1 / 46

Object Recognition by Implicit Invariants Jan Flusser Jaroslav Kautsky

Object Recognition by Implicit Invariants Jan Flusser Jaroslav Kautsky Filip Šroubek. Institute of Information Theory and Automation Prague, Czech Republic Flinders University of South Australia Adelaide, Australia. General m otiva tion.

judah
Download Presentation

Object Recognition by Implicit Invariants Jan Flusser Jaroslav Kautsky

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Object Recognition by Implicit Invariants Jan Flusser Jaroslav Kautsky Filip Šroubek Institute of Information Theory and AutomationPrague, Czech RepublicFlinders University of South AustraliaAdelaide, Australia

  2. General motivation How can we recognize deformed objects?

  3. Problem formulation Curved surface  deformation of the image g = D(f) D -unknown deformation operator

  4. What are explicit invariants? Functionals defined on the image space L such that • E(f) = E(D(f))for all admissibleD • Fourier descriptors, moment invariants, ...

  5. What are explicit invariants? Functionals defined on the image space L such that • E(f) = E(D(f))for all admissibleD • For many deformations explicit invariants do not exist.

  6. What are implicit invariants? Functionals defined on L x L such that • I(f,D(f)) = 0for all admissibleD • Implicit invariants exist for much bigger set of deformations

  7. Our assumption about D Image deformation is a polynomial transform r(x) of order > 1of the spatial coordinates f’(r(x)) = f(x)

  8. What are moments? Moments are “projections” of the image function into a polynomial basis

  9. How are the moments transformed? m’ = A.m • A depends on r and on the polynomial basis • A is not a square matrix • Transform r does not preserve the order of the moments • Explicit moment invariants cannot exist. If they existed, they would contain all moments.

  10. Construction of implicit momentinvariants • Eliminate the parameters of r from the system • Each equation of the reduced system is an implicit invariant m’ = A.m

  11. Artificial example

  12. Invariance property

  13. Robustness to noise

  14. Object recognitionAmsterdam Library of Object Imageshttp://staff.science.uva.nl/˜aloi/

  15. ALOI database 99% recognition rate

  16. The bottle

  17. The bottle

  18. The bottle again

  19. The bottle again

  20. The bottle again

  21. The bottle again

  22. The bottle again

  23. The bottle again

  24. The bottle again 100% recognition rate

  25. Implementation How to avoid numerical problems with high dynamic range of standard moments?

  26. Implementation How to avoid numerical problems with high dynamic range of standard moments? We used orthogonal Czebyshev polynomials

  27. Summary • We proposed a new concept of implicit invariants • We introduced implicit moment invariants to polynomial deformations of images

  28. Any questions? Thank you !

  29. Odtud dal uz to nebylo !

  30. Common types of moments Geometric moments

  31. Special case If an explicit invariant exist, then I(f,g) = |E(f) – E(g)|

  32. An example in 1D

  33. Orthogonal moments • Legendre • Zernike • Fourier-Mellin • Czebyshev • Krawtchuk, Hahn

  34. Outlook for the futureand open problems • Discriminability? • Robustness? • Other transforms?

  35. How is it connected with image fusion?

  36. Basic approaches Základní přístupy Brute force Normalized position  inverse problem Description of the objects by invariants

  37. An example in 2D

  38. Our assumption about D Image degradation is a polynomial transform r(x) of the spatial coordinates of order > 1

  39. Construction of implicit momentinvariants • Eliminate the parameters of r from the system • Each equation of the reduced system is an implicit invariant

  40. How are the moments transformed? • A depends on r and on the moment basis • A is not a square matrix • Transform r does not preserve the moment orders • Explicit moment invariants cannot exist. If they existed, they would contain all moments.

More Related