This invention describes several novel MRI "stains" to measure and display water diffusion anisotropy data obtained by diffusion tensor MRI (DT-MRI). One problem that this invention overcomes is that it significantly reduces the statistical bias in the mean and variance of the measured anisotropy of water diffusion caused by background noise in the MR images. These benefits are achieved by exploiting the idea that fiber tracts exhibiting diffusion anisotropy vary continuously in most regions. Thus, the principal axes of the diffusion tensor (or eigenvectors) can be used to improve the estimate of the principal diffusivities (or eigenvalues) within a local region of interest. These eigenvalues, in turn, are used to compute our improved local measures of diffusion anisotropy. Images or maps of water diffusion anisotropy are increasingly being used to gather structural information about fibrous tissue, such as white matter fibers as well as cardiac and skeletal muscle fibers in vivo, in health, disease, development, and aging. This invention results not only in a more accurate measurement of diffusion anisotropy, but it improves image quality and reduces scanning time in clinical and biological applications of DT-MRI. Since the reduction in diffusion anisotropy has been shown to be sensitive to nerve fiber degeneration, this new data should be useful in studies to screen for and determine the efficacy of neuroprotective agents, as well as streamline multi-site and longitudinal clinical trials designed to assess their safety and efficacy.