We present an energy matrix representation for multiband images that captures spatial and spectral properties. Using a physical model for spectral reflectance, we derive a pseudoinverse method for the comparison of energy matrices that is invariant to the spectral properties of the scene illumination. At the same time, this method determines the illumination change matrix, allowing direct comparison of images obtained under different illumination conditions. We demonstrate the performance of the method for both illumination-invariant recognition and illumination correction on a large set of multiband images. The energy matrices are generated using a small set of oriented steerable filters. We also demonstrate that a related set of rotationally symmetric filters can be used for recognition invariant to both illumination and rotation and that subsequent processing can be used to recover the rotation angle of a recognized object.