We propose a new approach for reconstructing a threedimensional object from a single two-dimensional freehand line drawing depicting it. A sketch is essentially a noisy projection of a 3D object onto an arbitrary 2D plane. Reconstruction is the inverse projection of the sketched geometry from two dimensions back into three dimensions. While humans can do this reverse-projection remarkably easily and almost without being aware of it, this process is mathematically indeterminate and is very difficult to emulate computationally. Here we propose that the ability of humans to perceive a previously unseen 3D object from single sketch is based on simple 2D-3D geometrical correlations that are learned from visual experience. We demonstrate how a simple correlation system that is exposed to many object-sketch pairs eventually learns to perform the inverse projection successfully for unseen objects. Conversely, we show how the same correlation data can be used to gauge the understandability of synthetically generated projections of given 3D objects. Using these principles we demonstrate for the first time a completely automatic conversion of a single freehand sketch into physical solid object. These results have implications for bidirectional human-computer communication of 3D graphic concepts, and might also shed light on the human visual system.