Shape anisotropy: tensor distance to anisotropy measure

Yonas T. Weldeselassie; Saba El-Hilo; M. Stella Atkins

doi:10.1117/12.878423

15 March 2011 Shape anisotropy: tensor distance to anisotropy measure

Yonas T. Weldeselassie, Saba El-Hilo, M. Stella Atkins

Proceedings Volume 7962, Medical Imaging 2011: Image Processing; 79624F (2011) https://doi.org/10.1117/12.878423
Event: SPIE Medical Imaging, 2011, Lake Buena Vista (Orlando), Florida, United States

Abstract

Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.

Citation Download Citation

Yonas T. Weldeselassie, Saba El-Hilo, and M. Stella Atkins "Shape anisotropy: tensor distance to anisotropy measure", Proc. SPIE 7962, Medical Imaging 2011: Image Processing, 79624F (15 March 2011); https://doi.org/10.1117/12.878423

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