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G.R. Amayeh Dr. S. Kasaei A.R. Tavakkoli

Sharif University of Technology A modified algorithm to obtain Translation, Rotation & Scale invariant Zernike Moment shape Descriptors. G.R. Amayeh Dr. S. Kasaei A.R. Tavakkoli. Introduction. Shape is one of the most important features to human for visual distinguishing system.

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G.R. Amayeh Dr. S. Kasaei A.R. Tavakkoli

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  1. Sharif University of TechnologyA modified algorithm to obtain Translation, Rotation & Scaleinvariant Zernike Moment shape Descriptors G.R. Amayeh Dr. S. Kasaei A.R. Tavakkoli

  2. Introduction • Shape is one of the most important features to human for visual distinguishing system. • Shape Descriptors • Contour-Base • Using contour information • Neglect image details • Region-Base • Using region information

  3. Shape Descriptors Fig.1: Same regions. Fig.2: Same contours.

  4. Zernike & Pseudo-Zernike Moments • Zernike Moments of Order n, with m-repetition: • Zernike Moment’s Basis Function (1) (2) (3)

  5. Zernike & Pseudo-Zernike Moments • Zernike Moment Radial Polynomials: • Pseudo-Zernike Radial Polynomials: (4) (5)

  6. A Cross Section ofRadial Polynomials of ZM & PsZM Fig.3 : ZM (blue) & Ps. ZM (red) of 4-order with repetition 0. Fig.4 : ZM (blue) & Ps. ZM (red) of 6-order with repetition 4. Fig.5 : ZM (blue) & Ps. ZM (red) of 5-order with repetition 1. Fig.6 : ZM (blue) & Ps. ZM (red) of 7-order with repetition 3.

  7. 3-D Illustration of Radial Polynomials of ZM & Ps.ZM Fig.7 : Radial polynomial of ZM of 7-order with repetition 1. Fig.8 : Radial polynomial of Ps. ZM of 7-order with repetition 1.

  8. Zernike Moments Properties • Invariance Properties: • Zernike Moments are Rotation Invariant • Rotation changes only moment’s phase. • Variance Properties: • Zernike Moments are Sensitive to Translation & Scaling.

  9. Achieving Invariant Properties • What is needed in segmentation problem? • Moments need to be invariant to rotation, scale and translation. • Solution to achieve invariant properties • Normalization method. • Improved Zernike Moments without Normalization (IZM). • Proposed Method.

  10. Normalization Method • Algorithm: • Translate image’s center of mass to origin. • Scale image:

  11. Normalization Method Fig.9 : From left to right, Original, Translated, & Scaled images (b=1800).

  12. Normalization Method Fig.10 : From left to right, original image & normalized images with different b s.

  13. Normalization Method Drawbacks • Interpolation Errors: • Down sampling image leads to loss of data. • Up sampling image adds wrong information to image.

  14. Improved Zernike Moments without Normalization • Algorithm: • Translate image’s center of mass to origin. • Finding the smallest surrounding circle and computing ZMs for this circle. • Normalize moments: Fig.11 : Images & fitted circles. (8)

  15. Drawbacks • Increased Quantization Error. • Since the SSC of images have a small number of pixels, image’s resolution is low and this causes more QE.

  16. Proposed Method • Algorithm: • Computing a Grid Map. • Performing translation and scale on the map indexes. Fig.12: Mapping.

  17. Proposed Method • Translate origin of coordination system to the center of mass (9) Fig(13). Translation of Coordination Origin.

  18. (10) Proposed Method • Scale coordination system

  19. Proposed Method • Computing Zernike Moment in new coordinate for where . • We can show that the moments of in the new coordinatesystem are equal to the moments of in the old coordinate system.

  20. Proposed Method b=800 b=1200 b=1800 b=2500 Fig.15 : From left to right, original image & normalized images with different b s.

  21. Proposed Method • Special case Fig.16 : Original image. Fig.17 : Zernike moments by proposed method (b=2550) & IZM (Improved ZM with out normalization ).

  22. Experimental Results Fig.16 : Original image & 70% scaled image. Fig.17 : Error of Zernike moments between original image & scaled image.

  23. Experimental Results Fig.18 : Original image & 55 degree rotated image. Fig.19 : Error of Zernike moments between original image & rotated image.

  24. Experimental Results Fig.21 : Error of Zernike moments between original & scaled images. Fig.20 : Original image & 120% scaled image.

  25. Experimental Results Fig.21 : Original image & 40 degree rotated image. Fig.23 : Error of Zernike moments between original image & rotated image.

  26. Conclusions • Principle of our method is same as the Normalization method. • Does not resize the original image. • No Interpolation Error. • Reduces the quantization error. (using beta parameter) • Trade off Between QE and power of distinguishing. • Has all the benefits of both pervious methods.

  27. The End

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