General Cramér-von Mises, a helpful ally for transparent object inspection using deflection maps?

Transparent materials are utilized in different products and have to meet high quality requirements, i.a., they have to be free from scattering defects. Such material defects are mainly manifested in changes of the direction of light transmitted through the object. Laser deflection scanners can acquire so-called four-dimensional light deflection maps conveying both, the spatial and angular information about captured light rays. In order to detect scattering defects, spatial discontinuities of the angular deflection distribution have to be extracted out of the deflection maps. This is necessary since the transparent object itself and possibly present scattering defects can deflect incident light rays into other directions. This contribution introduces a novel distance measure based on the generalized Cramér-von Mises distance that is suitable for comparing spatially adjacent deflection maps. The approach is evaluated by conducting experiments using both, simulated data and existing deflection maps acquired with a prototype of a deflection scanner. The results show, that the method is not as sensitive as the recently proposed earth mover's distance but might be able to yield spatially more accurate visualizations of scattering material defects.