Spatial randomness-based anomaly detection approach for monitoring local variations in multimode surface topography

Anomaly detection of three-dimensional (3D) topographic data is a challenging problem in spatial data analysis. In this paper, we investigate spatial patterns of 3D surface data that exhibit multiple in-control modes. In complex manufacturing processes, surfaces of final products could contain different topographic features from one in-control surface to another, thus making it difficult to monitor the surface with existing approaches, which rely on the assumption of the presence of single mode surface topography. We propose a novel anomaly detection approach for monitoring local topographic variations in the presence of multimode surface topography. We present a binarization model to capture the generic behavior of the multimode surfaces and enhance the representation of the surface. To systematically monitor the surface, we introduce a new probabilistic distance measure (PDM) that quantifies the similarity of spatial patterns between two binarized surfaces. The proposed PDM takes advantage of identifying local variations by utilizing the order neighbor statistics, which captures the local property on the surface. Experimental results with numerical simulation data and real-life paper surface data are provided to demonstrate the effectiveness of the proposed approach.