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Accurate calculation of Zernike moments

Authors:

Rahul UpnejaAuthors Info & Claims

Information Sciences—Informatics and Computer Science, Intelligent Systems, Applications: An International Journal, Volume 233

Pages 255 - 275

https://doi.org/10.1016/j.ins.2013.01.012

Published: 01 June 2013 Publication History

Abstract

Zernike moments (ZMs) are very effective global image descriptors which are used in many digital image processing applications. The digitization process compromises the accuracy of the moments and therefore, several of its properties are affected. There are two major discretization errors, namely, the geometric error and numerical integration error. In this paper we propose two new algorithms which eliminate these errors. The first algorithm performs the exact computation of geometric moments (GMs) over a unit disk and then uses GMs-to-ZMs relationship to compute the latter. This algorithm is computationally more expensive and it becomes numerically instable for higher order moments, therefore, we develop a second algorithm based on Gaussian quadrature numerical integration. The second algorithm reduces both the errors simultaneously and its accuracy increases as the degree of Gaussian quadrature numerical integration increases. The proposed algorithms are observed to provide very accurate ZMs which result in improved image reconstruction, reduction in reconstruction error and improvement in rotation and scale invariance. Exhaustive experiments are provided to support improved accuracy of ZMs and time complexity analysis is performed for the existing and the proposed methods.

References

[1]

Alghoniemy, M. and Tewfik, A.H., Geometric invariance in image watermarking. IEEE Trans. Image Process. v13. 145-153.

Digital Library

[2]

Ansary, T.F., Daoudi, M. and Vandeborre, J.-P., A Bayesian 3D search engine using adaptive views clustering. IEEE Trans. Multimedia. v9 i1. 78-88.

Digital Library

[3]

On the circle polynomials of Zernike and related orthogonal sets. Proc. Camb. Phil. Soc. v50. 40-48.

[4]

Bissantz, N., Holzmann, H. and Pawlak, M., Testing for image symmetries-with application to confocal microscopy. IEEE Trans. Inform. Theory. v55 i4. 1841-1855.

Digital Library

[5]

Broumandnia, A. and Shanbehzadeh, J., Fast Zernike wavelet moments for Farsi character recognition. Image Vis. Comput. v25. 717-729.

Digital Library

[6]

Chen, Z. and Sun, S.-K., A Zernike moment phase descriptor for local image representation and matching. IEEE Trans. Image Process. v19 i1. 205-219.

Digital Library

[7]

Gao, X., Wang, Q., Li, X., Tao, D. and Zhang, K., Zernike moment-based image super resolution. IEEE Trans. Image Proc. v20 i10. 2738-2747.

Digital Library

[8]

Hosny, K.M., A systematic method for efficient computation of full and subsets Zernike moments. Inform. Sci. v180. 2299-2313.

Digital Library

[9]

Hou, S. and Ramani, K., Calligraphic interfaces: classifier combination for sketch-based 3D part retrieval. Comput. Graph. v31 i4. 598-609.

Digital Library

[10]

Kan, C. and Srinath, M.D., Invariant character recognition with Zernike and orthogonal Fourier-Mellin moments. Pattern Recogn. v35. 143-154.

[11]

Kara, L.B. and Shimada, K., Sketch-based 3D-shape creation for industrial styling design. IEEE Comput. Graph. Appl. v27 i1. 60-71.

Digital Library

[12]

Khotanzad, A. and Lu, J.-H., Classification of invariant image representations using a neural network. IEEE Trans. Acoust., Speech, Signal Process. v38. 1028-1038.

[13]

Y.-S. Kim, W.-Y. Kim, Content-based trademark retrieval system using visually salient features, in: Proceedings of 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1997, pp. 307-312.

Digital Library

[14]

Kim, W-Y. and Kim, Y-S, Robust rotation angle estimator. IEEE Trans. Pattern Anal. Mach. Intell. v21 i8. 768-773.

