Weighted nuclear norm-driven segmentation of images with intensity inhomogeneity

Image segmentation aims to partition images into semantically meaningful regions. However, noise and intensity inhomogeneity often diminish the contrast between regions of interest (ROI) and background regions, leading to weak boundary artifacts that degrade segmentation accuracy. To address this challenge, we propose a novel segmentation model that extends the classical Chan-Vese framework by explicitly modeling intensity inhomogeneity as a combination of multiplicative and additive components for integrated correction. In our approach, the inhomogeneity field is characterized using a weighted nuclear norm, while heat kernel convolution is employed to approximate the boundary length of the ROI. Furthermore, to handle the constraints associated with multiplicative inhomogeneity, we leverage Lagrangian multipliers to reformulate the problem as an unconstrained optimization, which is then efficiently solved using the alternating direction method. Extensive experiments on synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art techniques in both segmentation accuracy and computational efficiency, highlighting its strong potential for practical applications.