We have developed a geometric deformable model that employs neighborhood influence to achieve robust segmentation for noisy and broken edges. The fundamental power of this strategy rests with the explicitly combination of regional inter-point constraints, image forces, and a priori boundary information for each geometric contour point within its adaptively determined local influence domain. This formulation thus naturally unifies the essences of the geometric and parametric snakes through automatic local scale selection, and exhibits their respective fundamental strengths of allowing stable boundary detection when the edge information is weak and possibly discontinuous, while maintaining the abilities to handle topological changes during front evolution. In particular, this paper presents an implementation of the method through local integration of the level set function and the image/prior-driven evolution forces, where the resulting partial differential equation is solved numerically using standard finite difference method. Experimental results on synthetic and real images demonstrate its superior performance.