Scan Statistics for the Detection of Anomalies in M -Dependent Random Fields with Applications to Image Data
研究了一类基于局部均值的扫描统计量在M相依随机场中的极限定理，可用于检测医学癌细胞、自动驾驶障碍物或建筑裂缝等异常区域，并在混凝土裂缝检测中展示了应用潜力。
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.