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Inhomogeneities in the fields of magnetic resonance (MR) systems cause the statistical characteristics of tissue classes to vary within the resulting MR images. These inhomogeneities must be taken into consideration when designing an algorithm for automated tissue classification. The traditional approach in image processing would be to apply a gain field correction technique to remove the inhomogeneities from the images. Statistical solutions would most likely focus on including spatial information in the feature space of the classifier so that it can be trained to model and adjust for the inhomogeneities. This paper will prove that neither of these general approaches offer a complete and viable solution. This paper will prove that neither of these general approaches offers a complete and viable solution. This paper will in fact show that not only do the inhomogeneities modify the local mean and variance of a tissue class as is commonly accepted, but the inhomogeneities also induce a rotation of the covariance matrices. As a result, gain field correction techniques cannot compensate for all of the artifacts associated with inhomogeneities. Additionally, it will be demonstrated that while statistical methods can capture all of the anomalies, the across patient and across time variations of the inhomogeneities necessitate frequent and time consuming retraining of any Bayesian classifier. This paper introduces a two stage process for MR tissue classification which addresses both of these issues by utilizing techniques from both image processing and statistics. First, a band-pass mean field corrector is used to alleviate the mean and variance deformations in each image. Then, using a kernel mixture model classifier couple to an interactive data augmentation tool, the user can selectively refine and explore the class representations for localized regions of the image and thereby capture the rotation of the covariance matrices. This approach is shown to outperform Gaussian classifiers and 4D mixture modeling techniques when both the final accuracy and user time requirements are considered.
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