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A purely geometric definition of Gaussian curva-ture is used for the extraction of the sign of Gauss-

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 one-to-one 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.


Source: Angelopoulou, Elli - Department of Computer Science, Friedrich Alexander University Erlangen Nürnberg


Collections: Computer Technologies and Information Sciences