## 1 Introduction  
Mastering the functional properties of manufactured surfaces is a major scientific and industrial challenge for a wide variety of applications [1]. The functional properties of surfaces cover a large spectrum. A non-exhaustive list includes tribological properties [2, 3], properties associated with material mechanics [4], wettability [5], biological properties, and functional parameters linked to light-surface interaction. This approach induces many issues and scientific challenges, in particular, the choice of measurement technology, the choice of the scale for both measurement and analysis tasks, and the choice of filtering and post-treatment methods. In this context, the RTI imaging method is currently experiencing significant growth [4, 6, 7] and is positioned as a complement to conventional techniques in industry, which are often based on 3D microscopy for the measurement of surface roughness. During the RTI acquisition, the orientation of the light source varies around the surface and passes through a hemispherical space (constant distance). A fixed camera positioned orthogonally to the surface captures the response of the surface (local reflectance) for different lighting angles (angular reflectance). From the acquisition, \(N\) stereo-photometric type images are obtained, each pixel of which corresponds to a discrete measurement of the reflectance of the corresponding point on the surface, as shown in Figure 1, where \(lu\) and \(lv\) represent the components associated with the directions of illumination projected in the horizontal plane. RTI was originally developed at HP labs by [PERSON] et al. [8,9] under a name, Polynomials Texture Mappings (PTM), that refers to the implemented modeling method. Other modeling methods have been developed, such as the HSH (Hemispherical Harmonics) model [10, 11, 12, 13], the DMD (Discrete Modal Decomposition) method [14, 15, 16, 17], and the approach based on RBF (Radial Basis Function) [18,19]. Particularly important development has occurred in the field of the digitization of historical and cultural heritage objects [20, 21, 22]. More recently, this technique has been implemented in the context of a wide variety of industrial applications. These applications have often been related to the challenge of mastering of surface appearance perception and the automation of inspection processes [23,24], although other applications have been found in biomedicine, forensics [25], materials mechanics [4,26], and the analysis of tribological properties [17]. The richness of the contribution of the RTI technique is linked to the quality and variety of surface information that it can estimate. Indeed, this type of acquisition makes it possible to characterize the local angular reflectance of surfaces, i.e., the way light is re-emitted at each point as a function of the angle of illumination. Certain descriptors can statistically describe the angular reflectance response of a surface from RTI data (Figure 2). This type of information is particularly relevant for issues related to surface appearance quality [27], where the challenge lies in increasing the robustness of the results obtained from conventionally implemented sensorial analysis [28, 29, 30]. The RTI technique makes it possible to estimate characteristics linked to the local micro-geometry of surfaces, such as local descriptors of slopes, curvatures, and even topographic descriptors, through integration following the stereophotometric technique. In addition, the specularity and diffusion components provide access to sub-pixel light behaviors, as responses from multiple surface points can be integrated into a single pixel. Thus, we can observe the response of a point on the surface despite it being geometrically of a smaller size than the resolution of the sensor. RTI acquisition and characterization makes it possible to more directly measure and describe aspect function, i.e., the effect that is not geometry intrinsic and is instead created by the geometry of the surface [7,31].