Image Description With Polar Harmonic Fourier Moments

Due to their good rotational invariance and stability, image continuous orthogonal moments are intensively applied in rotationally invariant recognition and image processing. However, most moments produce numerical instability, which impacts the image reconstruction and recognition performance. In t...

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Published inIEEE transactions on circuits and systems for video technology Vol. 30; no. 12; pp. 4440 - 4452
Main Authors Wang, Chunpeng, Wang, Xingyuan, Xia, Zhiqiu, Ma, Bin, Shi, Yun-Qing
Format Journal Article
LanguageEnglish
Published New York IEEE 01.12.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Chebyshev approximation
Continuous orthogonal moments
Harmonic analysis
Image processing
Image recognition
Image reconstruction
Invariants
Object recognition
polar harmonic Fourier moments
Radial basis function
Stability
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Abstract Due to their good rotational invariance and stability, image continuous orthogonal moments are intensively applied in rotationally invariant recognition and image processing. However, most moments produce numerical instability, which impacts the image reconstruction and recognition performance. In this paper, a new set of invariant continuous orthogonal moments, polar harmonic Fourier moments (PHFMs), free of numerical instability is designed. The radial basis functions (RBFs) of the PHFMs are much simpler than those of the Chebyshev-Fourier moments (CHFMs), orthogonal Fourier-Mellin moments (OFMMs), Zernike moments (ZMs), and pseudo-Zernike moments (PZMs). For the same degree, the RBFs of the PHFMs have more zeros and are more evenly distributed than those of the ZMs and PZMs. Therefore, PHFMs do not suffer from information suppression problem; hence, the image description ability of the PHFMs is superior to that of the ZMs and PZMs. Moreover, the RBFs of the PHFMs are always less than or equal to 1.0 near the unit disk center, whereas those of the OFMMs, PZMs, CHFMs, and radial harmonic Fourier moments (RHFMs) are infinite (implying numerical instability). This indicates that PHFMs can outperform these moments in image reconstruction tasks. We theoretically and experimentally demonstrate that PHFMs outperform the above moments in reconstructing images and recognizing rotationally invariant objects considering noise and various attacks. This paper also details the significance of the PHFM phase in image reconstruction, angle estimation using PHFMs, and the accurate moment selection of the PHFMs.
AbstractList Due to their good rotational invariance and stability, image continuous orthogonal moments are intensively applied in rotationally invariant recognition and image processing. However, most moments produce numerical instability, which impacts the image reconstruction and recognition performance. In this paper, a new set of invariant continuous orthogonal moments, polar harmonic Fourier moments (PHFMs), free of numerical instability is designed. The radial basis functions (RBFs) of the PHFMs are much simpler than those of the Chebyshev-Fourier moments (CHFMs), orthogonal Fourier-Mellin moments (OFMMs), Zernike moments (ZMs), and pseudo-Zernike moments (PZMs). For the same degree, the RBFs of the PHFMs have more zeros and are more evenly distributed than those of the ZMs and PZMs. Therefore, PHFMs do not suffer from information suppression problem; hence, the image description ability of the PHFMs is superior to that of the ZMs and PZMs. Moreover, the RBFs of the PHFMs are always less than or equal to 1.0 near the unit disk center, whereas those of the OFMMs, PZMs, CHFMs, and radial harmonic Fourier moments (RHFMs) are infinite (implying numerical instability). This indicates that PHFMs can outperform these moments in image reconstruction tasks. We theoretically and experimentally demonstrate that PHFMs outperform the above moments in reconstructing images and recognizing rotationally invariant objects considering noise and various attacks. This paper also details the significance of the PHFM phase in image reconstruction, angle estimation using PHFMs, and the accurate moment selection of the PHFMs.
