Titlebook: Ridges in Image and Data Analysis; David Eberly Book 1996 Springer Science+Business Media Dordrecht 1996 Riemannian geometry.computer visi

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Book 1996a concrete definition is provided. In almost all cases the concept is used for very specific ap­ plications. When analyzing images or data sets, it is very natural for a scientist to measure critical behavior by considering maxima or minima of the data. These critical points are relatively easy to c

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Ridges in Riemannian Geometry,or is the identity. The same concepts are definable even if ℝ. is assigned an arbitrary positive definite metric tensor. The extension to Riemannian geometry requires tensor calculus which is discussed in Section 2.3. Most notably the constructions involve the ideas of covariant and contravariant tensors and of covariant differentiation.

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Ridges of Functions Defined on Manifolds,d—dimensional ridges of a function defined on an n—dimensional manifold embedded in IR.. Section 5.2 provides an alternative definition for ridges based on principal curvatures and principal directions. Section 5.3 discusses a ridge definition which is an application of the definition of Section 5.2 to level sets.

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Ridges in Euclidean Geometry,for maximality of .(.) is made in a restricted neighborhood of .. A similar concept of . generalizes local minima, but since local minima of . are local maxima of —., it is sufficient to study only the concept of ridge.

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Ridges in Riemannian Geometry, is the set of .-tuples of real numbers. An implicit assumption was made that ℝ., as a geometric entity, is standard Euclidean space whose metric tensor is the identity. The same concepts are definable even if ℝ. is assigned an arbitrary positive definite metric tensor. The extension to Riemannian g

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