1. An image analysis apparatus for analyzing orientations of fiber bundles of X-yarns and Y-yarns from a three-dimensional image of a woven fabric made of fiber bundles of the X-yarns, the Y-yarns, and Z-yarns, the image analysis apparatus comprising: a binarization unit that binarizes the three-dimensional image; an overlapping area extraction unit that extracts an overlapping area, in which the X-yarns and the Y-yarns perpendicularly and three-dimensionally intersect with each other, from the binarized image; a reference direction determination unit that averages an overlapping direction of each voxel included in the overlapping area and determines the averaged direction as a reference direction; a Z-yarn removal unit that removes the Z-yarns from the binarized image by applying a directional distance method on a reference plane perpendicular to the reference direction; and a fiber bundle orientation estimation unit that applies the directional distance method again to the image, from which the Z-yarns have been removed, on the reference plane and estimates the orientations of the fiber bundles of the X-yarns and the Y-yarns on the basis of a directional distance calculated upon the application.