Balanced Phase Field model for Active Surfaces

Abstract

In this paper we present a balanced phase field model for active surfaces. This work is devoted to the generalization of the Balanced Phase Field Model for Active Contours devised to eliminate the often undesirable curvature-dependent shrinking of the zero level set while maintaining the smooth interface necessary to calculate the fundamental geometric quantities of the represented contour. As its antecedent work, the proposed model extends the Ginzburg-Landau phase field energy with a higher order smoothness term. The relative weights are determined with the analysis of the level set motion in a curvilinear system adapted to the zero level set. The proposed model exhibits strong shape maintaining capability without significant interference with the active (e.g. a segmentation) model.