We show how a novel, non-linear representation of edge structure can be used to improve the performance of model matching algorithms and object verification/recognition tasks. Rather than represent the image structure using intensity values or gradients, we use a measure which indicates the orientation of structures at each pixel, together with an indication of how reliable the orientation estimate is. Orientations in flat, noisy regions tend to be penalised whereas those near strong edges are favoured. We demonstrate that this representation leads to more accurate and reliable matching between models and new images, and leads to better recognition/verification of faces in an access control task.