NDLI: Fast Invariant Riemannian DT-MRI Regularization

Content Provider	IEEE Xplore Digital Library
Author	Gur, Y. Sochen, N.
Copyright Year	2007
Description	Author affiliation: Tel-Aviv Univ., Tel-Aviv (Gur, Y.; Sochen, N.)
Abstract	We present regularization by invariant denoising/smoothing of Diffusion Tensor MRI (DTI). Our solution to the problem emerges from a pure geometric point of view. The image domain and the image's values are combined together and described as a (mathematical) fiber bundle. The space of all possible DT images is the space of sections of this fiber bundle. DT image is a map that attaches a three-dimensional symmetric and positive-definite (SPD) matrix to each volume element. We treat the more general space $P_{n}$ of n-dimensional SPD matrices and introduce a natural GL(n)-invariant metric via the underlying algebraic structure. A metric over sections of the fiber bundle is induced then in terms of the natural metric on $P_{n}.$ This turns $P_{3}$ tensors, and in general $P_{n}$ tensors, into a Riemannian symmetric spaces. By means of the Beltrami framework we define a GL(n)-invariant functional over the space of sections. Then, by calculus of variations we derive the invariant equations of motion. We show that by choosing the Iwasawa coordinates the analytical calculations as well as the numerical implementation become simple. These coordinates evolve with respect to the geometry of the section via the induced metric. The numerical implementation of these flows via standard finite difference schemes is straightforward. The result is a full GL(n) invariant algorithm which is at least as fast and efficient as the Log-Euclidean method. Finally, we demonstrate this framework on real DTI data.
Starting Page	1
Ending Page	7
File Size	976545
Page Count	7
File Format	PDF
ISBN	9781424416301
ISSN	15505499
DOI	10.1109/ICCV.2007.4409142
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-10-14
Publisher Place	Brazil
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Diffusion tensor imaging Tensile stress Symmetric matrices Noise reduction Smoothing methods Magnetic resonance imaging Calculus Equations Geometry Finite difference methods
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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