Background and objective: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.

Methods: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 to enhance the methods to be more robust to noise and to employ the fourth order tensor data in order to handle the fiber crossings properly.

Results: We propose a way to choose the appropriate conformal class of metrics where the metric gets scaled according to tensor anisotropy. We use the logistic functions, which are commonly used in statistics as cumulative distribution functions. To prevent deviation of geodesics from the actual paths, we propose a hybrid ray-tracing approach. Furthermore, we suggest how to employ diagonal projections of 4th order tensors to perform fiber tracking in crossing regions.

Conclusions: The algorithms based on the newly suggested methods were succesfuly implemented, their performance was tested on both synthetic and real data, and compared to some of the previously known approaches.

背景与目的：测地线射线追踪方法已显示出其在白质结构中重建纤维的有效性。基于扩散张量空间的合理度量，它可以提供多种解决方案，并对噪声和纤维曲率具有鲁棒性。扩散张量空间度量的选择对该方法的结果有重大影响。我们的目标是建议算法的度量和修改，从而在将白质束构建为测地线时产生更令人满意的结果。

方法：从 DTI 模态开始，我们建议在扩散张量空间上重新调整最初选择的度量，以增加各向同性区域的大地测量成本。这种变化应该是共形的，以保持交叉光纤之间的角度。我们还建议增强这些方法，使其对噪声更加鲁棒，并使用四阶张量数据来正确处理光纤交叉。

结果：我们提出了一种方法来选择合适的共形度量类，其中度量根据张量各向异性进行缩放。我们使用统计中常用的逻辑函数作为累积分布函数。为了防止测地线偏离实际路径，我们提出了一种混合光线追踪方法。此外，我们建议如何使用四阶张量的对角线投影在交叉区域执行光纤跟踪。

结论：基于新建议方法的算法已成功实现，它们的性能在合成和真实数据上进行了测试，并与一些先前已知的方法进行了比较。