Cellular complexes: a tool for 3d homotopic segmentation in brain images

Cortex surface modeling is important in several domains including for solving the inverse problem in EEG and MEG. Whereas MRI can be used to build such a model, problems arise due to the partial volume effect that makes the cortex surface disappear in the foldings. To solve this problem the authors use a model, based on cellular complexes, that has good topological properties. This model allows to represent any object which is the combination of volumes, surfaces and curves in a discrete space. The authors define homotopic deformations on such a model by adapting the notion of simple points to their model. They use this homotopic deformable model to segment the cortex surface and to preserve the spherical topology of the surface during the deformation process. The model is initialized from the external brain surface and is then deformed towards the minimum value of an energy function that pushes the surface inside the foldings