In this paper, a novel level set approach is presented to segment only indicated objects from natural color images. To solve this challenging problem, users first initialize a contour inside the concerned object. The proposed level set model is then applied to achieve the object containing this initial region regardless of its shape and size. In our novel framework, the energy functional is a combination of two energy terms based on Bhattacharya flow and graph partitioning active contour. So that movement of the contour can be controlled toward object boundaries by correlative relationships between the interested region and surroundings. The experimental results obtained from our natural image collection show that the suggested method yields more accurate and better performance when comparing to other segmentation algorithms.