We propose a novel methodology for the detection and analysis of visual anomalies on challenging surfaces (metallic). The method is based on a local assessment of the reflectance across the inspected surface, using Reflectance Transformation Imaging data: a set of luminance images captured by a fixed camera while varying light spatial positions. The reflectance, in each pixel, is modelled by means of a projection of the measured luminances onto a basis of geometric functions, in this case, the Discrete Modal Decomposition (DMD) basis. However, a robust detection and analysis of surface visual anomalies requires that the method must not be affected neither by the geometry (sensor and surface orientation) nor by the texture pattern orientation of the inspected surface. We therefore introduce a rotation-invariant representation on the DMD, from which we devise saliency maps representing the local differences on reflectances. The methodology is tested on different engineering metallic samples exhibiting several types of defects. Compared to other saliency assessments, the results of our methodology demonstrate the best performance regarding anomaly detection, localisation and analysis.