Author Wang, Xingyuan
Wang, Chunpeng
Xia, Zhiqiu
Shi, Yun-Qing
Ma, Bin
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Cites_doi 10.1109/TIT.1962.1057692
10.1109/TASSP.1980.1163463
10.3390/rs9080790
10.1016/j.patcog.2014.02.014
10.1080/21681163.2018.1493619
10.1016/j.isprsjprs.2010.11.001
10.1016/j.ins.2015.04.030
10.1007/11559573_65
10.1364/JOSAA.19.001748
10.1364/JOSA.70.000920
10.1109/83.941859
10.1016/0167-8655(83)90085-5
10.1109/TMM.2017.2760098
10.1364/JOSAA.11.001748
10.1016/j.bspc.2017.08.018
10.1109/LGRS.2019.2936652
10.1016/j.sigpro.2006.07.007
10.1016/j.sigpro.2018.11.011
10.1016/j.jss.2012.08.015
10.1016/j.ins.2018.03.040
10.1109/34.3913
10.1109/TPAMI.2009.119
10.1016/j.ins.2018.08.028
10.1109/TIP.2003.818019
10.1016/j.image.2016.03.007
10.1007/s00138-017-0879-6
10.1109/TCYB.2018.2810806
10.1109/TPAMI.2018.2803828
10.1109/TPAMI.1984.4767594
10.1017/S0305004100029066
10.1016/j.patrec.2007.04.013
10.1007/s10851-013-0456-1
10.1016/j.optlastec.2018.03.033
10.1016/j.apm.2018.07.006
10.1016/j.patcog.2006.07.016
10.1109/TAES.2018.2856321
10.1364/JOSAA.20.000631
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References ref13
ref34
ref12
ref37
ref15
ref36
ref14
ref31
ref33
ref11
ref10
ref2
ref1
ref17
ref38
ref16
ref19
ref18
ref24
ref23
ref26
ref25
ref20
nayar (ref35) 1996
ref22
ref21
ref28
ref27
ref29
ref8
hu (ref3) 1962; 8
yap (ref30) 2010; 32
ref9
ref4
ref6
ref5
wang (ref32) 2016; 45
yap (ref7) 2003; 12
References_xml – volume: 8
  start-page: 179
  year: 1962
  ident: ref3
  article-title: Visual pattern recognition by moment invariants
  publication-title: IRE Trans Inf Theory
  doi: 10.1109/TIT.1962.1057692
– ident: ref33
  doi: 10.1109/TASSP.1980.1163463
– ident: ref36
  doi: 10.3390/rs9080790
– ident: ref26
  doi: 10.1016/j.patcog.2014.02.014
– ident: ref20
  doi: 10.1080/21681163.2018.1493619
– ident: ref37
  doi: 10.1016/j.isprsjprs.2010.11.001
– ident: ref15
  doi: 10.1016/j.ins.2015.04.030
– ident: ref8
  doi: 10.1007/11559573_65
– ident: ref21
  doi: 10.1364/JOSAA.19.001748
– ident: ref11
  doi: 10.1364/JOSA.70.000920
– ident: ref6
  doi: 10.1109/83.941859
– ident: ref4
  doi: 10.1016/0167-8655(83)90085-5
– ident: ref27
  doi: 10.1109/TMM.2017.2760098
– ident: ref19
  doi: 10.1364/JOSAA.11.001748
– ident: ref16
  doi: 10.1016/j.bspc.2017.08.018
– ident: ref2
  doi: 10.1109/LGRS.2019.2936652
– ident: ref9
  doi: 10.1016/j.sigpro.2006.07.007
– ident: ref34
  doi: 10.1016/j.sigpro.2018.11.011
– ident: ref18
  doi: 10.1016/j.jss.2012.08.015
– ident: ref38
  doi: 10.1016/j.ins.2018.03.040
– ident: ref13
  doi: 10.1109/34.3913
– volume: 32
  start-page: 1259
  year: 2010
  ident: ref30
  article-title: Two-dimensional polar harmonic transforms for invariant image representation
  publication-title: IEEE Trans Pattern Anal Mach Intell
  doi: 10.1109/TPAMI.2009.119
– ident: ref25
  doi: 10.1016/j.ins.2018.08.028
– volume: 12
  start-page: 1367
  year: 2003
  ident: ref7
  article-title: Image analysis by Krawtchouk moments
  publication-title: IEEE Trans Image Process
  doi: 10.1109/TIP.2003.818019
– volume: 45
  start-page: 10
  year: 2016
  ident: ref32
  article-title: Geometrically invariant image watermarking based on fast radial harmonic Fourier moments
  publication-title: Signal Process -Image
  doi: 10.1016/j.image.2016.03.007
– year: 1996
  ident: ref35
  article-title: Columbia object image library (coil 100)
– ident: ref17
  doi: 10.1007/s00138-017-0879-6
– ident: ref1
  doi: 10.1109/TCYB.2018.2810806
– ident: ref12
  doi: 10.1109/TPAMI.2018.2803828
– ident: ref5
  doi: 10.1109/TPAMI.1984.4767594
– ident: ref29
  doi: 10.1017/S0305004100029066
– ident: ref10
  doi: 10.1016/j.patrec.2007.04.013
– ident: ref28
  doi: 10.1007/s10851-013-0456-1
– ident: ref22
  doi: 10.1016/j.optlastec.2018.03.033
– ident: ref31
  doi: 10.1016/j.apm.2018.07.006
– ident: ref23
  doi: 10.1016/j.patcog.2006.07.016
– ident: ref14
  doi: 10.1109/TAES.2018.2856321
– ident: ref24
  doi: 10.1364/JOSAA.20.000631
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Snippet Due to their good rotational invariance and stability, image continuous orthogonal moments are intensively applied in rotationally invariant recognition and...
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SubjectTerms Chebyshev approximation
Continuous orthogonal moments
Harmonic analysis
Image processing
Image recognition
Image reconstruction
Invariants
Object recognition
polar harmonic Fourier moments
Radial basis function
Stability
Title Image Description With Polar Harmonic Fourier Moments
URI https://ieeexplore.ieee.org/document/8936392
https://www.proquest.com/docview/2468757215
Volume 30
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