  This paper explores the challenge of teaching a machine how to
reverse-engineer the grid-marked surfaces used to represent data in 3D surface
plots of two-variable functions. These are common in scientific and economic
publications; and humans can often interpret them with ease, quickly gleaning
general shape and curvature information from the simple collection of curves.
While machines have no such visual intuition, they do have the potential to
accurately extract the more detailed quantitative data that guided the
surface's construction. We approach this problem by synthesizing a new dataset
of 3D grid-marked surfaces (SurfaceGrid) and training a deep neural net to
estimate their shape. Our algorithm successfully recovers shape information
from synthetic 3D surface plots that have had axes and shading information
removed, been rendered with a variety of grid types, and viewed from a range of
viewpoints.
