Shape descriptors and statistical classification on areal topography data for tile inspection in tessellated surfaces

Verification of conformance to design specifications in production, and identification of defects related to wear or other damage during maintenance, are key metrological aspects that must be addressed for micro-scale tessellated surfaces. A new algorithmic approach is presented that operates on topography datasets as obtained by areal topography instruments. The approach combines segmentation algorithms with a novel implementation of the angular radial transform, originally adopted by the MPEG-7 standard, to implement shape descriptors and associated similarity metrics. Applications to the inspection and verification of laser-manufactured micro-embossing topographies are illustrated. The topographies are first segmented to extract the individual tiles; the tiles are then encoded through shape descriptors. Principal component analysis and cluster analysis are used to investigate the behaviour of the angular radial transform coefficients. Finally, an algorithmic classifier based on supervised learning (k-nearest neighbours) is implemented and shown to be effective at identifying defects and at discriminating between defect types.