Statistical Monitoring of Image Data under Jump Regression Framework

Abstract

Image monitoring is an important research problem that has wide applications in various fields, including manufacturing industries, satellite imaging, medical diagnostics, and so forth. This problem, however, presents a challenging big data issue in the sense that, (i) it is characterized by high velocity and high volume of the data streams, (ii) observed im- age intensity functions are discontinuous in nature, have spatial structures, and it often contains noise, (iii) a typical grayscale image has a large number of pixels, implying high- dimensional nature of the data, (iv) in some applications, image surface often contains artifacts and insignificant anomalies (e.g., shadows, clouds, etc.), (v) sequence of im- ages are often not geometrically aligned. In this dissertation, image monitoring schemes are developed on the basis of image intensity values, edges, and other complex features from the image surface. This dissertation aims to bridge the gap between the research fields of image processing and statistical process control and effectively address all the aforementioned issues. Our proposed methods in this dissertation make use of various state-of-the-art techniques from both research domains and help the research field of image monitoring stride forward. Numerical examples and statistical properties show that the proposed image comparison and monitoring methods in this dissertation perform well in various real-life scenarios. Furthermore, the novel methodological advancements proposed in this dissertation will be highly beneficial to the practitioners in various fields.