Topology Preserving Geometric Deformable Models for Brain Reconstruction

Abstract

Geometric deformable models, implemented via level-set methods, have advantages over parametric models due to their intrinsic behavior, parameterization independence, topological flexibility, lack of self-intersections, and good numerical stability. But topological flexibility actually hinders the application of geometric deformable models in cases where the model must conform to the known topology of the final object. In this chapter, we present a new geometric deformable model that preserves topology using the simple point concept from digital topology. The new model, which we refer to as topology preserving geometric deformable model (TGDM), conforms to the topology constraint while maintaining other desirable characteristics of standard geometric deformable models including sub-pixel accuracy and production of non-intersecting curves (or surfaces). We then use TGDM to find the inner, central, and outer surfaces of the human brain cortex from magnetic resonance (MR) images. The resulting algorithm is fast and numerically stable, and yields accurate brain surface reconstructions that are guaranteed to be topologically correct and free from self-intersections.