<title>Deformation of MR images using a local linear transformation</title>

A fully automatic method to deform medical images is proposed. The procedure is based on the application of a set of consecutive local linear transformations at fixed landmarks, generating a global non-linear deformation. Continuity is guaranteed by a smooth change form the landmark point to the neighborhood, which is a homotopy between an affine transformation and the identity map. Landmarks are distributed uniformly throughout both reference and target images and their density is increased to reach the desired similarity between both images. A hybrid genetic optimization algorithm is used to search for the transformation parameters by maximizing the normalized mutual information. It is shown, by means of the transformation of a circle into a triangle and vice versa, that the method has the capability to generate either sharp of smooth deformations. For magnetic resonance images, it is proved that the successive application of the local linear transformations allows us to increase the similarity between geometrically deformed images and target. The results suggest that the method can be applied to a wide range of non-rigid image registration problems.