Multi-object segmentation of brain structures in 3D MRI using a computerized atlas

We present a hierarchical multi-object surface-based deformable atlas for the automatic localization and identification of brain structures in MR images. The atlas is built as a multi-object set of 3D triangulated closed surfaces, each representing a given brain structure, and sharing its faces with neighboring structures. To support such a topology unambiguously, the multi-object mesh is build upon a Face Centered Cubic grid to maintain a unique kind of shared boundary elements. Hence, the voronoi neighborhoods of grid points are rhombic dodecahedra so that neighboring grid points always share a common face of a given size (cubic grid points can also share an edge or a corner). The registration of the atlas to a patient's MR image is done in two steps: a global registration based on the matching of the cortical surface and the ventricles followed by a multi-object active surface deformation to account for the local shape deformations. First, the cortical surface and the ventricular system are segmented using directional watersheds and mathematical morphology to simplify the shape of the objects. The registration criterion is then defined as a distance measure between these surfaces and the equivalent surfaces in the Computerized Brain Atlas (CBA, University hospital of Karolinska, Sweden) database. The distance measure is computed using a precomputed distance map from any point to the atlas’ reference surfaces. The global transformation is a linear combination of 30 de-correlated base functions whose coefficients are optimized by gradient-based minimization of the distance criterion. This provides us with an accurate localization of most structures in images of healthy patients. Experiments show that the localization of sub-cortical structures is very good, but the transformation is too global to account for local shape differences. Most sulci can be identified, their locations are correct, but their shape often differs significantly from the image data, especially on the top slices. As a refinement step, the globally registered atlas surfaces are locally deformed in a hierarchical way using multi-object active surfaces. The external force driving a surface towards the edges of the structure to be segmented in the image is a decreasing function of the gradient, and also includes prior information such as the expected gradient sign and the mean expected gray level the surface should surround. The energy is minimized by solving the corresponding Euler-Lagrange equation iteratively with finite element methods. The surfaces of the multi-object mesh are deformed in a hierarchical way, starting with objects having very well defined features in the image to objects showing less obvious features. Experiments involving several sub-cortical atlas objects are presented.