Diffusion Tensor Imaging (DTI) is a popular model for representing diffusion weighted magnetic resonance images due to its simplicity and the fact that it strikes a good balance between signal fit and robustness. Nevertheless, problematic issues remain. One of these concerns the problem of interpolation. Because the DTI assumption forces Apparent Diffusion Coefficients (ADCs) to fit quadratic forms, destructive interference of diffusivity patterns tends to mask information on orientations. For some applications, notably tractography, one would like an interpolated DTI tensor to reflect not only some weighted average of its immediate grid neighbours, but also to preserve orientation information available at those points. This is possible if one declines from the quadratic restriction, considering general homogeneous functions of degree two instead. We show that one may interpret the interpolated ADC as a family of DTI tensors, parametrized by orientation. Any choice of a preferred direction—notably a stipulated fiber tangent—singles out a unique DTI tensor instance. Results are physically plausible and intuitive.
|Title of host publication||Visualization and Processing of Higher Order Descriptors for Multi-Valued Data|
|Editors||I. Hotz, T. Schultz|
|Place of Publication||Cham|
|Number of pages||383|
|Publication status||Published - 2015|
|Name||Mathematics and Visualization|