In both human and machine perception, objects play an essential role. A key property is that they behave atomically: we may approximate them as moving rigidly, or treat them as smallest factors into which we decompose a scene, or predict the whole of their appearance having seen just a part. This simple fact about objects pervades computer vision: in the datasets and upstream tasks we use for pretraining, in explicit or implicit priors, and in many other ways. In this thesis, I present three works, which show a spectrum of the uses of object atomicity. In [46] we took prior segmentation methods and used them as off-the-shelf signals to improve image stitching. In [16] we use, at train time, labelled data but not pre-trained object segmentation to perform object-aware extrapolation. Finally in [17], we endow our prior knowledge about objectness as a low-rank constraint but do not use labelled data at all -- in fact, we show how we can recover some information about object boundaries.