  This paper addresses the problem of reconstructing the surface shape of
transparent objects. The difficulty of this problem originates from the
viewpoint dependent appearance of a transparent object, which quickly makes
reconstruction methods tailored for diffuse surfaces fail disgracefully. In
this paper, we introduce a fixed viewpoint approach to dense surface
reconstruction of transparent objects based on refraction of light. We present
a simple setup that allows us to alter the incident light paths before light
rays enter the object by immersing the object partially in a liquid, and
develop a method for recovering the object surface through reconstructing and
triangulating such incident light paths. Our proposed approach does not need to
model the complex interactions of light as it travels through the object,
neither does it assume any parametric form for the object shape nor the exact
number of refractions and reflections taken place along the light paths. It can
therefore handle transparent objects with a relatively complex shape and
structure, with unknown and inhomogeneous refractive index. We also show that
for thin transparent objects, our proposed acquisition setup can be further
simplified by adopting a single refraction approximation. Experimental results
on both synthetic and real data demonstrate the feasibility and accuracy of our
proposed approach.
