Measurement of the geometry of triple junctions between grain boundaries in polycrystalline materials is used to generate large sets of dihedral angles from which maps of the grain boundary energy are extracted. A preliminary analysis has been performed for samples of magnesia and aluminum based on a three-parameter description of grain boundaries. An extended form of orientation imaging microscopy (OIM) was used to measure both triple junction geometry via image analysis in the SEM and local grain orientation via electron back scatter diffraction. Serial sectioning with registry of both in-plane images and successive sections characterizes triple junction tangents from which true dihedral angles are calculated. If there is local equilibrium at each triple junction, we may apply Herring's relation. By limiting grain boundary character to a (three parameter) specification of misorientation for the preliminary analysis, we can neglect the torque terms and apply the sine law to the three boundaries. This provides two independent relations per triple junction between grain boundary energies and dihedral angles. By discretizing the misorientation and employing multiscale statistical analysis on large data sets, (relative) grain boundary energy as a function of boundary character can be extracted from triple junction geometry. The results are discussed with respect to current understanding of grain boundary structure based on their crystallography. The results suggest that a three parameter characterization of grain boundaries (lattice disorientation) is not an adequate description of boundary character. A full analysis including torque terms and a five parameter boundary description is under development.