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In this paper we address the problem of representing 3D visual data with parameterized volumetric shape primitives. Specifically, we present a (two-stage) approach built around convolutional neural networks (CNNs) capable of segmenting complex depth scenes into the simpler geometric structures that can be represented with superquadric models. In the first stage, our approach uses a Mask RCNN model to identify superquadric-like structures in depth scenes and then fits superquadric models to the segmented structures using a specially designed CNN regressor. Using our approach we are able to describe complex structures with a small number of interpretable parameters. We evaluated the proposed approach on synthetic as well as real-world depth data and show that our solution does not only result in competitive performance in comparison to the state-of-the-art, but is able to decompose scenes into a number of superquadric models at a fraction of the time required by competing approaches. We make all data and models used in the paper available from https://lmi.fe.uni-lj.si/en/research/resources/sq-seg.