Accurate segmentation of the breast region of interest (BROI) and breast density (BD) is a significant challenge during the analysis of breast MR images. Most of the existing methods for breast segmentation are semi-automatic and limited in their ability to achieve accurate results. This is because of difficulties in removing landmarks from noisy magnetic resonance images (MRI) due to similar intensity levels and the close connection to BROI. This study proposes an innovative, fully automatic and fast segmentation approach to identify and remove landmarks such as the heart and pectoral muscles. The BROI segmentation is carried out with a framework consisting of three major steps. Firstly, we use adaptive wiener filtering and k-means clustering to minimize the influence of noises, preserve edges and remove unwanted artefacts. The second step systematically excludes the heart area by utilizing active contour based level sets where initial contour points are determined by the maximum entropy thresholding and convolution method. Finally, a pectoral muscle is removed by using morphological operations and local adaptive thresholding on MR images. Prior to the elimination of the pectoral muscle, the MR image is sub divided into three sections: left, right, and central based on the geometrical information. Subsequently, a BD segmentation is achieved with 4 level fuzzy c-means (FCM) thresholding on the denoised BROI segmentation. The proposed method is validated using the 1350 breast images from 15 female subjects. The pixel-based quantitative analysis showed excellent segmentation results when compared with manually drawn BROI and BD. Furthermore, the presented results in terms of evaluation matrices: Acc, Sp, AUC, MR, P, Se and DSC demonstrate the high quality of segmentations using the proposed method. The average computational time for the segmentation of BROI and BD is 1 minute and 50 seconds.