# Quaternion Processing Techniques for Color Synthesized NDT Thermography
## 5 Discussion  
The results obtained with the proposed colorization methodology have been compared with conventional processing techniques, including the original sequence of thermographic data, the approximate polynomial sequences and their first two derivatives, as well as the principal component analysis applied to the original sequence. The metrics used to evaluate the quality of the results produced have been the SNR in the different versions described before. The SNR calculation procedure was automated, taking advantage of the prior knowledge of the position of the defects, locating the measurement areas of the defects and their corresponding healthy reference areas for each of the induced faults. Figure 10: Original data and final results obtained with the application of quaternionic filtering by spatial convolution to the sequence obtained after QFT and QPCA: (**a**) result for QFT with direction 33 at frame 4, (**b**) result for QFT with direction 33 and frame 16, (**c**) result for QPCA at frame 2, (**d**) result for QPCA at frame 3, (**e**) result for QFILT applied to input (**a**), (**f**) result for QFILT applied to input (**b**), (**g**) result for QFILT applied to input (**c**), (**h**) result for QFILT applied to input (**d**). Figure 9: Results obtained with the application of QPCA processing to the sequence colorized by Gaussian KPCA: (**a**) \(\sigma=0.1\) and frame 2, (**b**) \(\sigma=1\) and frame 3, (**c**) \(\sigma=1\) and frame 3, (**d**) \(\sigma=0.1\) and frame 2, (**e**) \(\sigma=0.1\) and frame 2, (**f**) \(\sigma=0.5\) and frame 1. To correctly compare data of different nature, such as the grayscale images of the original sequence and conventional processes, and the color images of the sequences resulting from the colorization processing, the definition for the SNR has been generalized. The magnitude used to calculate these metrics in grayscale images is the intensity or luminance of the image. In the case of color images represented in RGB space, this magnitude or similar does not exist, but the RGB components are available, which do not describe image intensity properties. To be able to compare color images with grayscale images, it is necessary to represent the color images in a space that separates the intensity characteristics from the characteristics exclusive to the color. Colors can be represented in the HSV space so that the value (V), hue (H) and saturation (S) of each pixel in the image are available [45]. The value component is naturally comparable to the intensity of grayscale images, while the other two components provide additional information unique to color images. Intuitively, it is reasonable to think that a color image provides more information than a grayscale image as it has two additional information channels. In this sense,  
The saturation component provides extra information about the intensity of the color, which could be related to the severity of a defect. However, the hue component is a magnitude that does not have a defined order, so the hue value does not provide useful information on the quality of defect detection as it cannot be compared in an orderly manner. Due to this limitation, it was decided to discard this color space to evaluate the results obtained in the colorization techniques. The color space that was finally used was the Lab space [46; 47]. The Lab color space (L*a*b* or CIELAB) is the color model normally used to describe all the colors that the human eye can perceive (Figure 11). It was developed specifically for this purpose by the Commission Internationale d'Eclairage (International Commission on Illumination). The goal of the Lab space is to produce a color space that is more \"perceptually linear\" than other color spaces, i.e., a change of the same amount in any color value produces a visual change of the same intensity. Due to the property of perceptual linearity of the Lab space, these parameters make it possible to quantify color variations and relate them to flaw detection levels.