No abstract

No abstract

Abstract. In inter-subject registration, one often lacks a good model of the transformation variability to choose the optimal regularization. Some works attempt to model the variability in a statistical way, but the re-introduction in a registration algorithm is not easy. In this paper, we interpret the elastic energy as the distance of the Green-St Venant strain tensor to the identity, which reflects the deviation of the local deformation from a rigid transformation. By changing the Euclidean metric for a more suitable Riemannian one, we define a consistent statistical framework to quantify the amount of deformation. In particular, the mean and the covariance matrix of the strain tensor can be consistently and efficiently computed from a population of non-linear transformations. These statistics are then used as parameters in a Mahalanobis distance to measure the statistical deviation from the observed variability, giving a new regularization criterion that we called the statistical Riemannian elasticity. This new criterion is able to handle anisotropic deformations and is inverse-consistent. Preliminary results show that it can be quite easily implemented in a non-rigid registration algorithms.

Abstract. Warping a digital atlas toward a patient image allows the simultaneous segmentation of several structures. This may be of great interest for cerebral images, since the brain contains a large number of small but important structures (optical nerves, grey nuclei, etc.). One important application is the conformal radiotherapy of cerebral tumor, where a precise delineation of all these structures is required. However, in this case, the variability induced by the tumor or a surgical resection, that are not present in the digital atlas, prevents an accurate registration between the atlas and the patient images. Since our registration method allows to locally control the amount of regularization, we are able to explicitly introduce those areas in the warping process. For computational efficiency, we have created a parallel implementation that can be used from the clinical environment through a grid interface.

Abstract. Deforming a digital atlas towards a patient image allows the simultaneous segmentation of several structures. Such an intersubject registration is difficult as the deformations to recover are highly inhomogeneous. A priori information about the local amount of deformation to expect is precious, since it allows to optimally balance the quality of the matching versus the regularity of the deformation. However, intersubject variability makes it hard to heuristically estimate the degree of deformation. Indeed, the sizes and shapes of various structures differ greatly and their relative positions vary in a rather complex manner. In this article, we perform a statistical study of the deformations yielded by the registration of an image database with an anatomical atlas, and we propose methods to re-inject this information into the registration. We show that this provides more accurate segmentations of brain structures.