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Curvature

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Computer Vision

Synonyms

Curvedness

Related Concepts

Geodesics, Distance Maps, and Curve Evolution

Definition

Curvature is a fundamental concept of differential geometry that represents local “curvedness” of some object such as a curve, a surface, and a Riemannian space.

Background

Dealing with the shape of an object is a fundamental issue of computer vision. It is necessary, for example, to represent the two-dimensional or three-dimensional shape of an object, to extract the object shape from various types of images, and to measure similarity between two object shapes. The application of differential geometry to these problems is getting more and more common in modern computer vision. Curvature is one of the most fundamental concept of differential geometry, and its use can be seen throughout all sorts of related problems. This entry explains basic definitions of the curvature of a plane curve and a surface in Euclidean space and summarizes their applications to a few major applications. See [8] for...

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Okatani, T. (2014). Curvature. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_405

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