Skip to main content
Log in

Exact Zernike and pseudo-Zernike moments image reconstruction based on circular overlapping blocks and Chamfer distance

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript


This study aims to explore a novel approach to reconstruct multi-gray-level images based on circular blocks reconstruction method using two exact and fast moments: Zernike (CBR-EZM) and pseudo-Zernike (CBR-EPZM): An image is first divided into a set of sub-images which are then reconstructed independently. We also introduced Chamfer distance (CD) to capitalize on the use of discrete distance instead of Euclidean one. The combination of our methods and CD leads to CBR-EZM-CD and CBR-EPZM-CD methods. Obviously, image partitioning offers significant advantages, but an undesirable circular blocking effect can occur. To mitigate this effect, we have implemented overlapping feature to our new methods leading to OCBR-EZM-CD and OCBR-EPZM-CD, by exploiting neighborhood information of the circular blocks. The main motivation of this novel approach is to explore new applications of Zernike and pseudo-Zernike moments. One of the fields is feature extraction for pattern recognition: Zernike and pseudo-Zernike moments are well known to capture only the global features, but thanks to the circular block reconstruction, we can now use those moments to extract also local features.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others


  1. Teague, M.: Image analysis via the general theory of moments. J. Opt. Soc. Am. 70(8), 920–930 (1980)

    Article  MathSciNet  Google Scholar 

  2. Teh, C.-H., Chin, R.T.: On image analysis by the methods of moments. IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 496–513 (1998)

    Article  MATH  Google Scholar 

  3. AL-Rawi, M.S.: Fast computation of Pseudo-Zernike moments. J. Real-Time Image Process. In: Proceedings (5), pp. 3–10 (2010). doi:10.1007/s11554-009-0118-0

  4. Mousavi, B.S., Soleymani, F., Razmjooy, N.: Fast semantic image classification by genetic algorithm using optimised fuzzy system based on Zernike moments. Signal Image Video Process. (2012). doi:10.1007/s11760-012-0311-7

  5. Goyal, A., Walia, E.: Variants of dense descriptors and Zernike moments as features for accurate shape-based image retrieval. Signal Image Video Process. (2012). doi:10.1007/s11760-012-0353-x

  6. Singh, C., Walia, E., Pooja, S., Upneja, R.: Analysis of algorithms for fast computation of Pseudo-Zernike moments and their numerical stability. Digital Signal Process. 22(6), 1031–1043 (2012)

    Article  MathSciNet  Google Scholar 

  7. Hosny, K.M.: Fast computation of accurate Zernike moments. J. Real-Time Image Process. 3, 97–107 (2008)

    Article  Google Scholar 

  8. Hosny, K.M.: Fast computation of accurate Pseudo-Zernike moments for binary and gray-level images. Int. Arab. J. Inf. Technol. 11(3), 243–249 (2014)

    MathSciNet  Google Scholar 

  9. Mukundan, K., Ramakrishnan, K.R.: Moment Functions in Image Analysis. World Scientific Publishing, Singapore (1998)

    MATH  Google Scholar 

  10. Papakostas, G.A., Boutalis, Y.S., Karras, D.A., Mertzios, B.G.: Efficient computation of Zernike and Pseudo-Zernike moments for pattern classification applications. Pattern Recognit. Image Anal. 20(1), 56–64 (2010)

    Article  MATH  Google Scholar 

  11. Chong, C.W., Mucundan, R., Raveendran, P.: An efficient algorithm for fast computation of Pseudo-Zernike moments. Int. J. Pattern. Recognit. Artif. Intell. 17(6), 1011–1023 (2003). doi:10.1142/S0218001403002769

    Article  Google Scholar 

  12. Wee, C.Y., Paramesran, R., Takeda, F.: New computational methods for full and subset Zernike moments. Inf. Sci. 159, 203–220 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Prata, A., Rusch, W.V.T.: Algorithm for computation of Zernike polynomials expansion coefficients. Appl. Opt. 28, 749–754 (1989)

    Article  Google Scholar 

  14. Liao, S.X.: Image analysis by moments’, Ph.D. Thesis, Department of Business Computing, Manitoba University, Manitoba (1993)

  15. Singh, C., Walia, E., Upneja, R.: Accurate calculation of Zernike moments. Inf. Sci. 233, 255–275 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Papakostas, G.A., Boutalis, Y.S., Papaodysseus, C.N., Fragoulis, D.K.: Numerical error analysis in Zernike moments computation. Image Vis. Comput. 24(9), 960–969 (2006)

    Article  MATH  Google Scholar 

  17. El Fadili, H., Zenkouar, K., Qjidaa, H.: Lapped block image analysis via the method of Legendre moments. EURASIP J. Appl. Sig. Process. (2003). doi:10.1155/S1110865703305062

  18. Bahaoui, Z., Zenkouar, K., El fadili, H., Qjidaa, H., Zarghili, A.: Global overlapping block based reconstruction using exact Legendre moments. In: Third IEEE International Colloquium in Information Science and Technology (CIST’14) (2014). doi:10.1109/CIST.2014.7016640

  19. Bahaoui, Z., Zenkouar, K., El Fadili, H., Qjidaa, H., Zarghili, A.: Blocking artifact removal using partial overlapping based on exact Legendre moments computation. J. Real-Time Image Process. (2014). doi:10.1007/s11554-014-0465-3

  20. Thiel, E.: Les distances de chanfrein en analyse d’image: fondements et application. Ph.D. thesis, UJF, Grenoble, Sept (1994)

  21. Borgefors, G.: Distance transformations in arbitrary dimensions. Comput. Vis. Graph. Image Proc. 27, 321–345 (1984)

    Article  Google Scholar 

  22. Akmal, M.B., Andmaragos, P.: Optimum design of Chamfer distance transforms. IEEE Trans. Image Proc. 7(10), 1477–1484 (1988)

    Article  Google Scholar 

  23. Fabbri, R., Costa, L., Torrelli, J., Bruno, O.: 2D Euclidean distance transform algorithms: a comparative survey. ACM Comput. Surv. 40(1), 1–44 (2008)

    Article  Google Scholar 

  24. Thiel, E., Montanvert, A.: Chamfer masks: discrete distance functions, geometric properties and optimization. In: Proceedings of 11th International Conference on Pattern Recognition, pp. 244–247 (1992)

  25. Reeve III, H.C., Lim, J.S.: Reduction of blocking effect in image coding. Proc. ICASSP 83, 1212–1215 (1988)

    Google Scholar 

  26. Malvar, H.S., David, Staelin, H.: The LOT: transform coding without blocking effects. IEEE Trans. Acoustics Speech Signal Process. 37(4), 553–559 (1989)

  27. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. Image Process. IEEE Trans. 13(4), 600–612 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Zaineb Bahaoui.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (docx 303 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bahaoui, Z., El Fadili, H., Zenkouar, K. et al. Exact Zernike and pseudo-Zernike moments image reconstruction based on circular overlapping blocks and Chamfer distance. SIViP 11, 1313–1320 (2017).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: