Abstract.We propose an algorithm allowing the construction of a structural representation of the cortical topography from a Tl-weighted 3D MR image. This representation is an attributed relational graph (ARG) inferred from the 3D skeleton of the object made up of the union of gray matter and cerebro-spinal fluid enclosed in the brain hull. In order to increase the robustness of the skeletonization, topological and regularization constraints are included in the segmentation process using an original method: the homotopically deformable regions. This method is halfway between deformable contour and Markovian segmentation approaches. The 3D skeleton is segmented in simple surfaces (SSs) constituting the ARG nodes (mainly cortical folds). The ARG relations are of two types: first, the SS pairs connected in the skeleton; second, the SS pairs delimi6ng a gyrus. The described algorithm has been developed in the frame of a project aiming at the automatic detection and recognition of the main cortical sulci. Indeed, the ARG is a synthetic representation of all the information required by the sulcus identification. This project will contribute to the development of new methodologies for human brain functional mapping and neurosurgery operation planning.

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Summary:We propose a fully nonsupervised methodol ogy dedicated to the fast registration of positron emission tomography (PET) and magnetic resonance images of the brain. First, discrete representations of the surfaces of interest (head or brain surface) are automatically ex tracted from both images. Then, a shape-independent sur face-matching algorithm gives a rigid body transforma tion, which allows the transfer of information between both modalities. A three-dimensional (3D) extension of the chamfer-matching principle makes up the core of this surface-matching algorithm. The optimal transformation is inferred from the minimization of a quadratic general ized distance between discrete surfaces, taking into ac count between-modality differences in the localization of A number of approaches to the analysis of phys iological data obtained from positron emission to mography (PET) require complementary anatomi cal information from another modality such as mag netic resonance imaging (MRI) (Mazziotta et aI., 1991). Since scans are not (and often cannot be) performed with perfectly reproducible patient posi tioning, increasing needs for accurate and reproduc ible three-dimensional (3D) registration methods have appeared. Most of the existing methods in volve user interaction. Procedural approaches, which rely on specific acquisition protocols [stereo taxic frames (Clarysse et aI., 1991), headholders (Bettinardi et aI., 1991), external markers (Koeppe et aI., 1991; Maguire et aI., 1991)], suffer from lack of versatility. Retrospective assisted approaches, 749 the segmented surfaces. The minimization process is ef ficiently performed via the precomputation of a 3D dis tance map. Validation studies using a dedicated brain shaped phantom have shown that the maximum registra tion error was of the order of the PET pixel size (2 mm) for the wide variety of tested configurations. The soft ware is routinely used today in a clinical context by the physiCians of the Service Hospitalier Frt!deric loliot (> 150 registrations performed). The entire registration process requires -5 min on a conventional workstation.

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We propose an algorithm allowing the construction of a high level representation of the cortical topography from a Ti-weighted 3D MR image. This representation is an attributed relational graph (ARG) inferred from the 3D skeleton of the object made up of the union of gray matter and cerebro-spinal fluid enclosed in the brain hull. In order to increase the robustness of the skeletonization, topological and regularization constraints are included in the segmentation process using an original method: the homotopically deformable regions. This method is halfway between deformable contour and Markovian segmentation approaches. The 3D skeleton is segmented in simple surfaces (SSs) constituting the ARG nodes (mainly sulcus parts). The ARG relations are of two types: first, the SSs pairs connected in the skeleton; second, the SSs pairs delimiting a gyrus. The described algorithm has been developed in the frame of a project aiming at the automatic detection and recognition of the main cortical sulci. Indeed, the ARG is a synthetic representation of all the information required by the sulcus identification. This project will contribute to the development of new methodologies for the human brain functional mapping.

A simple, low cost, and universal automatic 3 -D acquisition system was developped using active triangulation. Its main characteristics are:-its speed of acquisition (about 1 minute per object), -the density of its sampling (from 30,000 to 250,000 measures per object), -the structured lattice of the resulting data (distributed on parallel and meridian equidistant lines). From these data, it is possible to use several techniques of surface approximation to

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