Digital Library

[15]

Kim, H.S. and Lee, H.K., Invariant image watermarking using Zernike moments. IEEE Trans. Image Process. v13 i8. 766-775.

Digital Library

[16]

Li, S., Lee, M.-C. and Pun, C.-M., Complex Zernike moments features for shape based image retrieval. IEEE Trans. Syst., Man, Cybern - Part A: Syst. Hum. v39 i1. 227-237.

Digital Library

[17]

Liao, S.X. and Pawlak, M., On the accuracy of Zernike moments for image analysis. IEEE Trans. Pattern Anal. Mach. Intell. v20 i12. 1358-1364.

Digital Library

[18]

Lim, C.-L., Honarvar, B., Thung, K.-H. and Paramesran, R., Fast computation of exact Zernike moments using cascaded digital filters. Inform. Sci. v181. 3638-3651.

Digital Library

[19]

Lin, H., Si, J. and Abousleman, G.P., Orthogonal rotation invariant moments for digital image processing. IEEE Trans. Image Process. v17 i3. 272-282.

Digital Library

[20]

Pang, Y.H., Teoh, A.B.J., Ngo, D.C.L. and Hiew, F.S., Palmprint verifications with moments. J. WSCG. v12. 1-3.

[21]

Papakostas, G.A., Boutalis, Y.S., Karras, D.A. and Mertzios, B.G., A new class of Zernike moments for computer vision applications. Inform. Sci. v177. 2802-2819.

Digital Library

[22]

Pawlak, M., On the reconstruction aspect of moment descriptors. IEEE Trans. Inform. Theory. v38 i6. 1698-1708.

Digital Library

[23]

M. Pawlak, Image Analysis by Moments: Reconstruction and Computational Aspects, Oficyna Wydawnicza Politechniki Wroclawskiej, Wroclaw, 2006. <http://www.dbc.wroc.pl/dlibra/docmetadata?id=1432&from=&dirids=1>.

[24]

Rajaraman, V., Computer Oriented Numerical Methods. 2004. third ed. Prentice Hall of India, New Delhi, India.

[25]

Raveendran, P. and Omatu, S., Performance of an optimal subset of Zernike features for pattern classification. Inform. Sci. v1 i3. 133-147.

[26]

Revaud, J., Lavoue, G. and Baskurt, A., Improving Zernike moments comparison for optimal similarity and rotation angle retrieval. IEEE Trans. Pattern Anal. Mach. Intell. v31 i4. 627-636.

Digital Library

[27]

Singh, C., Improved quality of reconstructed images using floating point arithmetic for moment calculation. Pattern Recogn. v39. 2047-2064.

Digital Library

[28]

Singh, C. and Walia, E., Computation of Zernike moments in improved polar configuration. IET Image Process. v3 i4. 217-227.

[29]

Singh, C. and Walia, E., Algorithms for fast computation of Zernike moments and their numerical stability. Image Vis. Comput. v29 i4. 251-259.

Digital Library

[30]

Singh, C., Pooja, Improving image retrieval using combined features of Hough transform and Zernike moments. Opt. Lasers Eng. v49. 1384-1396.

[31]

Teague, M.R., Image analysis via the general theory of moments. J. Opt. Soc. Am. v70 i8. 920-930.

[32]

Teh, C.-H. and Chin, R.T., On image analysis by the methods of moments. IEEE Trans. Pattern. Anal. Mach. Intell. v10 i4. 496-513.

Digital Library

[33]

Wang, L. and Healey, G., Using Zernike moments for the illumination and geometry invariant classification of multispectral texture. IEEE Trans. Image Process. v7 i2. 196-203.

Digital Library

[34]

Wee, C.-Y., Paramesran, R. and Takeda, F., New computational methods for full and subset Zernike moments. Inform. Sci. v159. 203-220.

Digital Library

[35]

Wee, C.-Y. and Paramesran, R., On the computational aspects of Zernike moments. Image Vis. Comput. v25. 967-980.

