Brain magnetic resonance images (MRI) suffer from many artifacts such as noise and intensity inhomogeneity. Moreover, they contain an abundant amount of fine image structures, edges, and corners in various areas of the image. These anomalies and structural complexities affect the segmentation process of the brain MRI which is required by physicians for the diagnosis purpose. Recently, we have proposed a local Zernike moment (LZM)-based unbiased nonlocal means fuzzy C-means (LZM-UNLM-FCM) approach that has dealt with the noise artifact in the moment domain using the LZM approach. The method provides high segmentation results for the MR images corrupted with Rician noise. However, the method does not deal with the intensity inhomogeneity artifact effectively. Moreover, the method uses a regularization parameter that needs to be adjusted to obtain effective segmentation results. This paper presents an unsupervised local Zernike moment and unbiased nonlocal means-based bias corrected fuzzy C-means (LZM-UNLM-BCFCM) approach that deals with both noise and intensity inhomogeneity artifacts. The main concept behind the proposed method is to use the attractive properties of the LZMs to effectively filter the image by determining a large number of similar regions in an MR image which is mostly corrupted by Rician noise and intensity inhomogeneity. The ability of the LZMs to determine such regions in MR images consisting of fine tissue structures in any orientation is well utilized for dealing with the high levels of noise. The intensity inhomogeneity is removed by estimating the bias field pixel-by-pixel during the segmentation process using the filtered image without the use of regularization parameter. The bias field is estimated as a linear combination of the orthogonal polynomials in which the weights are obtained by minimizing the fuzzy objective function. Experimental results on both simulated and real MR images show the superiority of the proposed method as compared to other unsupervised state-of-the-art approaches.

脑磁共振图像（MRI）受到许多伪影的影响，例如噪音和强度不均匀性。而且，它们在图像的各个区域中包含大量的精细图像结构，边缘和拐角。这些异常和结构的复杂性影响了脑MRI的分割过程，这是医生为诊断目的所需的。最近，我们提出了一种基于局部Zernike矩（LZM）的无偏非局部均值模糊C均值（LZM-UNLM-FCM）方法，该方法已使用LZM方法处理了矩域中的噪声伪影。该方法为被Rician噪声破坏的MR图像提供了高分割结果。但是，该方法不能有效地处理强度不均匀伪影。此外，该方法使用需要调整的正则化参数以获得有效的分割结果。本文提出了一种无监督的局部Zernike矩和无偏的，基于非局部均值的偏差校正模糊C均值（LZM-UNLM-BCFCM）方法，该方法可同时处理噪声和强度非均匀性伪影。所提出方法背后的主要概念是利用LZM的吸引人的特性，通过确定MR图像中大量受Rician噪声和强度不均匀性破坏的相似区域来有效地过滤图像。LZM在包含任何方向的精细组织结构的MR图像中确定此类区域的能力已被很好地用于处理高水平的噪声。在不使用正则化参数的情况下，通过使用滤波图像在分割过程中逐像素估计偏置场，可以消除强度不均匀性。偏置场被估计为正交多项式的线性组合，其中权重通过最小化模糊目标函数获得。在模拟和真实MR图像上的实验结果表明，与其他无人监督的最新方法相比，该方法具有优越性。