# Reflectance Transformation Imaging as a Tool for Computer-Aided Visual Inspection
## 4 Results and Discussion  
The overall results presented in Figure 8 reflect the difference in perception between the surfaces reconstructed with the three modeling methods tested and the reference surface (raw data). It appears that with a median value of approximately 6%, PTM was rarely chosen compared with the HSH and DMD renderings. A considerable preference was observed for the DMD reconstructions, amassing 58% of the participants' clicks over 34% for HSH and 6% for PTM. Regarding the surface material (Figure 8b), we can notice that the HSH gain performance for surface sample \(S_{2}\) (Spectralon(R)) gained 50% of the participants' clicks against 48% for DMD, while HSH fell to 25% for \(S_{3}\), where the participants chose DMD as the most accurate model to reconstruct the angular reflection of light using the RTI system. Thus, it appears that even for diffuse surfaces (such as \(S_{1}\)), the HSH and DMD global modeling methods produced a lower difference in perception than the PTM method. However, we observed that the more complex the behavior was in terms of angular reflectance, the more the gap between the methods increased, with a clear advantage for the DMD method when the texture was anisotropic (such as \(S_{3}\)), which was consistent with the shapes and complexity of the decomposition bases implemented for the HSH and DMD methods. Figure 7: Example of images of appearance renderings with the three implemented models (random display) extracted from the DoE experimental videos (magnification: 40%; sampling density: 50). The top-left sub-image is the reference (acquisition). (**a,b**) Surface sample \(S_{1}\). (**c,d**) Surface sample \(S_{2}\). (**e,f**) Surface sample \(S_{3}\). The detailed results for the different factors and modalities of the design of the experiment are presented as a heatmaps associated with each surface sample (\(S_{1-3}\)) in Figure 9. As for the overall results, we observed a clear preference for the HSH and DMD methods in the perception of visual reconstructions. It can be noted that, particularly for the \(S_{3}\) surface sample and to a lesser extent the \(S_{1}\) surface sample, the PTM method saw its performance increase and the HSH method saw its performance decrease when the angular density increased. With the \(S_{1}\) sample also being relatively anisotropic (orientation of the fibers of the paper in two main directions), this result underlines once again the difficulty of the HSH approach to render the appearance produced by anisotropic textures. Concerning the magnification, it generally appears that the higher the magnification, the greater the difference between the methods, and the more the reconstructions associated with the DMD method were chosen. This result is explained by the fact that the higher the zoom, the smaller the integration zone and therefore the averaging of the reflectance behavior associated with each pixel, and the more the complexity of the measured behavior increased. The DMD method having a decomposition basis of greater complexity then made it possible to reconstruct the local visual rendering more accurately. Finally, concerning the effect of the density, we observed a relatively better result compared with the other methods of the PTM technique for 400 acquisition positions. This counter-intuitive result might be explained by the fact that sometimes, for high acquisition densities, the most efficient reconstruction techniques have the effect of including behaviors around the salient reconstruction angle and therefore represent in the renderings details not present in the raw image. This defect, which concerns high-frequency variations in angular reflectance frequency, is linked to the very principle of reconstruction techniques by global approximation. There is therefore, in terms of acquisition, an optimum in terms of the number of light positions associated with the RTI sequence, which is not necessarily associated with the densest possible acquisition.