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Definition
The extended Gaussian image (EGI) of a 3-D object is a function defined on a unit sphere. The value of the EGI at a point on the unit sphere is the inverse of the curvature at the corresponding point on the object – where the corresponding point is the one that has the same surface orientation. In the case of a polyhedral object, the value on the sphere is zero except for impulses at points on the sphere corresponding to faces of the polyhedron. The “size” or volume of each impulse is equal to the area of the corresponding face. The mapping from a 3-D polyhedron to the EGI is illustrated in Fig. 1. Figure 2 shows the mapping for a 3-D piecewise smooth object.
The EGI of a polyhedron. Left: cube with surface normals. Right: arrows on the unit sphere represent impulses corresponding to faces of the cube
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Kang, S.B., Horn, B.K. (2021). Extended Gaussian Image (EGI). In: Ikeuchi, K. (eds) Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-030-63416-2_651
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