Difference Detection Between Two Images for Image Monitoring

In manufacturing industries, images are commonly used for quality control purposes. In such applications, if the quality of the products is good, then their images should be all similar to the image of a good-quality product. Therefore, comparison of images is a fundamental task in image-based quality control. This problem, however, is complicated in the sense that (1) observed images often contain noise, and (2) the related images need to be geometrically matched up first because images of different products could be geometrically mismatched because the relative positions between a camera and different products are often not exactly the same. The first issue requires a statistical method that can remove noise, and the second issue is related to the so-called image registration problem in the image processing literature. In this article, we propose effective methods for detecting difference between two images of products, and our proposed methods can accommodate both noise and geometric mismatch mentioned above. Theoretical results and numerical examples show that they can work effectively in applications.