Magnetic Resonance Imaging (MRI) is essential for noninvasive generation of high-quality images of human tissues. Accurate segmentation of MRI data is critical for medical applications like brain anatomy analysis and disease detection. However, challenges such as intensity inhomogeneity, noise, and artifacts complicate this process. To address these issues, we propose a three-step framework exploiting the idea of Cartoon-Texture evolution to produce a denoised and debiased MR image. The first step involves identifying statistical information about the nature of the noise using a suitable image decomposition. In the second step, a multiplicative intrinsic component model is applied to a smother version of the image, simultaneously reconstructing the bias and removing noise using noise information from the previous step. At the final step, standard clustering techniques are used to create an accurate segmentation. Additionally, we present a convergence analysis of the ADMM scheme for solving the nonlinear optimization problem with multiaffine constraints resulting from the second step. Numerical tests demonstrate the effectiveness of our framework, especially in noisy brain segmentation, both from a qualitative and a quantitative viewpoint, compared to similar methods.