Stochastic Geometry Models for Metallic Surface Textures

In industry, automatic visual surface inspection is a common technique for quality control. Machine learning methods provide promising results for automated defect detection. Data in sufficient quantity and quality is needed to train robust models. Real image data, especially of defective surfaces, is commonly not available in the needed amount. For rarely produced objects, not all critical defect types may be included in the data set. In addition, real data has to be annotated manually. Synthetic data offers a suitable alternative. Therefore, the imaging environment including the camera, the light source and the object to be inspected as well as the imaging method have to be simulated. In this thesis we consider the details of the digital twin of the object to be inspected. We focus on metallic objects which are strongly reflective. Therefore, the visibility of surface defects highly depends on the surface texture. Hence, part one of this thesis deals with the simulation of two different surface textures resulting from the following surface processing methods: sandblasting and linear/spiral milling. Two different models have been developed based on real topography measurements. To model sandblasted surfaces, two steps are needed. To generate textures that cover the entire object surface, small patches are created first using the random phase noise (RPN). Then, those are stitched using an adaptation of the method from Efros and Freeman. Textures of milled surfaces are modeled by a multi-step model, considering the milling pattern, the movement of the milling head and the overlap of neighboring milling paths. Real parameters are included into the model. Part two of this thesis deals with the simulation of synthetic 3d defect geometries which can then be added to an object geometry. We restrict to common defect types that appear for cast objects, for example cracks, rat tails or lift-offs of the surface top layer. Parametric, defect-specific models are developed. In general, 2d Voronoi tessellations build the basis for the models since they reflect the poly-crystalline micro-structure of metal. The tessellations are used to model defects on different scales and to ensure variability also when using the same parameter configuration due to the underlying random point processes. The diversity of defect geometries within a defect class is obtained by different parameter configurations.