# Quaternion Processing Techniques for Color Synthesized NDT Thermography
## 4 Results
### Results in the Colorization Procedure  
The first stage in the evaluation of the proposed colorization techniques has consisted of calculating the polynomial approximations of the original sequence of computationally generated data. A total of 20 polynomial approximations have been calculated for degrees 3 to 22. No approximations of a degree lower than 3 have been calculated due to the high inaccuracy of the approximation obtained, nor have approximations been calculated for degrees greater than 22 because they do not provide additional information regarding approximations of lower degrees.  
After calculating the approximation data, dimensionality reduction techniques have been applied to the generated sequence to obtain a new sequence of color images with synthesized information. Finally, Quaternion Fourier Transformation (QFT) and Quaternion  
Figure 5: Experimental NDT thermographic inspections: (**a**) setup of the laboratory tests, (**b**) depth of defects in the inspected material.  
Principal Component Analysis have been applied to the synthesized sequences, and the resulting images have been processed by quaternionic filtering to optimize the visualization of the detections.  
Several reduction techniques have been analyzed, including PCA, KPCA, ICA and MNF. The parameters used for PCA and MNF are defined by the mathematical method itself. On the other hand, the kurtosis metric has been used in the ICA analysis, and kernels with standard deviation values of 0.01, 0.05, 0.1, 0.5, 1 and 5 have been used in the Gaussian KPCA. The computational algorithms for the application of these reduction methods have been programmed in MATLAB with the support of the hyperspectral analysis package [43].  
The different techniques have been applied to the original sequence of synthetic data, obtaining the corresponding processed sequences. It was found that the reduction technique that produced the best results, being able to synthesize the greatest amount of relevant information in 3 images, was the KPCA technique, followed by the MNF, PCA and ICA technique, respectively. Some representative results obtained with the different colorization techniques are shown in Figure 6.  
In general, and as can be seen in Figure 6, the results provided by the ICA and PCA reduction techniques produce a visualization of different defects using different color ranges, but on the contrary, these two techniques collect large amount of noise in the results, hiding defects that are visible by other reduction techniques (Figure 6a,b). The MNF technique significantly filters the noise level of the images; however, this filtering is produced at the expense of an important reduction in the signal value of defects, obtaining reduced detection levels (Figure 6c). Finally, the KPCA technique produces satisfactory results not only by reducing the noise level of the image but also by increasing the flaw detection capacity (Figure 6d).  
The reduction technique that produced the best results in terms of reducing noise levels and improving defect detection levels was the KPCA. For this reason, it has been chosen as the reduction technique to be applied for dimensionality reduction before the quaternionic processing.  
Figure 6: RGB images obtained by the projection of the results produced with the different dimensionality reduction techniques at the instant 5 s in the thermal sequence: (**a**) ICA, (**b**) PCA, (**c**) MNF, (**d**) KPCA.