Domain partitioning level set surface for topology constrained multi-object segmentation

The key feature of the geometric deformable models (GDMs) is that they naturally allow topological changes during the curve evolution process. However, for multiple objects with extremely small spatial separations, these GDMs would not be able to form separate final contour for each of the object because of the spatial limitation imposed by the finite difference computational grid. Further, a GDM contour could possibly leak out from the weaker edges of the target object and evolve towards nearby stronger edges of another object. In this paper, we present a topology constraining geometrical deformable model scheme to address these two situations. Utilizing the prior knowledge on the number of targets and their rough spatial positioning, we add an additional domain partitioning level set surface (DPLSS) which seeks between-object gaps and hence constrains the each boundary finding level set surface (BFLSS) to reside within its own designated region and evolve towards the respective object boundary. Relying on adaptive mesh-free particle representations of the analysis domains for DPLSS and BFLSSs, the relative spatial separation between each BFLSS and DPLSS can be flexibly and effectively magnified. Further, the evolution of the DPLSS and BFLSSs is processed in piecewise continuous fashion, through moving lease squares (MLS) approximations. to ensure high accuracy. Experiment results with synthetic and real images show great promise of this effort.