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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.

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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
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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

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
https://dl.acm.org/doi/10.1007/s11042-020-10444-0
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
https://dl.acm.org/doi/10.1155/2020/8822126
Joshi GVig RSingh S(2018)DCA‐based unimodal feature‐level fusion of orthogonal moments for Indian sign language datasetIET Computer Vision10.1049/iet-cvi.2017.039412:5(570-577)Online publication date: 28-Feb-2018
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