Image retargeting algorithms often create visually disturbing distortion. We introduce the property of scene consistency, which is held by images which contain no object distortion and have the correct object depth ordering. We present two new image retargeting algorithms that preserve scene consistency. These algorithms make use of a user-provided relative depth map, which can be created easily using a simple GrabCut-style interface. Our algorithms generalize seam carving. We decompose the image retargeting procedure into (a) removing image content with minimal distortion and (b) re-arrangement of known objects within the scene to maximize their visibility. Our algorithms optimize objectives (a) and (b) jointly. However, they differ considerably in how they achieve this. We discuss this in detail and present examples illustrating the rationale of preserving scene consistency in retargeting.