This paper describes the study of new methods for characterizing the orientation of fiber segments in low density paper towel from two- and three-dimensional X-radiographic data sets. The end use properties of the absorbent hygiene grades such as paper towels and tissues stem from an open porous structure where stochastically distributed fibers are contorted by post forming processes to increase bulk, stretch, flexibility and softness, while maintaining adequate strength. The orientation of free fiber segments that form the network are kinked and curved in three dimensions by processes including creping, through air drying and embossing. Providing a linkage between process conditions and the end use properties through the characterization of the network structure is the overarching goal of this investigation. A method is presented for mapping the 2D, in-plane orientation of fiber segments using soft (6kV) X-radiographs and an algorithm for calculating the image moments for circular sub-regions that surround each point. The eigenvectors form the major and minor axes of the inertial ellipse from which the principal orientation may be extracted. Colorized maps representing the local orientation are used to examine the effects of embossing and creping, as well as comparing different forming processes. A method for characterizing fiber segment orientation in three dimensions uses a similar approach applied to binarized X-ray micro-computed tomographic data sets. The inertial ellipsoid is determined by performing principal component analysis on the covariance matrix of the voxels contained within a spherical region surrounding each solid voxel within the structure. The eigenvectors are used to extract the shape and principal orientation of the ellipsoids which are plotted as colorized representations in 3D space. The 2D and 3D plots demonstrate the sensitivity of the method to orientation of fiber segment mass, while mean fiber orientation plots reveal differences between samples.