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We propose a novel algorithmic solution for estimating a three-dimensional model of an object observed in a single image. Based on a minimal user input, the algorithm interactively determines the objects' silhouette and subsequently computes a silhouette-consistent 3D model which is precisely the globally minimal surface with user-specified volume. In contrast to a recently published approach to single view reconstruction, the proposed algorithm does not constrain the resolution in the depth-direction, it assures the global optimum and is faster by about an order of magnitude. Experiments demonstrate that plausible high-resolution 3D models can be generated in fractions of a second and compare favorably with other methods.