Additive-Bias-Correction Variational Model for Noisy and Intensity-Inhomogeneous Image Segmentation
Po‐Wen Hsieh, Chung-Lin Tseng, Suh‐Yuh Yang · SIAM Journal on Imaging Sciences · 2025
Abstract. Segmenting noisy and intensity-inhomogeneous images presents a significant challenge in image segmentation. This paper proposes a novel additive-bias-correction (ABC) variational segmentation model combined with an efficient iterative convolution-thresholding (ICT) solver, termed the ABC-ICT method, to address this issue. The input image is assumed to be additively decomposed into three components: a homogeneous structure, a bias field characterizing the intensity inhomogeneity, and imaging noise. Based on this additive decomposition assumption, our variational minimization model, implemented using the ICT method, consists of four energy parts: total variation denoising, local image smoothing, local bias-corrected segmentation, and contour length regularization, enhancing its robustness to noise and intensity inhomogeneity. Due to the use of characteristic functions, the proposed ABC-ICT method typically converges faster than the commonly used level set approach, naturally handles topological changes, and facilitates multiphase segmentation. Additionally, it offers several advantages, including simultaneous image segmentation, intensity inhomogeneity correction, and noise removal. Moreover, the total energy decays with each iteration, ensuring that the iterative scheme always converges to a minimum. We validate the unconditionally energy-decaying property both theoretically and experimentally. Numerical experiments and comparisons with existing models demonstrate the effectiveness and efficiency of the proposed model.