Thus the Gauss-Kronecker curvature G(p) is nothing but the product of the

principal curvature at p.

of the sampling) is given by the maximal principal curvature.

g the Ricci curvature (see [1]), one can in some special cases, lower rates than the principal curvature rate given in Theorem 1.

n]] denoting the principal curvatures of E, at the point p [member of] [SIGMA].

We should remark here that while for general manifolds, as well as for some applications such as in Graphics, the use of the tubular radius is essential, in the case of signals and images, it suffices to consider solely the principal curvatures.

The eigenvalues and eigenvectors of the quadratic form correspond to the principal curvature values and to the directions of principal curvature.

If the two principal curvature values are positive, the interface portion is concave.

If the two principal curvature values are negative, the interface portion is convex.

Firstly, the definition of principal curvatures on an object surface is given.

If the curvature diagram degenerates to exactly one point then the surface has two constant principal curvatures which is possible only for a piece of a plane, a sphere or a circular cylinder.

Following the Jacobi equation and the linear equation with respect to the principal curvatures [k.

Assume that the hypothesis as above and in addition that at each point exactly two

principal curvatures are distinct and they have multiplicities > 1.