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Differential Invariants

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Computer Vision

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Synonyms

Local invariants

Related Concepts

Definition

Invariants are entities that do not change under the action of a transformation group, e.g., projective invariants are unchanged under projective transformations. One can distinguish between differential and algebraic invariants. Algebraic invariants involve algebraic forms such as points, lines, conics, etc., while differential invariants involve general differentiable curves and surfaces.

Background

This entry concentrates on differential invariants of curves, mostly in the plane. Also touched on are differential invariants of space curves and surfaces and of fields such as optic flow and shading.

Projective differential and algebraic invariants, well developed in the mathematical literature, were both introduced into computer vision in [1] in order to eliminate the search for the correct viewpoint when trying to recognize an object. Compared...

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References

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Author information

Authors and Affiliations

  1. Center for Automation Research, University of Maryland, College Park, MD, USA

    Isaac Weiss

Authors
  1. Isaac Weiss
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Corresponding author

Correspondence to Isaac Weiss .

Section Editor information

  1. KTH Royal Institute of Technology, Stockholm, Sweden

    Atsuto Maki

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Weiss, I. (2021). Differential Invariants. In: Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-030-03243-2_658-1

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  • DOI: https://doi.org/10.1007/978-3-030-03243-2_658-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03243-2

  • Online ISBN: 978-3-030-03243-2

  • eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering

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