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In this paper, we propose algorithms to manipulate 2D images in a way that is consistent with the 3D geometry of the scene that they capture. We present these algorithms in the context of creating "Out of Bounds" (OOB) images - compelling, depth-rich images generated from single, conventional 2D photographs (fig. 1). Starting from a single image our tool enables rapid OOB prototyping; i.e. the ability to quickly create and experiment with many different variants of the OOB effect before deciding which one best expresses the users' artistic intentions. We achieve this with a flexible work-flow driven by an intuitive user interface. The rich 3D perception of the final composition is achieved by exploiting two strong cues -- occlusions and shadows. A realistic-looking 3D frame is interactively inserted in the scene between segmented foreground objects and the background to generate novel occlusions and enhance the scene's perception of depth. This perception is further enhanced by adding new, realistic cast shadows. The key contributions of this paper are: (i) new algorithms for inserting simple 3D objects like frames in 2D images requiring minimal camera calibration, and (ii) new techniques for the realistic synthesis of cast shadows, even for complex 3D objects. These algorithms, although presented for OOB photography, may be directly used in general image composition tasks. With our tool, untrained users can turn ordinary photos into compelling OOB images in seconds. In contrast with existing workflows, at any time the artist can modify any aspect of the composition while avoiding time-consuming pixel painting operations. Such a tool has important commercial applications, and is much more suitable for OOB prototyping than existing image editors.