Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: application to white matter fiber tract mapping in the human brain

In our article entitled “Color Schemes to Represent the Orientation of Anisotropic Tissues From Diffusion Tensor Data: Application to White Matter Fiber Tract Mapping in the Human Brain,” which appeared in MRM 42:(3)526–540 Sept., 1999, we incorrectly reported some properties of the color scheme previously proposed by Jones, Williams, and Horsfield (1) (Ref. 26 in our original article). In particular, we incorrectly stated that their scheme would present “discontinuity” artifacts, i.e., sharp artifactual boundaries between complementary colors occurring in structures that are oriented approximately within the plane of the image. As we discuss in our article, these discontinuity artifacts originate from the antipodal symmetry of the eigenvectors of the diffusion tensor, and are present in color maps of fiber direction in which all directions are represented with unique hues (“No symmetry” schemes). “Rotational symmetry” schemes in which vector pairs with azimuthal angles ψ and (ψ + π) are depicted with the same hue do not exhibit these artifacts. After the publication of our article, Jones et al. pointed out to us that their scheme belongs to this second group of color representations and therefore does not suffer from a discontinuity artifact. We apologize to Jones and colleagues for our mistake, which originated from our incorrect interpretation of images they presented at the 1997 meeting of the ISMRM. In their color maps, white matter structures that are known to have a homogeneously varying fiber direction anatomically (such as the corpus callosum) were represented as having sharp color transitions, indicating abrupt changes in fiber orientation. The origin of these sharp transitions, however, should be attributed to perceptual nonuniformities in the color representation scheme they used, rather than to a discontinuity artifact. In the enclosed figure, which replaces Figure 4c in our original publication, Jones' scheme is correctly implemented. As a last remark, we want to underscore that we reported and analyzed Jones' color fiber direction mapping method in our article because it was one of the first that associated color with the components of the eigenvectors of the diffusion tensor. Our misinterpretation of the exact implementation of their method should not diminish the credit that these authors deserve for their interesting and original work: they provided the first example of a tensor-based color scheme which assumes rotational symmetry rather than no-symmetry, as we originally believed.