Accurate multi-class image segmentation using weak continuity constraints and neutrosophic set

Abstract In this paper, we propose a multi-class image segmentation method based on uncertainty management by weak continuity constraints and neutrosophic set (NS). To manage the uncertainties in the segmentation process, an image is mapped into the NS domain. In the NS domain, the image is represented as true, false, and indeterminate subsets. In the proposed method, accurate segmentation is achieved by minimizing an energy function in the NS domain. The theory of weak continuity constraints is integrated into the NS domain to generate the energy function. The weak continuity constraints take into account the spatial and boundary information of the segments to manage the uncertainties in the segmentation process. The proposed method can automatically segment an image iteratively without any prior knowledge about the number of classes. The performance of the proposed method is compared with state-of-the-art methods and it is found to be quite satisfactory. The proposed method’s performance under noise perturbations is statistically validated using a modified Cramer–Rao bound. The bound predicts the performance of image segmentation algorithms and serves as a benchmark for segmentation results.