The planning of conformal radiotherapy requires accurate localizations of the tumor and the critical structures. In existing planning systems, the segmentation of brain structures is manual and each structure has to be delineated in each slice of a 3D image. An automatic segmentation algorithm of all the critical structures in a patient image is then an invaluable tool for radiotherapy.
In order to segment all these structures in a specific patient's image, we use an anatomical atlas containing labels of the structures of the brain. The atlas was manually labeled from an artificial MR image (obtained from the BrainWeb). The first step of the general segmentation method is an affine matching between the atlas and the patient MRI (usually T1). The recovered transformation is then refined using nonrigid registration, and applied to the atlas labelization in order to obtain a segmentation of the patient image.
However, due to its multisubject nature, the nonrigid registration problem is generally difficult. Some registration algorithms [1] using inhomogeneous regularization were recently introduced. It applies a spatialdependent regularization: strong where the local deformability is low, and weak where it is high. Moreover, using tensors, the regularization can be directiondependent: the amount of deformation allowed can be separately tuned along spatial directions. However, the brain variability between subjects is not well known and this algorithm used a heuristic map of the deformability.
We have introduced in [2] a new framework to compute deformability statistics (either scalar or tensor based) over a database of patient MRI. The statistics are based on the jacobian matrix of the transformations:
(1) 
(2) 
where the first equation is the scalar measure, the second is the tensorbased measure and is the tensor associated with the Jacobian matrix. Using these two measures in the pipeline shown in figure 1, we are able to compute statistics over our database. To have more information, see our article [2].

These statistics are then used to guide the regularization of the deformation field. Thanks to this method, we obtain results both quantitatively and qualitatively better results (see figure 1).
