| | |
Summary: Abstract
An invariant local descriptor of smooth object sur-
faces is Gaussian curvature. We present an invari-
ant related to Gaussian curvature at an object point
is developed based upon the covariance matrix of
photometric values related to surface normals
within a local neighborhood about the point. We
employ three illumination conditions, two of which
are completely unknown. We never need to explic-
itly know the surface normal at a point. The three-
tuple of intensity values at a point is in one-to-one
correspondence with the surface normal at that
point. The determinant of the covariance matrix of
these three-tuples in the local neighborhood of an
object point is shown to be invariant with respect to
rotation and translation. A way of combining these
determinants over mutually illuminated object
point regions to form a signature distribution is for-
mulated that is rotation, translation, and, scale
invariant. This signature is shown to be invariant
|
