermeulen D., Suetens P., ''Nonrigid image registration using free-form deformations with a local rigidity constraint'', Lecture notes in computer science, vol. 3216, pp. 639-646, 2004 (Proceedings 7th international conference on medical image computing and computer-assisted intervention - MICCAI 2004, part I, September 26-29, 2004, Saint-Malo, France).