A Riemannian scalar measure for diffusion tensor images

Astola, Laura; Fuster, Andrea; Florack, Luc

doi:10.1016/j.patcog.2010.09.009

Cited by 12 publications

(9 citation statements)

References 25 publications

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“…The prevalence and geometry of sheet structures in the brain can potentially also be a novel feature to characterize brain structure, complementing the wide range of existing microstructural and geometrical measures (e.g. (Assaf et al, 2008; Astola et al, 2011; Dell’acqua et al, 2013; Fieremans et al, 2011; Leemans et al, 2006; Raffelt et al, 2012; Savadjiev et al, 2012; Tax et al, 2012; Zhang et al, 2012)).…”

Section: Introductionmentioning

confidence: 99%

Sheet Probability Index (SPI): Characterizing the geometrical organization of the white matter with diffusion MRI

et al. 2016

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The question whether our brain pathways adhere to a geometric grid structure has been a popular topic of debate in the diffusion imaging and neuroscience society. Wedeen et al. (2012a b) proposed that the brain’s white matter is organized like parallel sheets of interwoven pathways. Catani et al. (2012) concluded that this grid pattern is most likely an artifact, resulting from methodological biases that cause the tractography pathways to cross in orthogonal angles. To date, ambiguities in the mathematical conditions for a sheet structure to exist (e.g. its relation to orthogonal angles) combined with the lack of extensive quantitative evidence have prevented wide acceptance of the hypothesis. In this work, we formalize the relevant terminology and recapitulate the condition for a sheet structure to exist. Note that this condition is not related to the presence or absence of orthogonal crossing fibers, and that sheet structure is defined formally as a surface formed by two sets of interwoven pathways intersecting at arbitrary angles within the surface. To quantify the existence of sheet structure, we present a novel framework to compute the sheet probability index (SPI), which reflects the presence of sheet structure in discrete orientation data (e.g. fiber peaks derived from diffusion MRI). With simulation experiments we investigate the effect of spatial resolution, curvature of the fiber pathways, and measurement noise on the ability to detect sheet structure. In real diffusion MRI data experiments we can identify various regions where the data supports sheet structure (high SPI values), but also areas where the data does not support sheet structure (low SPI values) or where no reliable conclusion can be drawn. Several areas with high SPI values were found to be consistent across subjects, across multiple data sets obtained with different scanners, resolutions, and degrees of diffusion weighting, and across various modeling techniques. Under the strong assumption that the diffusion MRI peaks reflect true axons, our results would therefore indicate that pathways do not form sheet structures at every crossing fiber region but instead at well-defined locations in the brain. With this framework, sheet structure location, extent, and orientation could potentially serve as new structural features of brain tissue. The proposed method can be extended to quantify sheet structure in directional data obtained with techniques other than diffusion MRI, which is essential for further validation.

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Section: Introductionmentioning

confidence: 99%

Sheet Probability Index (SPI): Characterizing the geometrical organization of the white matter with diffusion MRI

et al. 2016

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“…Another advantage with respect to other types of tracking algorithms is that geodesic tractography tends to be more robust to noise. Finally, it has the conceptual advantage that Riemannian geometry is a well understood and powerful theoretical machinery, facilitating mathematical modelling and algorithmics [2][3][4]6,12,[15][16][17][24][25][26]30,31,33,35].…”

Section: Introductionmentioning

confidence: 99%

Adjugate Diffusion Tensors for Geodesic Tractography in White Matter

et al. 2015

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One of the approaches in diffusion tensor imaging is to consider a Riemannian metric given by the inverse diffusion tensor. Such a metric is used for geodesic tractography and connectivity analysis in white matter. We propose a metric tensor given by the adjugate rather than the previously proposed inverse diffusion tensor. The adjugate metric can also be employed in the sharpening framework. Tractography experiments on synthetic and real brain diffusion data show improvement for high-curvature tracts and in the vicinity of isotropic diffusion regions relative to most results for inverse (sharpened) diffusion tensors, and especially on real data. In addition, adjugate tensors are shown to be more robust to noise.

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“…For example, Riemann scalar measure has been applied to diffusion tensor imaging [28]. An early work by Huttenlocher et al found that Hausdorff distance is especially useful in dealing with images with small perturbation [29].…”

Section: Y Feng Et Al / a Modified Fcm For Mr Images Segmentationmentioning

confidence: 99%

A modified fuzzy C-means method for segmenting MR images using non-local information

Feng¹,

Guo²,

Zhang³

et al. 2016

THC

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Abstract. BACKGROUND:In recent years, MR images have been increasingly used in therapeutic applications such as image-guided radiotherapy (IGRT). However, images with low contrast values and noises present challenges for image segmentation. OBJECTIVE: The objective of this study is to develop a robust method based on fuzzy C-means (FCM) method which can segment MR images polluted with Gaussian noise. METHODS: A modified FCM algorithm accommodating non-local pixel information via Hausdorff distance was developed for segmenting MR images. The membership and objective functions were modified accordingly. Segmentations with different weights of the Hausdorff distance were compared. RESULTS: Segmentation tests using synthetic and MR images showed that the proposed algorithm was better at resolving boundaries and more robust to Gaussian noise. By segmenting a sample MR image of a tumor, we further showed the capability of the method in capturing the centroid of the target region. CONCLUSIONS: The modified FCM algorithm with neighboring information can be used to segment blurry images with potential applications in segmenting motion MR images in image-guided radiotherapy (IGRT).

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A Riemannian scalar measure for diffusion tensor images

Cited by 12 publications

References 25 publications

Sheet Probability Index (SPI): Characterizing the geometrical organization of the white matter with diffusion MRI

Sheet Probability Index (SPI): Characterizing the geometrical organization of the white matter with diffusion MRI

Adjugate Diffusion Tensors for Geodesic Tractography in White Matter

A modified fuzzy C-means method for segmenting MR images using non-local information

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