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We introduce novel data structures and algorithms for clustering white matter fiber tracts to improve accuracy
and robustness of existing techniques. Our novel fiber grid combined with a new randomized soft-division
algorithm allows for defining the fiber similarity more precisely and efficiently than a feature space. A fine-tuning
of several parameters to a particular fiber set - as it is often required if using a feature space - becomes obsolete.
The idea is to utilize a 3D grid where each fiber point is assigned to cells with a certain weight. From this grid, an
affinity matrix representing the fiber similarity can be calculated very efficiently in time O(n) in the average case,
where n denotes the number of fibers. This is superior to feature space methods which need O(n2) time. Our novel
eigenvalue regression is capable of determining a reasonable number of clusters as it accounts for inter-cluster
connectivity. It performs a linear regression of the eigenvalues of the affinity matrix to find the point of maximum
curvature in a list of descending order. This allows for identifying inner clusters within coarse structures, which
automatically and drastically reduces the a-priori knowledge required for achieving plausible clustering results.
Our extended multiple eigenvector clustering exhibits a drastically improved robustness compared to the well-known
elongated clustering, which also includes an automatic detection of the number of clusters. We present
several examples of artificial and real fiber sets clustered by our approach to support the clinical suitability and
robustness of the proposed techniques.
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Jan Klein, Philip Bittihn, Peter Ledochowitsch, Horst K. Hahn, Olaf Konrad, Jan Rexilius, Heinz-Otto Peitgen, "Grid-based spectral fiber clustering," Proc. SPIE 6509, Medical Imaging 2007: Visualization and Image-Guided Procedures, 65091E (21 March 2007);