In this paper, we present the concept of diffusing models to perform image-to-image matching. Having two images to match, the main idea is to consider the objects boundaries in one image as semi-permeable membranes and to let the other image, considered as a deformable grid model, diffuse through these interfaces, by the action of effectors situated within the membranes. We illustrate this concept by an analogy with Maxwell's demons. We show that this concept relates to more traditional ones, based on attraction, with an intermediate step being optical flow techniques. We use the concept of diffusing models to derive three different non-rigid matching algorithms, one using all the intensity levels in the static image, one using only contour points, and a last one operating on already segmented images. Finally, we present results with synthesized deformations and real medical images, with applications to heart motion tracking and three-dimensional inter-patients matching.

We present a completely automatic method to build stable average anatomical models of the human brain using a set of magnetic resonance (MR) images. The models computed present two important characteristics: an average intensity and an average shape, both in a single image. We provide results showing convergence toward the centroid of the image set used for the computation of the model. In particular, the RMS distances between the model and the MR images contained in the set stabilize in a range of 2.88 to 3.36 mm from a range of 4.62 to 5.51 mm initially after only one iteration. As for the influence of the reference image chosen for the model construction, this is minimal with differences of about 1.0 mm, from approximately 3.5 mm initially. These results ensure the usefulness of our approach.

I n this paper, we propose a new method to estimate a rigid transform from a set of 3 -0 matched points OT matched frames, and we concentrate on the analysis of the uncertainty of the estimated transform. The theoretical contributions are an intrinsic model of noise for tran,sfomnations based on composition rather than addition, a unified formalism for the estimation of both the rigid transform and its covariance matrix for points or frames correspondences, and also a statistical validation method to verify the error estimation, which applies even when n o "ground truth" is available. The practical contribution as the validation of OUT transf o r m estimation method in the case of 3-D medical images, which shows that a precision of the registration, far below the size of a voxel, can be achieved.

The study presented in this paper tests the hypothesis that the combination of a global similarity transformation and local free-form deformations can be used for the accurate segmentation of internal structures in MR images of the brain. To quantitatively evaluate our approach, the entire brain, the cerebellum, and the head of the caudate have been segmented manually by two raters on one of the volumes (the reference volume) and mapped back onto all the other volumes, using the computed transformations. The contours so obtained have been compared to contours drawn manually around the structures of interest in each individual brain. Manual delineation was performed twice by the same two raters to test inter- and intrarater variability. For the brain and the cerebellum, results indicate that for each rater, contours obtained manually and contours obtained automatically by deforming his own atlas are virtually indistinguishable. Furthermore, contours obtained manually by one rater and contours obtained automatically by deforming this rater's own atlas are more similar than contours obtained manually by two raters. For the caudate, manual intra- and interrater similarity indexes remain slightly better than manual versus automatic indexes, mainly because of the spatial resolution of the images used in this study. Qualitative results also suggest that this method can be used for the segmentation of more complex structures, such as the hippocampus.

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