# Quaternion Processing Techniques for Color Synthesized NDT Thermography
###### Abstract  
Infrared thermography is a widely used technology that has been successfully applied to many and varied applications. These applications include the use as a non-destructive testing tool to assess the integrity state of materials. The current level of development of this application is high and its effectiveness is widely verified. There are application protocols and methodologies that have demonstrated a high capacity to extract relevant information from the captured thermal signals and guarantee the detection of anomalies in the inspected materials. However, there is still room for improvement in certain aspects, such as the increase of the detection capacity and the definition of a detailed characterization procedure of indications, that must be investigated further to reduce uncertainties and optimize this technology. In this work, an innovative thermographic data analysis methodology is proposed that extracts a greater amount of information from the recorded sequences by applying advanced processing techniques to the results. The extracted information is synthesized into three channels that may be represented through real color images and processed by quaternion algebra techniques to improve the detection level and facilitate the classification of defects. To validate the proposed methodology, synthetic data and actual experimental sequences have been analyzed. Seven different definitions of signal-to-noise ratio (SNR) have been used to assess the increment in the detection capacity, and a generalized application procedure has been proposed to extend their use to color images. The results verify the capacity of this methodology, showing significant increments in the SNR compared to conventional processing techniques in thermographic NDT. infrared thermography; non-destructive testing; processing technique; dimensionality reduction; colorization; quaternion +
Footnote †: journal: Applied Sci. 12 January 2021  
Dept. of the ACM/Mechanical Design of the ACM/Mechanical  
heat flows produced in the inspected objects and the effects on the thermal radiation they emit. Infrared imaging technology has evolved rapidly in the recent years. From the earliest experiments with \"calorific rays\" detector materials carried out by [PERSON] in 1800 [7] to the present, infrared (IR) sensors have been developed extensively, from thermal devices equipped with scanning systems to modern photonic sensors arranged in focal plane arrays and thermal cameras for smartphones [8; 9]. Thermal stimulation techniques for infrared thermographic NDT have also evolved over time, so the use of some of these techniques is currently well established [10]. These technological advances together with the decrease of manufacturing costs have stimulated the rapid expansion of IRT technology, including its application as NDT technique, which currently provides high levels of defect detection. However, in addition to infrared sensors and thermal stimulation systems, the IRT NDT technique also requires an efficient and precise methodology for the analysis of the results that ensures the correct characterization of the detected indications and enables the accurate determination of key parameters such as the size of the detected defects, the depth at which they are found and their nature [11; 12]. Infrared thermography is a technology of proven effectiveness for its application as NDT technique; however, one of its main limitations is the lack of a general criterion to correctly characterize the detected defects. Numerous analysis methodologies based on different data processing techniques are available presently, but generally the characteristics of the detected defects that they produce depend on many factors, such as their nature and depth, so the same result may correspond to different fault conditions [13; 14]. Furthermore, each processing technique provides higher detection capacity for different faults, and different processing techniques show each defect by different signal characteristics.