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Erschienen in:
1996 | OriginalPaper | Buchkapitel
Ridges in Riemannian Geometry
verfasst von : David Eberly
Erschienen in: Ridges in Image and Data Analysis
Verlag: Springer Netherlands
Enthalten in: Professional Book Archive
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Chapter 3 discussed the fundamental concepts of generalized local extrema and height ridges. The concepts were applied to functions f: ℝn → ℝ where ℝn is the set of n-tuples of real numbers. An implicit assumption was made that ℝn, as a geometric entity, is standard Euclidean space whose metric tensor is the identity. The same concepts are definable even if ℝn 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.