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Computer Vision pp 327–329Cite as

Geodesics, Distance Maps, and Curve Evolution

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Synonyms

Geodesic active contour; Segmentation; Variational methods

Related Concepts

Edge Detection; Semantic Image Segmentation

Definition

Geodesics are locally the shortest paths in some space. Equivalently, geodesics are curves for which small perturbation increases their length according to some measure. A minimal geodesic corresponds to the shortest geodesic connecting two points. In computer vision and pattern recognition, the way distance is measured and the resulting geodesics define the specific application, see [1] for a pedagogical introduction to the field of numerical geometry of images.

Background

Edge detectors can be defined from a variational perspective where an edge is a curve along which the image gradient aligns with the curve’s normal [2–6]. These types of edges are geodesics in the sense of integrating the inner product between the curve’s normal and the image gradient and by Green’s Theorem can be shown to be the Marr-Hildreth edge detectors [7], also known as...

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, Technion – Israel Institute of Technology, Haifa, Israel

    Ron Kimmel

Authors
  1. Ron Kimmel
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Editor information

Editors and Affiliations

  1. Institute of Industrial Science, The University of Tokyo, Tokyo, Japan

    Katsushi Ikeuchi

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© 2014 Springer Science+Business Media New York

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Kimmel, R. (2014). Geodesics, Distance Maps, and Curve Evolution. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_769

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