# Reflectance Transformation Imaging as a Tool for Computer-Aided Visual Inspection
## 2 Background on the Implemented Techniques
### Perceptual Assessment  
As mentioned above, surfaces are still often inspected by visual sensory analysis. In the industrial context, the results obtained by this type of approach remain the gold standard. Moreover, with the human perception mechanisms being very complex, the only manner of verifying the results obtained by means of instrumental measurement is comparison with sensory measurements. Thus, the proposed method is based on psychometric experiments. We detail here the main approaches to evaluate the perceived quality of images (or image sequences) reconstructed by the RTI technique.  
Several subjective scaling methods can be used to measure the perceived quality of images and find the relation between physical characterization and the stimulus [50]. One of the most common approaches is Absolute Category Rating (ACR), where the evaluation of the test sequences uses a category scale. ACR with a hidden reference (ACR-HR) is a variation of this approach that implements a hidden reference test sequence. An alternative is the Degradation Category Rating (DCR) [50], where the degradation, (i.e., the distance to the reference image) is rated on a five-point scale. Test sequences can also be displayed in pairs of references and stimuli. This is particularly the case for the double stimulus impairment scale method. Each pair is then displayed simultaneously on the same monitor, which reduces the experiment's time and helps subjects to rate the stimulus in parallel comparison to the reference. Another pair approach is the Pair Comparison method (PC) [51], where two images are presented and the operator has to decide which image possesses more of an investigated attribute. We chose to implement the principle of the PC method. Indeed, because of the choice of factors and modalities of the DoE, and also because the experiment was conducted from reconstructed videos and not static images, the experimentation time is an important criterion. The PC approach indeed saves time due to the simultaneous viewing of the analyzed videos and the absence of distance quantification. Moreover, the literature about RTI has shown that the reconstruction models were very influential on the quality of the reconstruction. We therefore chose to extend the PC approach to a triple comparison, which made it possible to evaluate the three selected models simultaneously. This approach is detailed in Section 3.2.  
Another important point is the implementation of a training phase prior to the psychometric evaluation. Indeed, to ensure the subjects' full understanding of the requested task (familiarization with the assessment tool and instructions) and stabilize the subjects'evaluation, a preliminary training session is recommended for each subject using at least five representative test sequences (ITU-R Standard, [50]). Indeed, the training session allows the participants to become aware of the type of images or videos that they will have to evaluate and the scale of variation that they will encounter, which can help to notably improve the intra-observer repeatability. Two pieces of information need to be assessed for choosing training sequences [50]: the Spatial perceptual Information (_SI_) and the Temporal perceptual Information (_TI_). The SI indicates the amount of spatial detail of a sequence. This descriptor is based on the Sobel filter, and its mathematical expression is given in Equation (1). TI describes the difference between the same pixels' values in two successive frames. Its expression is given in Equation (2):  
\[SI=Max_{time}\{std_{space}[Sobel(F_{n})]\} \tag{1}\]  
\[TI=Max_{time}\{std_{space}[\Delta(i,j)]\}\ \ \ with\ \ \Delta(i,j)=F_{n}(i,j)-F_{n-1}(i,j) \tag{2}\]  
where \(Sobel(F_{n})\) represents the filtered frame at time (\(F_{n}\)), \(std_{space}\) is the standard deviation computed over the pixels, and \(max_{time}\) is the maximum value in the time series.  
The implementation of this training phase in our methodology for the RTI-based approach is presented below in Section 3.