Efficient Fiber Clustering using Parameterized Polynomials

摘要

In the past few years, fiber clustering algorithms have shown to be a very powerful tool for grouping white matter connections tracked in DTI images into anatomically meaningful bundles. They improve the visualization and perception, and could enable robust quantification and comparison between individuals. However, most existing techniques perform a coarse approximation of the fibers due to the high complexity of the underlying clustering problem or do not allow for an efficient clustering in real time. In this paper, we introduce new algorithms and data structures which overcome both problems. The fibers are represented very precisely and efficiently by parameterized polynomials defining the x-, y-, and z-component individually. A two-step clustering method determines possible clusters having a Gaussian distributed structure within one component and, afterwards, verifies their existences by principal component analysis (PCA) with respect to the other two components. As the PCA has to be performed only n times for a constant number of points, the clustering can be done in linear time O(n), where n denotes the number of fibers. This drastically improves on existing techniques, which have a high, quadratic running time, and it allows for an efficient whole brain fiber clustering. Furthermore, our new algorithms can easily be used for detecting corresponding clusters in different brains without time-consuming registration methods. We show a high reliability, robustness and efficiency of our new algorithms based on several artificial and real fiber sets that include different elements of fiber architecture such as fiber kissing, crossing and nested fiber bundles.