Clustering Fiber Traces Using Normalized Cuts

Abstract

In this paper we present a framework for unsupervised segmentation of white matter fiber traces obtained from diffusion weighted MRI data. Fiber traces are compared pairwise to create a weighted undirected graph which is partitioned into coherent sets using the normalized cut (N cut) criterion. A simple and yet effective method for pairwise comparison of fiber traces is presented which in combination with the N cut criterion is shown to produce plausible segmentations of both synthetic and real fiber trace data. Segmentations are visualized as colored stream-tubes or transformed to a segmentation of voxel space, revealing structures in a way that looks promising for future explorative studies of diffusion weighted MRI data.

Fig. 1

An overview of the proposed method. Whether the result should be in voxels or fiber traces depends highly on the application. Fiber traces are flexible, they are for instance able to represent multiple fiber directions going thru a point in space. Voxels are on the other hand more suitable for volume rendering.

Fig. 2

Top left A set of synthetic fiber traces in 2-D. Top middle: The matrix W. Rows and columns sorted according to the second smallest eigenvector. The Gaussian kernel have been chosen so that five clusters present themselves naturally. Top right: The 15 smallest eigenvalues of (D − W)/D. Bottom: Segmentation obtained from recursive bipartitioning of the fiber traces. Maximum value of the N cut set to 0.2, 2.5 and 4.5 respectively.

Fig. 3

Left: Axial view of a segmentation obtained from recursive bipartitioning of the white matter fiber traces. Maximum value of the N cut was set to 1.5 and Gaussian kernel σ = 20. . The colors of fiber traces indicate cluster membership. Middle: Coronal view. Right: The matrix W. Rows and columns sorted according to the second smallest eigenvector.

Fig. 4

Pseudo-coloring of fiber traces. RGB colors are derived directly from scaled versions of the 2nd, 3rd and 4th eigenvector of (D − W)/D. Using a very large Gaussian kernel, σ = 100, results in a soft clustering effect. Note the enhanced perception of fiber connectivity and shape, despite the lack of discrete clusters. Left: Whole brain white matter visualized using pseudo-colored fiber traces. Middle: A subset of the white matter fiber traces visualized using pseudo-colored fiber traces. Right: Pseudo-coloring of voxels belonging to white matter enhance perception of connectivity in slices or volumes. To fill in holes in white matter when fiber traces were transformed to voxels, a nearest-neighbor approach combined with a white matter mask was used.