# Quaternion Processing Techniques for Color Synthesized NDT Thermography
## 6 Conclusions  
In this study, a new methodology for the processing and analysis of NDT thermographic sequences is proposed. This methodology consists of two stages. The first stage applies a novel method called Thermographic Colorization by Computational Synthesis (TCCS), which extracts a large amount of relevant information from NDT thermographic inspections and synthesize it in a single-color video sequence. The second stage applies quaternionic algebra operations to the produced color images to optimize the visualization and characterization of the detected defects.  
The information synthesis process is carried out by means of dimensionality reduction techniques. In this study, four reduction techniques have been analyzed: Independent Component Analysis, Principal Component Analysis, Kernel Principal Component Analysis and Minimum Noise Fraction, proving that the KPCA technique produces the best results. After the data synthesis colorization stage, color image processing techniques based on quaternion algebra operations are applied. Three different techniques of quaternion analysis have been applied: Quaternion Fourier transform, Quaternionic Principal Components Analysis and Quaternionic Filtering by Spatial Convolution.  
A graphical method for optimizing the analysis directions in QFT has been developed that enables the automatization of this quaternionic processing. This method is based on the use of spheres to define the directions of analysis, synthesize the information about the output signal levels through the color of each point on the sphere, and graphically represent the final results produced by the assessment metrics.  
The use of color images as results of NDT thermographic inspections makes the conventional SNR definitions used to assess the results not directly applicable. In order to assess results represented by color images and compare them with conventional results represented by grayscale images, the application method of SNR metrics has been generalized in this study. For this, a perceptually linear color space (Lab) has been used, to which the color and gray data are transformed, and the definition of SNR has been adapted to extend it to the 3D case.  
The evaluation of the results obtained has shown that the proposed methodology improves the results compared to conventional thermographic NDT processing, increasing the level of detection and improving the distinction of the defects by their representation in different color shades. The results have been evaluated with different definitions of SNR, for most of which the quaternionic Fourier and principal component analyses produce a high increase in the SNR level. It has been found that quaternionic filtering by spatial convolution does not produce an increase in SNR, even though it improves the visualization of the detected defects and facilitates their characterization. This shows that the SNR metric is not suitable for evaluating processing results whose effect is focused on edge enhancement.  
Finally, the analysis of the results obtained using different SNR metrics has demonstrated that the choice of the SNR definition to assess the results has a great impact in the final values, and it can be concluded that the values obtained with different SNR definitions are not comparable among them, producing values of very different orders of magnitude for the same defect.  
Conceptualization, P.V., R.U. and J.P.; methodology, P.V. and I.S.d.O.; software, P.V. and R.U.; validation, P.V., R.U. and J.P.; formal analysis, P.V.; investigation, P.V.; resources, R.U., J.P. and I.S.d.O.; data curation, P.V. and I.S.d.O.; writing--original draft preparation, P.V.; writing--review and editing, P.V., R.U. and J.P.; visualization, I.S.d.O.; supervision, R.U., J.P. and I.S.d.O.; project administration, P.V. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.