Intensity inhomogeneity causes many difficulties in image segmentation and the understanding of magnetic resonance (MR) images. Bias correction is an important method for addressing the intensity inhomogeneity of MR images before quantitative analysis. In this paper, a modified model is developed for segmenting images with intensity inhomogeneity and estimating the bias field simultaneously. In the modified model, a clustering criterion energy function is defined by considering the difference between the measured image and estimated image in local region. By using this difference in local region, the modified method can obtain accurate segmentation results and an accurate estimation of the bias field. The energy function is incorporated into a level set formulation with a level set regularization term, and the energy minimization is conducted by a level set evolution process. The proposed model first appeared as a two-phase model and then extended to a multi-phase one. The experimental results demonstrate the advantages of our model in terms of accuracy and insensitivity to the location of the initial contours. In particular, our method has been applied to various synthetic and real images with desirable results.

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Breast cancer is one of the leading cause of death among women. Because of harmless and low cost, ultrasound is one of the most often used methods for breast cancer detection. However, tumor detection is very difficult in ultrasound images due to their specular nature and low quality of ultrasound images and most of the existing methods need to manually select ROI. In this paper, we proposed a novel automatic method for breast ultrasound (BUS) image tumor detection. We using the fuzzy logic theory and transform an US image into fuzzy domain. An iterative method is used to find threshold. The experimental results demonstrate that the proposed approach can automatically detect the tumor in BUS image with high accuracy. It can process low quality ultrasound image very well.

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Variational models involving Euler's elastica energy have a wide range of applications in digital image processing. Recently, fast methods, such as the proximal-augmented Lagrangian method (PALM), have been successfully used to solve nonlinear higher order models for image restoration. In this paper, we extend fast method PALM to Euler's elastica deconvolution models with quadratic and nonquadratic fidelity terms. The proposed variational model can eliminate blur and noise and preserve edges while reducing the blocky and staircase artifacts during image restoration. We present an efficient and effective solution to the proposed minimization problems by a proximal-based numerical scheme. Our numerical experiments demonstrate several results on image deblurring and denoising, which shows a clear improvement of the proposed model over standard variational models such as total variation and Hessian-based model. INDEX TERMS Augmented Lagrangian method, Euler's elastica regularization, proximal method, image deconvolution.