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Graph cuts (GC) and the active contour model (ACM) have become two of the most important schemes in image segmentation. Recently, many researches tend to unify the two schemes to obtain new models for efficient calculation and global minimisation. However, the existing GC based ACMs not only cannot achieve local segmentation, but also suffer from the determination of the regularising parameter, which is used to balance the edge and region terms in the existing GC based ACMs. Proposed is a new GC based ACM (NGC-ACM) to solve the two problems above. First, a new energy function without the regularising parameter is proposed for segmentation, which avoids the edge and region balance problem. Secondly, through constructing a specified graph, the proposed model can achieve selective local or global segmentation, which not only can extract all the objects globally, but also can extract the desired object locally. Experiments on synthetic and real images demonstrate the advantages of the proposed NGC-ACM over the existing GC based ACMs like GC based geodesic active contours with region forces (GC-GACWRF) in solving the two problems above.