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We present a new approach to reconstruct the shape of a 3D object or scene from a set of calibrated images. The central idea of our method is to combine the topological flexibility of a point-based geometry representation with the robust reconstruction properties of scene-aligned planar primitives. This can be achieved by approximating the shape with a set of surface elements (surfels) in the form of planar disks which are independently fitted such that their footprint in the input images matches. Instead of using an artificial energy functional to promote the smoothness of the recovered surface during fitting, we use the smoothness assumption only to initialize planar primitives and to check the feasibility of the fitting result. After an initial disk has been found, the recovered region is iteratively expanded by growing further disks in tangent direction. The expansion stops when a disk rotates by more than a given threshold during the fitting step. A global sampling strategy guarantees that eventually the whole surface is covered. Our technique does not depend on a shape prior or silhouette information for the initialization and it can automatically and simultaneously recover the geometry, topology, and visibility information which makes it superior to other state-of-the-art techniques. We demonstrate with several high-quality reconstruction examples that our algorithm performs highly robustly and is tolerant to a wide range of image capture modalities.