Digital Library

[36]

Y. Xin, M. Pawlak, S. Liao, Image reconstruction with polar Zernike moments, in: Proc. Int. Conf. Advances in Pattern Recognition, Bath, UK, 2005, pp. 394-403.

Digital Library

[37]

Xin, Y., Liao, S. and Pawlak, M., On the improvement of rotational invariance of Zernike moments. Proc. IEEE Int. Conf. Image Process. v2. 842-845.

[38]

Accurate computation of Zernike moments in polar coordinates. IEEE Trans. Image Process. v16 i2. 581-587.

Digital Library

[39]

Xin, Y., Liao, S. and Pawlak, M., Circularly orthogonal moments for geometrically robust image watermarking. Pattern Recogn. v40. 3740-3752.

Digital Library

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Published In

cover image Information Sciences: an International Journal

Information Sciences: an International Journal Volume 233, Issue

June, 2013

321 pages

ISSN:0020-0255

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Copyright © Elsevier Inc. © 2013.

Publisher

Elsevier Science Inc.

United States

Publication History

Published: 01 June 2013

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Cited By

Kumar ASingh CSachan M(2025)A moment-based pooling approach in convolutional neural networks for breast cancer histopathology image classificationNeural Computing and Applications10.1007/s00521-024-10406-937:2(1127-1156)Online publication date: 1-Jan-2025
https://dl.acm.org/doi/10.1007/s00521-024-10406-9
Singh CRanade SKaur DBala A(2024)A kernelized-bias-corrected fuzzy C-means approach with moment domain filtering for segmenting brain magnetic resonance imagesSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-023-09379-z28:3(1909-1933)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1007/s00500-023-09379-z
Yang JZeng ZKwong TTang YWang Y(2023)Local Orthogonal Moments for Local FeaturesIEEE Transactions on Image Processing10.1109/TIP.2023.327952532(3266-3280)Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1109/TIP.2023.3279525
Fu DZhou XXu LHou KChen X(2023)Robust Reversible Watermarking by Fractional Order Zernike Moments and Pseudo-Zernike MomentsIEEE Transactions on Circuits and Systems for Video Technology10.1109/TCSVT.2023.327911633:12(7310-7326)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1109/TCSVT.2023.3279116
Hjouji AEL-Mekkaoui J(2022)The 2-Orthogonal and Orthogonal Radial Shape Moments for Image Representation and RecognitionJournal of Mathematical Imaging and Vision10.1007/s10851-022-01113-y65:2(277-301)Online publication date: 16-Aug-2022
https://dl.acm.org/doi/10.1007/s10851-022-01113-y
Wang XZhang YTian JNiu PYang H(2022)Accurate quaternion fractional-order pseudo-Jacobi–Fourier momentsPattern Analysis & Applications10.1007/s10044-022-01071-625:4(731-755)Online publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1007/s10044-022-01071-6
Zhao ZKuang XZhu YLiang YXuan Y(2021)Combined kernel for fast GPU computation of Zernike momentsJournal of Real-Time Image Processing10.1007/s11554-020-00979-818:3(431-444)Online publication date: 1-Jun-2021
https://dl.acm.org/doi/10.1007/s11554-020-00979-8
Hosny KMagdy TLashin N(2021)Improved color texture recognition using multi-channel orthogonal moments and local binary patternMultimedia Tools and Applications10.1007/s11042-020-10444-080:9(13179-13194)Online publication date: 1-Apr-2021
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El Ogri OKarmouni HYamni MSayyouri MQjidaa HMaaroufi MAlami B(2021)Novel fractional-order Jacobi moments and invariant moments for pattern recognition applicationsNeural Computing and Applications10.1007/s00521-021-05977-w33:20(13539-13565)Online publication date: 1-Oct-2021
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Xu SHao QMa BWang CLi J(2020)Accurate Computation of Fractional-Order Exponential MomentsSecurity and Communication Networks10.1155/2020/88221262020Online publication date: 1-Jan-2020
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