Abstract
Orientation distribution functions (ODFs) are widely used to resolve fiber crossing problems in high angular resolution diffusion imaging (HARDI). The characteristics of the ODFs are often assessed using a visual criterion, although the use of objective criteria is also reported, which are directly borrowed from classic signal and image processing theory because they are intuitive and simple to compute. However, they are not always pertinent for the characterization of ODFs. We propose a more general paradigm for assessing the characteristics of ODFs. The idea consists in regarding an ODF as a three-dimensional (3D) point cloud, projecting the 3D point cloud onto an angle-distance map, constructing an angle-distance matrix, and calculating metrics such as length ratio, separability, and uncertainty. The results from both simulated and real data show that the proposed metrics allow for the assessment of the characteristics of ODFs in a quantitative and relatively complete manner.
Highlights
The orientation distribution function (ODF) [1] is a quantity used to describe the orientation architecture of the tissue’s fibers or fiber bundles; it gives the probability of diffusion in different directions
The proposed metrics were compared with existing metrics such as MSE, sKL, root-mean square error (RMSE), and normalized mean squared error (NMSE)
The proposed morphological metrics have been tested on different ODFs corresponding to different configurations of one fiber, two fibers, or three fibers
Summary
The orientation distribution function (ODF) [1] is a quantity used to describe the orientation architecture of the tissue’s fibers or fiber bundles; it gives the probability of diffusion in different directions. ODF is often estimated or reconstructed from high angular resolution diffusion imaging (HARDI) such as q-ball imaging (QBI) [2] using spherical sampling. In this field, most existing works put emphasis on improving the quality of ODF using normalization and regularization [2,3], change of basis [4,5,6], sharping deconvolution [7], compressed sensing [8], etc. Other quantities have been used to describe fiber orientation or crossing, including the fiber orientation distribution (FOD) from the spherical deconvolution method [9,10], the orientation map derived from the diffusion orientation transform (DOT) based on the Fourier transform relationship between water displacement probability and PLOS ONE | DOI:10.1371/journal.pone.0150161. Other quantities have been used to describe fiber orientation or crossing, including the fiber orientation distribution (FOD) from the spherical deconvolution method [9,10], the orientation map derived from the diffusion orientation transform (DOT) based on the Fourier transform relationship between water displacement probability and PLOS ONE | DOI:10.1371/journal.pone.0150161 February 26, 2016
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