Abstract

Ridges are generalizations of local maxima for smooth functions of n independent variables. At a ridge point x the function has a local maximum when restricted to an affine (n - d)- dimensional plane located at x, the plane varying with x. The set of ridge points generically lie on d-dimensional manifolds. The ridge definition is extremely flexible since the dimension d and the affine planes can be chosen to suit an application's needs. Fast algorithms for constructing 1-dimensional ridges in n-dimensional images are presented in this paper. The algorithms require an initial approximation to a ridge point, which can be supplied interactively or via a model of a previously analyzed image. Similar algorithms can be implemented for higher dimensional ridges.

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