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Euclidean Geometry

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Computer Vision

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Related Concepts

Algebraic Curve; Camera Calibration

Definition

Euclidean geometry deals with properties of geometric configurations that are preserved under isometric (or length preserving) transformations. Alternatively, it may be characterized as a mathematical theory based on an axiom system (that can be traced back to Euclid) expressing, in modern terminology, incidence, order, congruence, continuity, and parallelity. Euclidean geometry is today a special case of many geometric theories (projective, affine, and Riemannian geometries, Hilbert spaces …).

Historical Background

Euclidean geometry has a long and glorious history (cf. [1,  2,  3]), having lived at the core of the development of science and culture since antiquity. It is today not an area of research per se, but still plays an important role in many contexts.

Euclidean geometry is one of the oldest manifestations of humans in science. The latter part of the word geometry originates from the Greek word metri’a for measure,...

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References

  1. Berger M (1987) Geometry I and II. Springer Universitext. Springer, Berlin/Heidelberg/New York/London/Paris/Tokyo

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  6. Greenberg MJ (2008) Euclidean and non-Euclidean geomtries: Development and history. W.H. Freeman

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  7. Hartley R, Zisserman A (2003) Multiple view geometry in computer vision, 2nd edn. Cambridge University Press, Cambridge

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Author information

Authors and Affiliations

  1. Centre for Mathematical Sciences, Lund University, PO Box 118, Lund, Sweden

    Gunnar Sparr

Authors
  1. Gunnar Sparr
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Corresponding author

Correspondence to Gunnar Sparr .

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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Sparr, G. (2014). Euclidean Geometry. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_751

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