An illustration of classified white matter associative fibers. The ultimate goal of this work is to produce a classification of the data obtained from dMRI in such a way that the main fiber bundles are properly identified. From 20th U.S. edition of Gray’s Anatomy of the Human Body (public domain) 

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... reconstruction of the fiber tracts may provide new biomarkers in white matter pathologies and segmentation of these tracts could also improve our understanding of the functional role these tracts have and the cognitive consequences of their disruption. However, none of the existing methods that recover axonal fiber connectivity can directly be used in order segment well-known fiber bundles as the ones shown in figure 1 from [Gray, 1918]. In this work, we provide two techniques in order to recover white matter structures. ...

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... u i is the i th gradient direction on the sphere, n is the number of fibers and 1/n is the volume fraction of the of each fiber. In practice, we use N = 12 from a 3 rd order tessellation of the icosahedron, b = 700 s/mm 2 and n = 1 or 2. matrix, where the two bundles are clearly distinguished is shown in figure 11(a), the bigger 10 eigenvalues, of the normalized affinity matrix are shown in figure 11(b) and the 2-dimensional normalized embedding in figure 11(c). It can be noticed by observing the eigenvalues plot, that the clusters to be found is 2 and that they are clearly separable in this embedding. ...

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... u i is the i th gradient direction on the sphere, n is the number of fibers and 1/n is the volume fraction of the of each fiber. In practice, we use N = 12 from a 3 rd order tessellation of the icosahedron, b = 700 s/mm 2 and n = 1 or 2. matrix, where the two bundles are clearly distinguished is shown in figure 11(a), the bigger 10 eigenvalues, of the normalized affinity matrix are shown in figure 11(b) and the 2-dimensional normalized embedding in figure 11(c). It can be noticed by observing the eigenvalues plot, that the clusters to be found is 2 and that they are clearly separable in this embedding. ...

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... u i is the i th gradient direction on the sphere, n is the number of fibers and 1/n is the volume fraction of the of each fiber. In practice, we use N = 12 from a 3 rd order tessellation of the icosahedron, b = 700 s/mm 2 and n = 1 or 2. matrix, where the two bundles are clearly distinguished is shown in figure 11(a), the bigger 10 eigenvalues, of the normalized affinity matrix are shown in figure 11(b) and the 2-dimensional normalized embedding in figure 11(c). It can be noticed by observing the eigenvalues plot, that the clusters to be found is 2 and that they are clearly separable in this embedding. ...

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... in figure 12, the results with a σ = 10 can be seen, in this case, the k-means method will not succeed in clustering the bundles, showing that the success of the clustering final step based on the k-means algorithm, as recommended in [Shi and Malik, 2000;Belkin and Niyogi, 2003;Lafon and Lee, 2006], is highly sensitive to the adopted parameters. ...

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... sampled clusters In order to exhibit the sensitivity of the Normalized Cuts based algorithm [Brun et al., 2004;Maddah et al., 2005;O'Donnell and Westin, 2006] to hypothesis 2, a non-uniform seeding of the synthetic CC fiber bundle was performed as shown in figure 13 where 269 tracts conform the CC and 40 the CG. ...

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... results of the embedding and clustering procedure are shown in figure 14. Observing the eigenvalues plot, it can be noticed that the number of clusters to be found is between 3 and 4; with respect to the embedding, it shows several number of clusters, derived from the non-uniform sampling of the CC. ...

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... dataset is taken from the Slicer user training 101 webpage, http://wiki.na-mic.org/Wiki/images/7/72/Tensor_data. figure 10 generated with a kernel with parameter σ = 2, the biggest 10 eigenvalues of the affinity matrix and the 2D normalized embedding space. Observing the eigenvalues plot, the number of clusters to be found is two and it can be noted that simple clustering methods, as k-means, will succeed performing the clustering of these elements. ...

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... the eigenvalues plot, the number of clusters to be found is two and it can be noted that simple clustering methods, as k-means, will succeed performing the clustering of these elements. figure 10 generated with a kernel with parameter σ = 10, the biggest eigenvalues not counting of the affinity matrix and the 2D normalized embedding space. Observing the eigenvalues plot, the number of clusters to be found is still two, but it can be noted that k-means clustering, will not succeed performing the clustering of these elements. ...

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... in section 4.1.1, the clustering algorithm is executed over the data shown in figure 15 taking σ = 2. The results of the embedding and clustering procedure are shown in figure 16. ...

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... clustering algorithm is executed over the data shown in figure 15 taking σ = 2. The results of the embedding and clustering procedure are shown in figure 16. Observing the eigenvalues plot, it can be noticed that the number of clusters to be found is 3, while the expected number of clusters is 2. With respect to the embedding, it shows several number of clusters, derived from the non-uniform sampling of the fibers. ...

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... results of applying this normalization to the data given in section 4.1.1 are shown in figure 17. In the eigenvalue plot, figure 17(b), it can be noted that there are two clusters, which can be separated easily in the embedding shown in Furthermore, the results of applying the same procedure to the real data set presented in section 4.1.2, ...

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... results of applying this normalization to the data given in section 4.1.1 are shown in figure 17. In the eigenvalue plot, figure 17(b), it can be noted that there are two clusters, which can be separated easily in the embedding shown in Furthermore, the results of applying the same procedure to the real data set presented in section 4.1.2, taking σ = 5, are shown in figure 18 3 . ...

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... the eigenvalue plot, figure 17(b), it can be noted that there are two clusters, which can be separated easily in the embedding shown in Furthermore, the results of applying the same procedure to the real data set presented in section 4.1.2, taking σ = 5, are shown in figure 18 3 . In the eigenvalue plot, figure 18(b), it can be noted that there are two clusters, which can be separated easily in the embedding shown in figure 18(c). ...

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... σ = 5, are shown in figure 18 3 . In the eigenvalue plot, figure 18(b), it can be noted that there are two clusters, which can be separated easily in the embedding shown in figure 18(c). Finally the correct clustering is exhibited in figure 18(d). ...

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... σ = 5, are shown in figure 18 3 . In the eigenvalue plot, figure 18(b), it can be noted that there are two clusters, which can be separated easily in the embedding shown in figure 18(c). Finally the correct clustering is exhibited in figure 18(d). ...

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... the eigenvalue plot, figure 18(b), it can be noted that there are two clusters, which can be separated easily in the embedding shown in figure 18(c). Finally the correct clustering is exhibited in figure 18(d). ...

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... order to show the block structure of the affinity matrix, it is shown reordered using the second eigenvector in figure 18(e) as shown in [Behrens, 2004, ...

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... tractography was done seeding from each of these points and finally our spectral clustering and embedding algorithm was applied to these fiber tracts. Results are shown in figure 19. It can be seen that our algorithm was able to distinguish between different sets of associative fiber within each lobe (cyan, orange, yellow), the projection fibers connecting the cortex to the thalamus (blue) and two bundles of commisural fibers, the anterior and posterior commisures (green, red). is colored differently. ...