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Geometric Moments for Image Reconstruction: A Comparative Study

Explore the use of geometric moments including Legendre, Zernike, Fourier-Mellin, Czebyshev, Krawtchuk, and Hahn in image reconstruction. Learn the definition, orthogonality, rotation properties, and invariants of these moments. Discover how to avoid numerical problems and recurrent calculations while reconstructing noise-free or noisy images.

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Geometric Moments for Image Reconstruction: A Comparative Study

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

  2. Two reasons for using OG moments • Avoiding numerical problems with high values, recurrent calculations • Image reconstruction

  3. Image reconstruction from geometric moments

  4. Legendre polynomials Definition Orthogonality

  5. Legendre polynomials

  6. Legendre moments

  7. Legendre moments

  8. Zernike polynomials Definition Orthogonality

  9. Zernike moments

  10. Zernike moments

  11. Rotation property of Zernike moments The magnitude is preserved, the phase is shifted by qα. Invariants are constructed by phase cancellation

  12. Rotation invariants from Zernike moments

  13. Reconstruction from moments

  14. Reconstruction of a noise-free image

  15. Reconstruction of a noisy image

  16. Reconstruction of a noisy image

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