Our goal in this paper is to investigate properties of 3D shape that can be determined from a single image. We define 3D shape attributes -- generic properties of the shape that capture curvature, contact and occupied space. Our first objective is to infer these 3D shape attributes from a single image. A second objective is to infer a 3D shape embedding -- a low dimensional vector representing the 3D shape. We study how the 3D shape attributes and embedding can be obtained from a single image by training a Convolutional Neural Network (CNN) for this task. We start with synthetic images so that the contribution of various cues and nuisance parameters can be controlled. We then turn to real images and introduce a large scale image dataset of sculptures containing 143K images covering 2197 works from 242 artists. For the CNN trained on the sculpture dataset we show the following: (i) which regions of the imaged sculpture are used by the CNN to infer the 3D shape attributes; (ii) that the shape embedding can be used to match previously unseen sculptures largely independent of viewpoint; and (iii) that the 3D attributes generalize to images of other (non-sculpture) object classes.
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