A new Mahalanobis distance measure for clustering of fiber tracts

INTRODUCTION Data analysis in Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is highly sophisticated and can be thought of as a “pipeline” of closely connected processing and modeling steps. Cluster analysis of the orientation of the fiber direction and fiber tracts is typically carried on the major eigenvector. This type of cluster analysis is also important in reducing sorting bias in the eigenvalues of the diffusion tensor [1-3]. In this work, we present a simple and novel generalization of Mahalanobis distance measure for the dyadics of the eigenvector for the purposes of clustering fiber tracts and fiber orientation. This approach is built upon a series of works by Koay et al.[4-6], especially the error propagation framework for DT-MRI as presented in [5]. This approach is straight forward and the Mahalanobis distance measure for the dyadics can computed efficiently without ad hoc combinatorial optimization that is typical in the eigenvector-clustering techniques, e.g., [1,2]. The proposed Mahalanobis distance measure is the ideal measure for clustering fiber tracts. METHODS AND RESULTS The dyadics formalism is a relatively well known technique in DTI [1,7]. A dyadic tensor of a vector, T z y x q q q ] , , [ = q is simply the matrix outer product of q , which is given by: