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To achieve robustness against different images, a novel region-based geometric deformable model framework employing neighboring information constraints is proposed. The fundamental power of this strategy makes uses of the image information at the support domain around each point of interest, thus effectively enlarges the capture range of each point to have a better regional understanding of the information within its local neighborhood. In other words, we establish the Mumford-Shah energy functional on each image point with its local neighborhood in a way such that it is capable of providing sufficient information to define a desired segmentation which is robust against intensity inhomogeneity and noise impact. The resulting partial differential equation is solved numerically by the finite differences schemes on pixel-by-pixel domain. Experimental results on synthetic and real images demonstrate its superior performance.