# Quaternion Processing Techniques for Color Synthesized NDT Thermography
## 5 Discussion
### Analysis of the Results and Comparison to Common Processing Techniques  
In this study, a large amount of data has been generated as a result of the analysis of different dimensionality reduction techniques, different quaternionic data processing techniques and the application of different SNR metrics on a total of 34 defects. The presentation and discussion of the results has been simplified to show those of greater relevance. For this, the results obtained for the dimensionality reduction techniques using Gaussian KPCA are presented below, with the QFT, QPCA and quaternionic filtering by spatial convolution (QFILT) processing, and the seven different SNR metrics calculated for the synthetic defects located under 1 mm (def1), 3 mm (def2) and 5 mm (def3), and the experimental defects located deeper and with larger size (def4), medium size (def5) and smaller size (def6). Figure 12 shows the graphical representation by bar diagrams of the maximum SNR values obtained for the defects analyzed with the different quaternionic processing techniques together with the values obtained with conventional thermographic data processing techniques (polynomial fitting, first and second derivatives, and PCA) as well as the value obtained with the original sequence. The y-axis values are represented in a logarithmic scale to correctly visualize the data for all cases. The SNR values have been calculated for the intensity data considering them as gray colors, i.e., assigning the 3 color components the same value, equal to the value of its intensity, and applying the same procedure as for the color data produced in the quaternionic processing. It can be observed in Figure 12 that the ranges of the values obtained for the different cases of SNR are very different, which means that different definitions of SNR are not mutually comparable. In most cases, larger and more superficial defects produce higher SNR values. It can be verified that quaternionic processing techniques produce higher SNR values than conventional ones for all the SNR cases except for SNR7, where the experimental defects produce maximum values for first derivative and conventional PCA. QFT processing has provided maximum SNR values for all the synthetic defect cases, while QPCA has provided maximum SNR values for the experimental defects. In general, the QFILT processing does not increase the SNR with respect to QFT and QPCA, what can be justified by the effect that this processing produces to the input data. The area inside the defects acquires a homogeneous shade tending to gray, while the edges are highlighted with colors. Most probably the use of another sharpness-type metric provided a more favorable evaluation for this quaternionic processing. Figure 13 shows the maximum SNR values obtained for the analyzed defects by applying quaternionic processing to the different cases of dimensionality reduction by Gaussian KPCA. The y-axis values are represented in a logarithmic scale to correctly visualize the data for all cases. It is verified again that the ranges of values obtained for the different cases of SNR are very different, which means that different definitions of SNR are not mutually comparable. Figure 12: Maximum SNR values obtained with the proposed quaternion processing techniques and the conventional thermographic processing techniques: (**a**) SNR1, (**b**) SNR2, (**c**) SNR3, (**d**) SNR4, (**e**) SNR5, (**f**) SNR6, (**g**) SNR7. Figure 13: Maximum SNR values obtained with Gaussian KPCA dimensionality reduction technique applied with different variance values: (**a**) SNR1, (**b**) SNR2, (**c**) SNR3, (**d**) SNR4, (**e**) SNR5, (**f**) SNR6, (**g**) SNR7. It is observed that the maximum values of SNR are produced for different values of variance depending on the defects analyzed and the metric used. For SNR1, the maximum values for synthetic defects are obtained with variances greater than 0.05, while for experimental defects they are obtained for variances greater than 0.1. In both cases the variance of 0.01 obtained acceptable results.