Image segmentation is a fundamental and challenging task in image processing and computer vision. The colour image segmentation is attracting more attention as the colour image provides more information than the grey image. A variational model based on a convex K-means approach to segment colour images is proposed. The proposed variational method uses a combination of l 1 and l 2 regularizers to maintain edge information of objects in images while overcoming the staircase effect. Meanwhile, our one-stage strategy is an improved version based on the smoothing and thresholding strategy, which contributes to improving the accuracy of segmentation. The proposed method performs the following steps. First, the colour set which can be determined by human or the K-means method is specified. Second, a variational model to obtain the most appropriate colour for each pixel from the colour set via convex relaxation and lifting is used. The Chambolle-Pock algorithm and simplex projection are applied to solve the variational model effectively. Experimental results and comparison analysis demonstrate the effectiveness and robustness of the method. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Image segmentation is a fundamental and challenging task in image processing and computer vision. The color image segmentation is attracting more attention due to the color image provides more information than the gray image. In this paper, we propose a variational model based on a convex K-means approach to segment color images. The proposed variational method uses a combination of l1 and l2 regularizers to maintain edge information of objects in images while overcoming the staircase effect. Meanwhile, our onestage strategy is an improved version based on the smoothing and thresholding strategy, which contributes to improving the accuracy of segmentation. The proposed method performs the following steps. First, we specify the color set which can be determined by human or the K-means method. Second, we use a variational model to obtain the most appropriate color for each pixel from the color set via convex relaxation and lifting. The Chambolle-Pock algorithm and simplex projection are applied to solve the variational model effectively. Experimental results and comparison analysis demonstrate the effectiveness and robustness of our method.

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