# Multivariate Analysis of Transient State Infrared Images in Production Line Quality Control Systems
## 3 Application of PCA to Infrared Image Analysis in Production Line Quality Control Systems  
Data mining that leads to information extracting is one of the biggest challenges of contemporary science and one of the main needs of modern industry. In many present-day applications the problem is not to get the data but to analyze a huge amount of easily accessible information in order to make some decisions. Multivariate methods are a tool that can be used to solve this problem. Thermal image analysis belongs to this group of applications for which multivariate methods, including PCA, can be very useful. They become more and more popular in other fields and for sure they deserve also more attention from the infrared community.  
It must be stressed that the effectiveness of PCA in the solution of a particular problem should always be verified. There is no guarantee that classifiers based on PCA features will work well, because PCA determines the projection of the data that enables the best reconstruction and not necessarily the best classification. So far PCA of infrared images has been used for non-destructive testing of materials [14; 15; 16; 17]. It is especially useful for data compression in non-destructive examination and an IR-video sequence and what follows the reduction of processing times required for image classification [18; 19; 20]. However, there are almost no references on the application of PCA approach to high volume production line quality control [6]. Recently, application of the Candid Covariance-Free Incremental Principal Component Thermography (CCIPCT) as well as the Sparse Principal Component Analysis (SPCA) based K-means clustering for automatic defect segmentation in infrared non-destructive testing have been proposed [21; 22]. The CCIPCT method is an extension of Principal Component Thermography (PCT) which has been proposed as a method for defect depth characterization [23; 24]. The other relatively new PCA application consists in the enhancement of contrast [25] and removal of the noise and information redundancy of the infrared image sequences [26].  
The transformation of the original thermal images into principal components applied in production line quality control has been illustrated in Figure 1. The detailed description of the procedure and the classification algorithm have been given in [6]. In this paper, analysis and discussion of time evolution and selection of principal components is a key problem.  
The analysis of temporal evolution of principal components aimed at the optimization of production line quality control for home appliances has been carried out taking refrigerators as a device under test (DUT). They can be regarded as complex units exhibiting a dynamic thermal process after switching on. Although the first question was how to set the time of inspection in order to get the best quality control results, the performed analysis have led us to answers regarding some other questions and more general recommendations valid when dealing with PCA in such application [6]. A typical layout of the production line quality control system based on infrared imaging has been presented in Figure 2.  
Figure 1: Block diagram of the quality control principal component analysis (PCA)-based algorithm and data at its successive steps. PCs: Principal components.  
Figure 2: Exemplary production line quality control system with a device under test (DUT) inspected with the help of an infrared camera (IR)—sources of radiation received by the camera have been presented.  
If infrared images have the resolution of 320 \(\times\) 240 pixels then the input feature space is 76800-dimensional assuming that each pixel is an input variable. The reduction of the dimension of the feature space to 2D presented by [PERSON] and [PERSON] [6] allowed for fast classification and simple interpretation and visualization of classification results. Of course, it brings about loss of information, which can be accepted as long as the correct classification is possible.