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Anomaly detection in random fields is an important problem in manyapplications including the detection of cancerous cells in medicine, obstaclesin autonomous driving and cracks in the construction material of buildings.Such anomalies are often visible as areas with different expected valuescompared to the background noise. Scan statistics based on local means have thepotential to detect such local anomalies by enhancing relevant features. Wederive limit theorems for a general class of such statistics over M-dependentrandom fields of arbitrary but fixed dimension. By allowing for a variety ofcombinations and contrasts of sample means over differently-shaped localwindows, this yields a flexible class of scan statistics that can be tailoredto the particular application of interest. The latter is demonstrated for crackdetection in 2D-images of different types of concrete. Together with asimulation study this indicates the potential of the proposed methodology forthe detection of anomalies in a variety of situations.

Scan statistics for the detection of anomalies in M-dependent random fields with applications to image data