Various tools exist to extract diffusion measures from tract profiles. However, they lack the precision in terms of statistical analysis since the tract shapes are registered to a common template. Although this analysis leads to meaningful results, we postulate that there is a significant geometric information in the along-tract diffusion profiles that is unaccounted for. Here we propose a novel method for aligning shapes of diffusion profiles across populations. This method offers improved matching and statistical analysis of along-tract diffusion profiles. Furthermore, this method could be used to perform multivariate statistical analysis of along-tract diffusion profiles in an invariant manner.