  The geodesic ray-tracing method has shown its effectiveness for the
reconstruction of fibers in white matter structure. Based on reasonable metrics
on the spaces of the diffusion tensors, it can provide multiple solutions and
get robust to noise and curvatures of fibers. The choice of the metric on the
spaces of diffusion tensors has a significant impact on the outcome of this
method. Our objective is to suggest metrics and modifications of the algorithms
leading to more satisfactory results in the construction of white matter tracts
as geodesics. Starting with the DTI modality, we propose to rescale the
initially chosen metric on the space of diffusion tensors to increase the
geodetic cost in the isotropic regions. This change should be conformal in
order to preserve the angles between crossing fibers. We also suggest enhancing
the methods to be more robust to noise and employing the fourth-order tensor
data in order to handle the fiber crossings properly.
