Upper quantile-based CUSUM-type control chart for detecting small changes in image data.

Image monitoring is an important research problem that has wide applications in various fields, including manufacturing industries, satellite imaging, medical diagnostics, and so forth. Traditional image monitoring control charts perform rather poorly when the changes occur at very small regions of the image, and when the changes of image intensity values are small in those regions. Their performances get worse if the images contain noise, and the changes occur near the edges of image objects. In applications such as manufacturing industries, the changes in the images are often too small to be detected by human eyes. In this article, we propose a CUSUM-type control chart for online monitoring of grayscale images. Depending on what kind of changes we wish to detect, big or small, we propose to use a certain upper quantile of the local CUSUM statistics. We incorporate a state-of-the-art jump preserving image smoothing technique in the proposed chart that ensures good performance even in presence of low to moderate noise. Theoretical justifications, and superior performance in numerical comparisons ensure that the proposed control chart can be useful to many researchers and practitioners.