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Even small variations of the curvature of a surface may cause malfunction of a part or be perceived as visually unpleasant. However, in the case of specular and painted surfaces, curvature defects can hardly be detected with traditional measurement methods like triangulation or stereoscopy. We describe new strategies to measure the curvature of such surfaces based on deflectometry. This technique mimics the behavior of a human observer by using the object under examination as a mirror. By analyzing its imaging properties, a partial inference on the surface shape is possible. With this approach, much better results can be achieved as compared with triangulation methods. Furthermore, a reliable measurement of defects showing depths of only a few micrometers is enabled.