We present a method for discovering object models from 3D meshes of indoor environments. Our algorithm first decomposes the scene into a set of candidate mesh segments and then ranks each segment according to its “objectness” — a quality that distinguishes objects from clutter. To do so, we propose five intrinsic shape measures: compactness, symmetry, smoothness, and local and global convexity. We additionally propose a recurrence measure, codifying the intuition that frequently occurring geometries are more likely to correspond to complete objects. We evaluate our method in both supervised and unsupervised regimes on a dataset of 58 indoor scenes collected using an Open Source implementation of Kinect Fusion. We show that our approach can reliably and efficiently distinguish objects from clutter, with Average Precision score of .92. We make our dataset available to the public.