 
Summary: Abstract
A purely geometric definition of Gaussian curva
ture is used for the extraction of the sign of Gauss
ian curvature from photometric data. Consider a
point p on a smooth surface S and a closed curve
on S which encloses p. The image of on the unit
normal Gaussian sphere is a new curve . The sign
of Gaussian curvature at p is determined by the rel
ative orientations of the closed curves and . The
relative orientation of two such curves is directly
computed from intensity data. We employ three
unknown illumination conditions to create a photo
metric scatter plot. This plot is in onetoone corre
spondence with the subset of the unit Gaussian
sphere containing the mutually illuminated surface
normals. This permits direct computation of the
sign of Gaussian curvature without the recovery of
surface normals. Our method is albedo invariant.
We assume diffuse reflectance, but the nature of
diffuse reflectance can be general and unknown.
