The fuzzy c-means (FCM) algorithm is widely used for image segmentation based on clustering. However, it is sensitive to noise, and its convergence is affected by the data distribution. FCM relies on the Euclidean distance metric, which fails to account for variations in the distances within similar and compact clusters. Moreover, the distance metric is not locally adaptive to the shape of clusters. This paper introduces a robust Gustafson-Kessel (RGK) clustering algorithm to address these limitations for brain tissue segmentation using MRI images. To achieve accurate segmentation under varying noise levels and intensity non-uniformity (INU), a Wiener filter integrated with wavelet transform (WFWT) is employed as a preprocessing step to enhance image quality while preserving object edges. The Mahalanobis distance is used for clustering to better adapt to the shape of the clusters. Additionally, the RGK algorithm incorporates membership matrix filtering to exploit the local spatial constraint. The proposed RGK algorithm was evaluated using two datasets: the BrainWeb simulated dataset and MRI scans from 10 healthy individuals at the Golghasht Medical Imaging Center in Tabriz (GMICT), Iran. In RGK, it is not necessary to compute the distance between pixels within local spatial neighbors and clusters. Experimental results demonstrate that the RGK algorithm outperforms traditional FCM-based methods in the segmentation of brain tissues.