Charles Poirier^{1} and Maxime Descoteaux^{1}

^{1}Computer Sciences, Université de Sherbrooke, Sherbrooke, QC, Canada

Although the voxel-wise signal acquired by diffusion MRI is symmetric, it is not always the case of the underlying fiber configurations. We present angle-aware bilateral filtering, an intuitive method for denoising fiber ODF fields revealing asymmetric fiber ODFs. To evaluate the effect of the filtering, tractography is performed on the resulting asymmetric fiber ODF field. Compared to the tractogram obtained from the original fiber ODF field, we show that using asymmetric filtered fiber ODF field as input to a fiber tracking algorithm reduces the ratio of incomplete streamlines and false connections and increases the proportion of true connections.

The bilateral filter uses a combination of Gaussians for domain and range filtering. Because fODF are defined in the 5-dimensional (5D) spatio-angular domain, we extend bilateral filtering to consider the variation in angle between the sampled fODF directions and the directions to neighbour voxels by adding a third Gaussian distribution for angular domain filtering (figure 1). Formally, the filtered fODF $$$\phi'(x, u)$$$ for voxel $$$x$$$ and unit direction $$$u$$$ is given by

$$

\phi'(x, u) = \frac{1}{W(x, u)}\sum_{y \in N(x)} G_{\sigma_{spatial}}(||y - x||)\cdot G_{\sigma_{angular}}\left(\arccos(u\cdot\frac{y - x}{||y - x||})\right)\cdot G_{\sigma_{range}}(|\phi(x, u) - \phi(y,u)|)\cdot \phi(x,u),

$$

where $$$N(x)$$$ is the set of neighbours of $$$x$$$, $$$G_{\sigma}$$$ is the normal distribution of standard deviation $$$\sigma$$$ and $$$\phi(x, u)$$$ is the input fODF. The resulting SF is not restricted to being antipodally symmetric and can be expressed in a full SH basis (available in DIPY

For tracking on asymmetric fODF, we use an in-house local tracking implementation. In comparison to the DIPY local tracking implementation, where the next direction is chosen using the

FODF of maximum SH order 8 taken from a simulated version of the FiberCup phantom

The bundle-wise TC overlap achieved by the best tractogram (figure 3) shows that

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DOI: https://doi.org/10.58530/2022/3552