MINIMAL-SURFACES - A GEOMETRIC 3-DIMENSIONAL SEGMENTATION APPROACH

A novel geometric approach for three dimensional object segmentation i s presented. The scheme is based on geometric deformable surfaces movi ng towards the objects to be detected, We show that this model is rela ted to the computation of surfaces of minimal area (local minimal surf aces). The space where these surfaces are computed is induced from the three dimensional image in which the objects are to be detected. The general approach also shows the relation between classical deformable surfaces obtained via energy minimization and geometric ones derived f rom curvature flows in the surface evolution framework. The scheme is stable, robust, and automatically handles changes in the surface topol ogy during the deformation. Results related to existence, uniqueness, stability, and correctness of the solution to this geometric deformabl e model are presented as well. Based on an efficient numerical algorit hm for surface evolution, we present a number of examples of object de tection in real and synthetic images.