Dense 3D reconstruction still remains a hard task for a broad number of object classes which are not sufficiently textured or contain transparent and reflective parts. Shape priors are the tool of choice when the input data itself is not descriptive enough to get a faithful reconstruction. We propose a novel shape prior formulation that splits the object into multiple convex parts. The reconstruction problem is posed as a volumetric multi-label segmentation. Each of the transitions between

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... s is penalized with its individual anisotropic smoothness term. This powerful formulation allows us to represent a descriptive shape prior. For the object classes used in this paper the individual segments naturally correspond to different semantic parts of the object. This leads to a semantic segmentation as a side product of our shape prior formulation. We evaluate our method on several challenging real-world datasets. Our results show that we can resolve issues such as undesired holes and disconnected parts. Taking into account a segmentation of the free space, we show that we are able to reconstruct concavities, such as the interior of a mug.