MRI tissue classification and bias field estimation based on coherent local intensity clustering: a unified energy minimization framework.

This paper presents a new energy minimization method for simultaneous tissue classification and bias field estimation of magnetic resonance (MR) images. We first derive an important characteristic of local image intensities--the intensities of different tissues within a neighborhood form separable clusters, and the center of each cluster can be well approximated by the product of the bias within the neighborhood and a tissue-dependent constant. We then introduce a coherent local intensity clustering (CLIC) criterion function as a metric to evaluate tissue classification and bias field estimation. An integration of this metric defines an energy on a bias field, membership functions of the tissues, and the parameters that approximate the true signal from the corresponding tissues. Thus, tissue classification and bias field estimation are simultaneously achieved by minimizing this energy. The smoothness of the derived optimal bias field is ensured by the spatially coherent nature of the CLIC criterion function. As a result, no extra effort is needed to smooth the bias field in our method. Moreover, the proposed algorithm is robust to the choice of initial conditions, thereby allowing fully automatic applications. Our algorithm has been applied to high field and ultra high field MR images with promising results.