A convex selective segmentation model based on a piece-wise constant metric-guided edge detector function

The challenge of segmentation for noisy images, especially those that have light in their backgrounds, still exists in many advanced state-of-the-art segmentation models. Furthermore, it is a tedious activity and significantly difficult to segment such images. In this article, we offer and propose a novel variational model for the concurrent restoration and segmentation of noisy images that have intensity inhomogeneity and high contrast background illumination and light. The suggested concept combines the multi-phase segmentation technology with the statistical approach in terms of local region knowledge and details of circular regions that are, in fact, centered at every pixel to enable in-homogeneous image restoration. Nevertheless, the suggested approach is expressed as a fuzzy set and is resolved using the multiplier alternating direction minimization approach. Through several tests and numerical simulations with plausible assumptions, we have evaluated the correctness, accuracy, and resilience of the suggested model over various kinds of real and synthesized images in the existence of intensity inhomogeneity and light in the background. Additionally, the findings are contrasted with those from cutting-edge two-phase and multi-phase methods, proving the superiority of our proposed approach for images with noise, background light, and inhomogeneity. We observed that the three models considered in the comparison to our proposed model fail to properly segment the object of interest. Furthermore, the Jaccard similarity metric shows the capability of our model to handle accurate segmentation of complex shapes with intensity.