Variational Image Segmentation Model Coupled with Image Restoration Achievements

Image segmentation and image restoration are two important topics in image processing with great achievements. In this paper, we propose a new multiphase segmentation model by combining image restoration and image segmentation models. Utilizing image restoration aspects, the proposed segmentation model can effectively and robustly tackle high noisy images, blurry images, images with missing pixels, and vector-valued images. 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 missing pixels after coupling a new data fidelity term which comes from image restoration topics. It can be solved efficiently using the alternating minimization algorithm, and we prove the convergence of this algorithm with three variables under mild condition. Experiments on many synthetic and real-world images demonstrate that our method gives better segmentation results in comparison to others state-of-the-art segmentation models especially for blurry images and images with missing pixels values.Comment: 23 page

Image Segmentation with Multidimensional Refinement Indicators

We transpose an optimal control technique to the image segmentation problem. The idea is to consider image segmentation as a parameter estimation problem. The parameter to estimate is the color of the pixels of the image. We use the adaptive parameterization technique which builds iteratively an optimal representation of the parameter into uniform regions that form a partition of the domain, hence corresponding to a segmentation of the image. We minimize an error function during the iterations, and the partition of the image into regions is optimally driven by the gradient of this error. The resulting segmentation algorithm inherits desirable properties from its optimal control origin: soundness, robustness, and flexibility