General orientation transform for the estimation of fiber orientations in white matter tissues

The orientation distribution function (ODF), which is obtained from the radial integral of the probability density function weighted by rn$$ {r}^n $$ ( r$$ r $$ is the radial length), has been used to estimate fiber orientations of white matter tissues. Currently, there is no general expression of the ODF that is suitable for any n value in the HARDI methods.A novel methodology is proposed to calculate the ODF for any n>-1$$ n>-1 $$ through the Taylor series expansion and a generalized expression for -1