A central problem in vision is the recovery of the 3D structure of a scene from a single 2D projection. The interpretation of planar line-drawings represents one of the most challenging instances of this highly underconstrained problem. Quite intriguingly, the human visual system can readily accomplish this task. This paper reports on an attempt to understand and computationally mimic this important perceptual ability. It has long been suggested that humans use principles of simplicity in achieving this percept. Barrow and Tenenbaum, and more recenrly, Marill, have proposed that standard deviation of the included angles should be used as a measure of complexity; minimizing this metric leads ro perceptually correct interpretations for many line-drawings. However, we have found that the use of this measure alone results in unexpected and bizarre interpretarions for certain figures. We have devised a new approach that utilizes three types of measures: angle variance, planarity of faces and overall compactness. When these measures are appropriately combined, the model interprets a wide variety of line-drawings of polyhedral objects in a manner consistent with human perception. Our model is also robust in the sense that it works without the need for parameter tweaking to handle different cases.