# Reflectance Transformation Imaging as a Tool for Computer-Aided Visual Inspection
## 2 Background on the Implemented Techniques  
### Reflectance Transformation Imaging  
The Reflectance Transformation Imaging (RTI) technique [31; 32; 33] consists of acquiring a series of images from several light directions using a camera positioned orthogonally to the inspected surface. Each image of the acquired Multi-Light Image Collections (MLICs) corresponds to an illumination direction and represents a discrete measurement of the luminance in one lightning direction. The angular reflectance of each pixel is then modeled as illustrated in Figure 1 (modeling section), where the measured luminance values are represented in the normalized \((L_{\mu},L_{\
u})\) space as defined in [32] and the vertical axis is associated with the sensor gray level range (\([0,255]\)). These local experimental models make possible the relighting, (i.e., the continuous reconstruction of the visual rendering of the inspected surface) for virtual illumination angles. The principle of this technique is illustrated in Figure 1, where PTM, HSH, and DMD are RTI reconstruction models and stand for Polynomial Texture Mappings, Hemispherical Harmonics, and Discrete Modal Decomposition, respectively. Many new RTI acquisition modalities have recently been developed, including multi-spectral approaches [34; 35], approaches to measure the complete luminance dynamic (HD-RTI, [36; 37; 38]) self-adaptive approaches to determine the relevant lighting directions (NBLP-RTI, [39]), and even robot-based RTI systems [40]. Within the framework of this research, we focus on the RTI acquisition parameters associated with the conventional approach. In a non-exhaustive way, these parameters are associated with the spectral content of the lighting implemented, the distribution of the lighting positions, their number or density [41; 42], or even the measurement scale. In terms of processing, the main parameter is linked to the choice of the modeling method. Processing an RTI set of images allows one to model the local angular reflectance at each point or pixel of the inspected surface and allows  
Figure 1: Principle of the RTI technique from acquisition to relighting. The RTI acquisition is the system that allows acquisition of a surface to be made. (**a**–**c**) Modeling is using the acquisitions to model the behavior per pixel. Visual relighting allows to reconstruct from the models an image lighted with a specific light position. the relighting of the surface in virtually any arbitrary direction of light. Originally, there was the Polynomial Texture Mappings (PTM) [32; 33; 43] approach, based on second-order polynomials. This method is simple, robust, and easy to implement, but it has the disadvantage of excessively smoothing the measured luminance point clouds, which alters the quality of the reconstructions when the surfaces are not Lambertian [44]. Other approaches were then developed to overcome this limit, in particular the HSH method based on Hemispherical Harmonics [45] and Discrete Modal Decomposition (DMD) [44; 46; 47]. This last approach implements the natural modes of vibration to form the basis of decomposition. More recently, local interpolation approaches have shown interesting results, such as the Radial Basis Function [48] or even machine learning approaches [49]. In this paper, we have chosen to study three parameters that the authors identified to be particularly influential in previous studies related to Reflectance Transformation Imaging. However, the methodology presented in these works is generic in the sense that it allows, whatever the choice of factors, quantifying the effect of the RTI factors of acquisition and processing in terms of visual perception. The chosen parameters are the density of lighting directions during the RTI acquisition sequence, the measurement scale, and the chosen modeling method.The modalities and levels chosen for the experience plan are detailed in Section 3.