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• A variational level set model based on additive image decomposition is proposed. • A novel indirect regularization scheme is introduced in the model. • The proposed model can effectively segment intensity inhomogeneous images with noise. The variational level set model is widely used in image segmentation. However, it suffers from the limited performance when the images are contaminated by noise and intensity inhomogeneity. To solve this problem, a variational level set model based on additive decomposition is proposed in this paper. First, we decompose the image into three components: structure, intensity inhomogeneity and noise, which are regularized by different metrics. Specially, the structure component is regularized as a piecewise constant function in bounded variation (BV) space; the intensity inhomogeneity is modeled as a smooth function that is regularized by H 1 space, and the residual containing noise is measured by L 2 norm. Furthermore, a new indirect regularization term for level set function is designed to enhance the accuracy of the segmentation outcomes. And then, alternate direction iteration algorithm combining with gradient descent and ADMM to solve the proposed model. Experiments on both synthetic and real images validate the proposed model. Compared with five state-of-the-art models, the experimental results demonstrate that the proposed model exhibits the significant improvement in both accuracy and efficiency, outperforming all other methods. Quantitative evaluations show the average segmentation coefficients for Jaccard, Dice and Accuracy against ground truth are 0.93, 0.95 and 0.96, respectively, and the average running time is 0.80 seconds, further confirming its superior performance. [ABSTRACT FROM AUTHOR]

Total variation (TV) regularization model has the excellent performance in noise-removing and edge-preserving. However, it often yields staircase artifacts in the smooth region of the restorations. To attack this problem, we propose a generalized hybrid nonconvex variational regularization model in this paper, which utilizes two nonconvex regularizers to impose the priors to the two different components of the images, respectively. One is nonconvex TV regularizer that measures the piecewise constant component of the input image, and the other is nonconvex Laplacian regularizer that models the piecewise smooth component. New model inherits the advantages of the nonconvex regularization and the first- and second-order hybrid variational regularization, which can well remove the noises while preserving edges and reducing staircase artifacts. To solve this nonconvex minimization problem efficiently, we propose a first-order algorithm based on alternating direction method of multipliers (ADMM) combining with majorization–minimization (MM) scheme. In addition, a sufficient condition for the convergence of the proposed algorithm is provided. In the experiments, we compare the proposed model with several state-of-the-art image denoising models, numerical results illustrate the effectiveness of the proposed model and algorithm for both synthetic and real images in terms of peak signal to noise ratio (PSNR) and structural similarity (SSIM) indexes. [ABSTRACT FROM AUTHOR]