A variational image segmentation model with intensity correction in the presence of high level multiplicative noise
Yamei Zhou, Zhichang Guo, Yao Li, Boying Wu · Inverse Problems and Imaging · 2025
The presence of multiplicative noise can result in a reduction in the contrast between the segmentation region and the background region, which presents a significant challenge in the development of an effective segmentation method. Some classical methods employ a two-step approach. The initial step involves the removal of multiplicative noise from the image, thereby enhancing the contrast. The subsequent step utilises classical segmentation methods to segment the image. However, it is difficult to achieve an effective balance between the two steps. For this reason, this paper presents a novel approach that integrates the image segmentation term with the denoising term in a variational level set framework. In particular, a nonlinear transformation function is introduced into the denoising fitting term with the objective of correcting the intensity range and improving the quality of the image. To solve this variational model, we employ the alternating iterative method to simultaneously perform the segmentation and denoising tasks while enhancing the image. To efficiently solve our proposed model, we first decouple it into several easily solvable subproblems and then employ the additive operator splitting (AOS) algorithm and the scalar auxiliary variable (SAV) algorithm to solve them. Compared to the classical segmentation models, the proposed model provides higher accuracy in segmenting images degraded by multiplicative noise and images with intensity inhomogeneity.