目的 由于灰度不均匀图像在不同目标区域的灰度分布存在严重的重叠，对其进行分割仍然是一个难题；同时，图像中的噪声严重降低了图像分割的准确性。因此，传统水平集方法无法鲁棒、精确、快速地对具有灰度不均匀性和噪声的图像进行分割。针对这一问题，提出一种基于局部区域信息的快速水平集图像分割方法。方法 灰度不均匀图像通常被描述为一个分段常数图像乘以一个缓慢变化的偏移场。首先，通过一个经过微调的多尺度均值滤波器来估计图像的偏移场，并对图像进行预处理以减轻图像的不均匀性；然后，利用基于偏移场校正的方法和基于局部区域信息拟合的方法分别构建能量项，并利用演化曲线轮廓内外图像灰度分布的重叠程度，构建权重函数自适应调整两个能量项之间的权重；最后，引入全方差规则项对水平集进行约束，增强了数值计算的稳定性和对噪声的鲁棒性，并通过加性算子分裂策略实现水平集快速演化。结果 在具有不同灰度不均匀性和噪声图像上的分割结果表明，所提方法不但对初始轮廓的位置、灰度不均匀性和各种噪声具有较强的鲁棒性，而且具有高达94.5%的分割精度和较高的分割效率，与传统水平集方法相比分割精度至少提高了20.6%，分割效率是LIC（local intensity clustering）模型的9倍；结论 本文提出一种基于局部区域信息的快速水平集图像分割方法。实验结果表明，与传统水平集方法相比具有较高的分割精度和分割效率，可以很好地应用于具有灰度不均匀和噪声的医学、红外和自然图像等的分割。

Objective Image segmentation is important in computer vision and image processing. The level-set method has been widely used for image segmentation because it can handle complex topological changes. Intensity inhomogeneity, which is usually caused by a defect in the imaging device or illumination variation, is a common phenomenon in real-world images. Images with intensity inhomogeneity are difficult to segment due to the overlap of the intensity distributions between different object regions. Meanwhile, noise severely reduces the segmentation accuracy. Therefore, the traditional level-set method cannot robustly, accurately, and quickly segment images with intensity inhomogeneity and noise. To address this problem, a fast level-set method based on local region information is proposed for segmenting images in the presence of intensity inhomogeneity and noise. Method An intensity inhomogeneous image is usually described as a piecewise constant image multiplied by a slowly varying bias field. The bias field can be estimated by a multi-scale mean filter because it varies slowly over the entire image domain. However, the traditional multi-scale mean filter utilizes a fixed number of scales to estimate the bias field; hence, it may not correctly estimate the bias field for a small-sized image with severe intensity inhomogeneity. Therefore, a fine-tuned multi-scale mean filter is utilized to roughly estimate the bias field and preprocess the image to mitigate image intensity inhomogeneity. Then, the processed image is used to construct a bias correction-based pressure function, with which the image with weak intensity inhomogeneity can be quickly segmented and the bias field can be estimated simultaneously. The original image is also utilized to design a local region-based pressure function that can provide accurate segmentation for the region near the object boundaries. In addition, image entropy is integrated into the local region-based pressure function to extract additional local intensity information from the boundary region. The two pressure functions proposed are then embedded into the level-set framework to build two energy terms. A weight function is also constructed to balance the two energy terms by using the coefficient of joint variation that estimates the degree of overlap of the intensity distributions between the image regions inside and outside the contour of the evolution curve. The weight function can adaptively adjust the weights of the two energy terms according to the overlap of the intensity distributions between different image segmentation regions, thereby improving the efficiency and accuracy of the model in segmenting intensity inhomogeneity images. Subsequently, the total variance-based regularization function is utilized to regularize the evolution of the level-set function, thus enhancing the stability of numerical calculation and reducing the impact of noise. The two proposed energy terms and the regularization term are used to construct the final energy function. By minimizing the final energy function, the proposed method can segment the image and estimate the bias field simultaneously. In the numerical implementation, the additive operator splitting (AOS) scheme is employed to decompose the level-set evolution equation into linear and nonlinear differential equations. The linear differential equation can be quickly solved by the explicit iterative scheme, and the nonlinear differential equation can be solved quickly by the implicit iterative scheme and fast Fourier transform. Moreover, a Gaussian filter with a small-scale parameter is utilized to smooth the level-set function and reduce the impact of noise. Result To demonstrate the proposed method's performance, the method is applied to several synthetic, infrared, and medical images with intensity inhomogeneity and noise and compared with traditional level-set-based segmentation models. The proposed method is applied on five images with intensity inhomogeneity or noise to qualitatively analyze its effectiveness. Results show that the images are correctly segmented, and the bias fields can be accurately estimated simultaneously. Then, the proposed method is applied to three inhomogeneous images with different initial contours to demonstrate its robustness to the initial contour. The method is also utilized to segment two types of images with different degrees of intensity inhomogeneity and quantitatively compared with several level-set-based segmentation methods to demonstrate the proposed method's robustness to the degree of intensity inhomogeneity. In addition, the proposed method is applied to homogenous and inhomogeneous images with different kinds of noise and compared with several level-set-segmentation methods to demonstrate its robustness to noise. The effectiveness of the proposed weight function is also analyzed. Finally, the proposed method is quantitatively analyzed on several images with intensity inhomogeneity and noise. Compared with traditional level-set methods, the proposed method obtains the highest segmentation accuracy of 94.5%, and it requires the least number of iterations and the second least amount of computation time. The segmentation accuracy is at least 20.6% higher than that of traditional level-set methods, and the segmentation efficiency is nine times higher than that of the LIC model. Experimental results demonstrate that compared with traditional level-set methods, the proposed method is not only robust to the position of the initial contour and various noises but also has higher segmentation accuracy and efficiency for images with noise and different degrees of intensity inhomogeneity. Conclusion This study proposes a fast level-set image segmentation method based on local region information to segment images in the presence of noise and intensity inhomogeneity. The fine-tuned multi-scale mean filter can roughly estimate the bias field. The two proposed pressure functions can provide appropriate local information to segment images with different degrees of intensity inhomogeneity. The regularization term makes the proposed method robust to noise, and the AOS scheme accelerates the convergence of the proposed method. Experimental results show that the proposed method can effectively, robustly, accurately, and efficiently segment images with intensity inhomogeneity and noise. The proposed method can be applied to the segmentation of medical, infrared, and natural images with intensity inhomogeneity and noise.