# Multivariate Analysis of Transient State Infrared Images in Production Line Quality Control Systems
## 1 Introduction  
The constant development of measuring techniques and equipment results in a huge amount of data available for quality control tasks. Thermal imaging and thermal cameras are very good examples of this trend [1]. However, the progress in hardware capabilities would be useless if not followed by the progress in algorithms and software [2,3]. Of course, new algorithms force hardware development, too. In general, both key players in quality control, i.e., hardware and software, influence each other. A pattern recognition system used for industrial quality control based on infrared images has to be highly reliable and fast. While the reliability is a self-evident feature of any system aimed at industry, the acceptable time for testing a single device is highly dependent on the application. Sometimes the algorithm that is too slow for the production line application gives the most accurate results. Therefore, especially in the case of very high-volume production lines, the choice of the algorithm should be a compromise between the classification reliability and speed of calculation. This paper is devoted to the application of a well-known multivariate algorithm, i.e., PCA, to analysis of data acquired with the help of thermal cameras. The successful application of such algorithms in other fields allows us to expect improvement of production line quality control results. Multivariate algorithms enable reduction of the dimension of input space in classification problems and so they make them easier to solve [4]. It is especially important in the case of n \(\times\) m images for which each pixel can be treated as a separate piece of information, and so the dimension of the input space can be as high as n \(\times\) m [5]. Depending on the resolution, information included in adjacent pixels can be more or less correlated and feature extraction is indispensable [6]. Quality control can be based on single thermal images (2D data) but the output signal of a thermal camera is a 3D signal. In this paper, the importance of the third dimension through detailed analysis of the time evolution of features extracted using a multivariate algorithm has been shown. Such an approach, i.e., temporal analysis of PCA results aimed at acquisition time selection, has not been presented in the literature. The current state of the art of applications of PCA in infrared imaging has been presented in Section 3. So far, the testing time has been selected on the base of temporal thermal contrast evolution [7]. Some rough estimations have been also used to set the acquisition time which should be optimal to perform quality control [8; 9; 10]. However, such estimations usually suffer from overestimating the required time which is especially undesirable in production line applications. Moreover, this research has revealed that in some cases waiting too long can decrease the efficiency of the quality control based on thermal images. Transient state analysis of thermal images has been considered in many papers. In the simplest case the feature extraction has not been applied and each pixel of the thermal image has been used for classification [5; 10; 11]--the comparison of heating and cooling patterns for each pixel or the number of pixels above a threshold value allows for the detection of elements or regions with defects. Sometimes it is enough to monitor time changes of maximum temperature. Advanced temporal analysis, but not based on a multivariate approach, can be found in [2]--the classification is based on time waveforms representing statistical features extracted from the fused infrared and vision images. The other application of infrared temporal analysis consists in the calculation of energy balance and heating curves of electrical machines which afterwards can be used for defect detection [12]. The temperature time history of the thermographic data is also used to extract the region of interest before applying post-processing and classification methods [13].