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Copyright notice

  • The slides can be used freely for non-profit education provided that the source is appropriately cited. Please report any usage on a regular basis (namely in university courses) to the authors.

  • For commercial usage ask the authors for permission.

  • © Jan Flusser, Tomas Suk, and Barbara Zitová, 2008





Traffic surveillance - can we recognize the license plates?



Recognition (classification) = assigning a pattern/object to one of pre-defined classes

  • Recognition (classification) = assigning a pattern/object to one of pre-defined classes

  • The object is described by its features

  • Features – measurable quantities, usually form an n-D vector in a metric space



Non-ideal imaging conditions  degradation of the image

  • Non-ideal imaging conditions  degradation of the image

  • g = D(f)

  • D - unknown degradation operator



Základní přístupy



What are invariants?

  • Invariants are functionals defined on the image space such that

  • I(f) = I(D(f)) for all admissible D





What are invariants?

  • Invariants are functionals defined on the image space such that

  • I(f) = I(D(f)) for all admissible D

  • I(f1), I(f2) “different enough“ for different f1, f2







What are moment invariants?

  • Functions of image moments, invariant to certain class of image degradations

  • Rotation, translation, scaling

  • Affine transform

  • Elastic deformations

  • Convolution/blurring

  • Combined invariants



What are moments?

  • Moments are “projections” of the image function into a polynomial basis



The most common moments

  • Geometric moments



Geometric moments – the meaning

  • Geometric moments – the meaning



Uniqueness theorem

  • Uniqueness theorem







Invariants to translation



Invariants to translation



Invariants to translation and scaling



Invariants to translation and scaling



Invariants to translation and scaling



Invariants to translation and scaling





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