Segmentation through point-based multiscale deformable model

We propose a local weak form formulation for the geometric deformable model (GDM) which is capable of achieving robust segmentation results for noisy and broken edges. The local weak form partial differential equation (PDE) is solved on the analysis/evolution domain which is adaptively sampled by unstructured point cloud for improved accuracy and/or reduced computational cost. The fundamental power of this strategy rests with the explicit integration of neighboring information when constructing inter-point constraint and image-derived evolution force for each front point within a local influence domain adaptively determined by geometry and image information. As a result, this local weak form GDM naturally unifies the essences of the geometric and parametric snakes through automatic local scale selection at each contour point, 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 evolution forces. Experimental results on synthetic and real images demonstrate its superior performance.