MRI Brain Tissue Classification by Maximizing Mutual Information

Tissue classification in MR images of human brains is an important problem in medical image analysis. The fundamental task in tissue classification is to classify the voxels in the volumetric ($3$D) MR data into gray matter, white matter, and cerebrospinal fluid tissue types. This has numerous applications related to diagnosis, surgical planning, image-guided interventions, monitoring therapy, and clinical drug trials. Such applications include the study of neuro-degenerative disorders such as Alzheimer's disease, generation of patient-specific conductivity maps for EEG source localization, determination of cortical thickness and substructure volumes in Schizophrenia, and partial-volume correction for low-resolution image modalities such as positron emission tomography.

Manual segmentation or classification of high-resolution $3$D images is a tedious task, which is impractical for large amounts of data. Because of the complexity of this task, such classifications can be very error prone and exhibit nontrivial inter-expert and intra-expert variability [30]. Fully automatic or unsupervised methods, on the other and, virtually eliminate the need for manual interaction, and thus such methods for brain tissue classification have received significant attention in the literature.

Current state-of-the-art methods for automatic brain tissue classification typically incorporate the following strategies: (a) parametric statistical modeling, e.g., Gaussian, of voxel grayscale intensity for each tissue class, (b) Markov-random-field (MRF) modeling to enforce spatial smoothness on the classification, (c) methods to explicitly correct for the inhomogeneities inherent in MR images, and (d) probabilistic-brain-atlas information in the classification method. Several factors, however, continue to pose significant challenges to the state of the art:

• 
  The intensities and contrast in MR images varies significantly with the pulse sequence, and several other scanner parameters. The quality of MR data also shows a certain amount of variation when produced at multiple sites with different MR scanners.
  
• 
  MRI-acquisition artifacts, which include the Rician nature of the noise in magnitude-MR data [115] and partial voluming effects [94], can cause the data to significantly deviate from the Gaussian tissue-intensity models, thereby compromising the quality of the classification.
  
• 
  Many methods treat the inhomogeneity as multiplicative noise (bias field) and explicitly correct the MR intensities to reduce its effect. For certain kinds of coil configurations or applications, such as neonatal brain MRI, however, inhomogeneities do not adhere to standard multiplicative models [134].

To address these issues in an effective way, we propose an unsupervised classification approach that adapts to the data. One adaptation strategy is to automatically learn the underlying image statistics from the data and construct a classification strategy based on that model. This chapter presents a novel method [163,5] for MRI brain tissue classification that incorporates an adaptive nonparametric model of neighborhood/Markov statistics. The method incorporates the information content in the neighborhoods in the classification process. Together with a weak smoothness constraint on the estimated Markov statistics, it virtually eliminates the need for explicit smoothness constraints on the class-label image. The method produces an optimal classification by iteratively maximizing a mutual-information metric that relies on Markov PDFs. The algorithm adjusts all its important internal parameters automatically using a data-driven approach and information-theoretic metrics. Combined with an atlas-based initialization, it is fully unsupervised. It incorporates a priori information in probabilistic-brain-atlases via a Bayesian formulation. Experiments on real, simulated, and multimodal data demonstrate the significant advantages of the method over the current state-of-the-art. The method also performs reasonably well without any explicit inhomogeneity correction.