A control chart for monitoring images using jump location curves

Image monitoring is a relatively new research area in statistics and machine learning that has wide applications in various fields including medical diagnostics and subsequently disease monitoring, satellite imaging, security systems, and so forth. In the literature, a vast majority of the methods use image intensity changes to detect out of control images. However, this approach is often unreasonable in many real-life applications where a change in contrast between the background and foreground of an image should not indicate an out of control image as long as the boundaries of the image objects remain unchanged. In this article, we propose a Shewhart-type control chart to monitor grayscale images using detected edges of the images. The central idea is to monitor the Hausdorff distance between the point-set of detected edge pixels in each image from the corresponding point-set of the estimated true in-control image. The proposed monitoring procedure should be easy to execute many real-life applications. Numerical studies show that it performs well in various types of situations in comparison with a number of competing methods.