Discrete Modal Decomposition: a new approach for the reflectance modeling and rendering of real surfaces

Reflectance Transformation Imaging is a recent technique allowing for the measurement and the modeling of one of the most influential parameters on the appearance of a surface, namely the angular reflectance, thanks to the change in the direction of the lighting during acquisition. From these photometric stereo images (discrete data), the angular reflectance is modeled to allow both interactive and continuous relighting of the inspected surface. Two families of functions, based on polynomials and on hemispherical harmonics, are cited and used in the literature at this aim, respectively, associated to the PTM and HSH techniques. In this paper, we propose a novel method called Discrete Modal Decomposition (DMD) based on a particular and appropriate Eigen basis derived from a structural dynamic problem. The performance of the proposed method is compared with the PTM and HSH results on three real surfaces showing different reflection behaviors. Comparisons are made in terms of both visual rendering and of statistical error (local and global). The obtained results show that the DMD is more efficient in that it allows for a more accurate modeling of the angular reflectance when light-matter interaction is complex such as the presence of shadows, specularities and inter-reflections.