Spatially weighted graph theory-based approach for monitoring faults in 3D topographic surfaces

Three-dimensional (3D) optical systems have been recently deployed for the assessment of 3D topography of finished products during manufacturing processes. Although the 3D topographic data contain rich information about the product and manufacturing processes, existing monitoring approaches are incapable of capturing the complex characteristics between the topographic values, which makes them ineffective in detecting local and spatial surface faults. We develop a spatially weighted graph theory-based approach for accurate monitoring of 3D topographic surfaces. We imporove the representation of surface characteristicsby proposing the in-control multi-region surface segmentation algorithm, which segments the observed topographic pixels into clusters according to the information learned from in-control surfaces. We propose the maximum local spatial randomness feature for the effective description of local and spatial topographic characteristics. After representing the surface characteristics as a spatially weighted graph network, we monitor its connectivity through the developed spatial graph connectivity statistic. The proposed approach is robust in detecting and locating different forms of local and spatial faults that appear on simulated and real-life topographic surfaces and outperforms the existing monitoring approaches.