Scan Statistics for the Detection of Anomalies in M-Dependent Random Fields with Applications to Image Data

Anomaly detection in random fields is an important problem in many applications including the detection of cancerous cells in medicine, obstacles in autonomous driving and cracks in the construction material of buildings. Such anomalies are often visible as areas with different expected values compared to the background noise. Scan statistics based on local means have the potential to detect such local anomalies by enhancing relevant features. We derive limit theorems for a general class of such statistics over M-dependent random fields of arbitrary but fixed dimension. By allowing for a variety of combinations and contrasts of sample means over differently shaped local windows, this yields a flexible class of scan statistics that can be tailored to the particular application of interest. The latter is demonstrated for crack detection in 2D-images of different types of concrete. Together with a simulation study this indicates the potential of the proposed methodology for the detection of anomalies in a variety of situations. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.