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The energy function of active contour model is not convex, so the solution of a minimization problem is prone to fall into a local minimum. Dealing with the problem, this paper proposed a novel convex active contour model for interactive color image segmentation. It defined a new energy function including not only image edge and color information, but also a spatial information term which was adaptively fused with the color information. It defined the spatial information term by fuzzy connectedness and introduced to get more accurate segmentation results. In the energy numerical minimization process, it used split Bregman method to obtain a global solution. Experimental results demonstrate that the proposed method can accurately and quickly get desired segmentation results. [ABSTRACT FROM AUTHOR]