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Projective moment invariants.

Tomas Suk1, Jan Flusser

  • 1Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, 182 08 Prague 8, Czech Republic. suk@utia.cas.cz

IEEE Transactions on Pattern Analysis and Machine Intelligence
|January 12, 2005
PubMed
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Projective moment invariants, previously thought nonexistent, are demonstrated to exist. These invariants are revealed as infinite series involving moments with both positive and negative indices, challenging prior assumptions in geometric analysis.

Area of Science:

  • Computer Vision
  • Geometric Algebra
  • Image Analysis

Background:

  • Projective transformations are fundamental in computer vision and image analysis.
  • The existence of moment invariants under projective transformations has been a long-standing open problem.
  • Previous research suggested that such invariants could not be formulated.

Purpose of the Study:

  • To investigate the existence of moment invariants under projective transformations.
  • To challenge the prevailing belief that projective moment invariants do not exist.
  • To introduce a novel formulation for projective moment invariants.

Main Methods:

  • The study employs a theoretical approach based on the properties of moments.
  • Analysis involves exploring infinite series expansions of moment functions.

Related Experiment Videos

  • Mathematical derivations are used to establish the existence and form of the invariants.

    • Main Results:

    • The paper proves the existence of moment invariants with respect to projective transformations.
    • These invariants are shown to be expressible as infinite series.
    • The series include moments with both positive and negative indices, a novel finding.

    Conclusions:

    • Projective moment invariants exist and can be represented by infinite series.
    • This finding opens new avenues for invariant representation in geometric and image analysis.
    • The developed framework provides a new tool for understanding projective geometry in image processing.