The task of partitioning convex shape objects from images is a hot research topic, since this kind of object can be widely found in natural images. The difficulties in achieving this task lie in the fact that these objects are usually partly interrupted by undesired background scenes. To estimate the whole boundaries of these objects, different neural networks are designed to ensure the convexity of corresponding image segmentation results. To make use of well-trained neural networks to promote the performances of convex shape image segmentation tasks, in this paper a new image segmentation model is proposed in the variational framework. In this model, a fuzzy membership function, instead of a classical binary label function, is employed to indicate image regions. To ensure fuzzy membership functions can approximate to binary label functions well, an edge-preserving smoothness regularizer is constructed from an off-the-shelf plug-and-play network denoiser, since an image denoising process can also be seen as an edge-preserving smoothing process. From the numerical results, our proposed method could generate better segmentation results on real images, and our image segmentation results were less affected by the initialization of our method than the results obtained from classical methods.

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