1. A fiber rendering apparatus comprising: a device for specifying a region of interest or volumetric region of interest in three-dimensional image data collected by a diffusion tensor method in an MRI apparatus; a device for defining regular grid points in the region of interest or volumetric region of interest; a device for defining points obtained by randomly moving the grid points in a two-dimensional or three-dimensional manner as tracking start points; a device for performing diffusion tensor analysis on each tracking start point in the three-dimensional image data to determine a direction of a principal axis vector; a device for tracking a fiber by repeatedly selecting a neighbor point along the direction of the principal axis vector and performing diffusion tensor analysis on the neighbor point to determine a direction of a principal axis vector; and a device for producing and displaying an image of the tracked fibers as viewed in a desired view direction.