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- Surface normal vector information for any object can be
mapped onto a unit sphere, called the Gaussian sphere.
- Mapping is called the Gaussian image of the object.
- The mapping is: Surface normals for each point of the object are
placed so that their
- tails lie at the centre of the Gaussian sphere
- heads lie on a point on the sphere appropriate to the particular
We can extend this process so that
- a weight is assigned to each point on
the Gaussian sphere equal to the area of the surface having the given normal
- This mapping is
called the extended Gaussian image (EGI).
- Weights are represented
by vectors parallel to the surface normals, with length equal to the weight.
example of such an extended Gaussian image is shown in
Fig. The EGI of a block
Using three-dimensional solid models of objects (see
- The corresponding EGIs for each stored object
model can be computed and saved in the model database
- Model stored as a surface
normal vector histogram.
- Surface normals easily extracted from Image (plane fitting)
- Once a
match is found (by comparing EGI histograms) both the identity and orientation
of the object may be calculated.
- EGIs only uniquely define convex objects.
- An infinite number of non-convex objects can possess the same EGI.
Fig. Examples of objects with the same EGI