Variational image segmentation model coupled with image restoration achievements

• Provide a new methodology and a new model for multiphase image segmentation.
• Extend the piecewise constant Mumford–Shah model to handle blurry case easily.
• Has the ability to segment images with Gaussian, Poisson, and impulsive noises.
• Effective in segmenting vector-valued image and image observed with information loss.
• The convergence of the AM algorithm with three variables adopted is proved.

Image segmentation and image restoration are two important topics in image processing with a number of important applications. In this paper, we propose a new multiphase segmentation model by combining image restoration and image segmentation models. Utilizing aspects of image restoration, the proposed segmentation model can effectively and robustly tackle images with a high level of noise or blurriness, missing pixels or vector values. In particular, one of the most important segmentation models, the piecewise constant Mumford–Shah model, can be extended easily in this way to segment gray and vector-valued images corrupted, for example, by noise, blur or information loss after coupling a new data fidelity term which borrowed from the field of image restoration. It can be solved efficiently using the alternating minimization algorithm, and we prove the convergence of this algorithm with three variables under mild conditions. Experiments on many synthetic and real-world images demonstrate that our method gives better segmentation results in terms of quality and quantity in comparison to other state-of-the-art segmentation models, especially for blurry images and those with information loss.