Intensity inhomogeneity (IIH) and noise are ubiquitous in images acquired by a variety of imaging modalities, which pose an ongoing challenge for segmentation methods used in many applications. This paper proposes a level set evolution equation based on fractional derivative to address the IIH and noise issues in image segmentation, which integrates the information from the input and guidance images. The proposed model is a linear diffusion equation of level set function with nonlinear edge-stopping and guidance sources, in which the edge-stopping source is derived from the input image and a local statistical model (Bayesian formulation) in the level set framework, whereas the guidance source is derived from the guidance image and the fitting term of the popular Chan-Vese model. The guidance source ensures swift contour movement toward the boundary of the objects and enhances the robustness to noise and contour initialization, while the edge-stopping source is used to stop the evolving contour on the boundary of the objects later in the evolution. To tackle the challenge of obtaining accurate guidance images for many applications, an adaptive variable-order of fractional derivative robust to IIH and noise is introduced to generate the desired guidance image from the input image. The proposed diffusion equation with sources is solved numerically by the series splitting method and finite difference scheme. Experimental results on synthetic and real images show that the proposed model has higher performance in terms of accuracy and efficiency of segmentation, compared to several state-of-the-art level set models.

中文翻译：

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基于分数引导的水平集演化，用于强度不均匀的噪声图像分割

强度不均匀性 (IIH) 和噪声在各种成像方式采集的图像中普遍存在，这对许多应用中使用的分割方法提出了持续的挑战。本文提出了一种基于分数阶导数的水平集演化方程来解决图像分割中的IIH和噪声问题，该方程集成了来自输入图像和引导图像的信息。所提出的模型是具有非线性边缘停止和引导源的水平集函数的线性扩散方程，其中边缘停止源是从输入图像和水平集框架中的局部统计模型（贝叶斯公式）导出的，而引导源来源于流行的Chan-Vese模型的引导图像和拟合项。引导源确保轮廓向对象边界快速移动，并增强对噪声和轮廓初始化的鲁棒性，而边缘停止源用于在演化后期停止对象边界上的演化轮廓。为了应对为许多应用获得准确引导图像的挑战，引入了对 IIH 和噪声具有鲁棒性的自适应变阶分数导数，以从输入图像生成所需的引导图像。所提出的带源扩散方程通过级数分裂法和有限差分格式进行数值求解。合成图像和真实图像的实验结果表明，与几种最先进的水平集模型相比，所提出的模型在分割的准确性和效率方面具有更高的性能。