The interpretation of line drawings is known to be very difficult, and has a long history in vision research.
However for certain restricted but important types of drawings we have been able to produce good 3-D
interpretations quite efficiently using only local image-plane computations. The types of drawings we can
handle are line drawings of 3-D space curves, for instance, a drawing of the 3-D path followed by a butterfly
or a line drawing of a potato chip.
Such line drawings are, of course, intrinsically ambiguous - there is simply not enough information in
the 2-D image to arrive at a unique 3-D interpretation. Despite this difficulty, there remains the fact that
for any given image all people see pretty much exactly the same 3-D interpretation (or sometimes a small
number of interpretations). People, therefore, must be bringing additional knowledge or assumptions to
In this paper we show that by picking the smoothest 3-D space curve that is consistent with the image
data we can obtain a 3-D interpretation which is very similar to the people's interpretation. The teleological
motivation for selecting the smoothest 3-D space curve is that it is the most stable 3-D interpretation, and
thus in one sense the most likely 3-D interpretation. The process of computing the smoothest 3-D space
curve is carried out by simple, local processing that can be implemented by a neural network.