In this paper, we present a novel, robust multi-view normal field integration technique for reconstructing the full 3D shape of mirroring objects. We employ a turntable-based setup with several cameras and displays. These are used to display illumination patterns which are reflected by the object surface. The pattern information observed in the cameras enables the calculation of individual volumetric normal fields for each combination of camera, display and turntable angle. As the pattern information might be blurred depending on the surface curvature or due to non-perfect mirroring surface characteristics, we locally adapt the decoding to the finest still resolvable pattern resolution. In complex real-world scenarios, the normal fields contain regions without observations due to occlusions and outliers due to interreflections and noise. Therefore, a robust reconstruction using only normal information is challenging. Via a non-parametric clustering of normal hypotheses derived for each point in the scene, we obtain both the most likely local surface normal and a local surface consistency estimate. This information is utilized in an iterative min-cut based variational approach to reconstruct the surface geometry.