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Geometric moment invariants to spatial transform and N-fold symmetric blur.

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Title: Geometric moment invariants to spatial transform and N-fold symmetric blur.
Authors: Mo, Hanlin1,2 (AUTHOR) mohanlin@ict.ac.cn, Hao, Hongxiang1,2 (AUTHOR), Li, Hua1,2 (AUTHOR)
Source: Pattern Recognition. Jul2021, Vol. 115, pN.PAG-N.PAG. 1p.
Subjects: Rotational symmetry, Image retrieval
Abstract: • Suppose the PSF has N -fold rotational symmetry, we prove its geometric moments of the same order are linearly dependent. • A new method is proposed to determine whether an existing similarity or affine moment invariant also has invariance to N -fold symmetric blur. • We analyse classical moment invariants, and find that five of Hu moment invariants are naturally invariant to N -fold symmetric blur. • We first prove the existence of moment invariants to both affine transform and N -fold symmetric blur. • The experiments on synthetic and real images are conducted. We find Hu moment invariants outperform most of widely used blur moment invariants. In this paper, we focus on the derivation of blur moment invariants. Blur moment invariants are image moment-based features, which preserve their values when the image is convolved by a point-spread function (PSF). Suppose a PSF has N -fold rotational symmetry, we prove its geometric moments of the same order are linearly dependent. Depending on this property, a new approach is proposed to determine whether an existing similarity or affine moment invariant also has invariance to N -fold symmetric blur. Unlike earlier work, this method is not based on complicated operators and construction formulas. We use it to analyse classical moment-based features, and surprisingly find that five of Hu moment invariants are naturally invariant to N -fold symmetric blur. Meanwhile, we first prove the existence of moment invariants to both affine transform and N -fold symmetric blur. The experiments using synthetic and real blur image datasets are carried out to test these expectations. And the results show that five Hu moment invariants outperform some widely used blur moment invariants and non-moment image features in image retrieval, classification and template matching. [ABSTRACT FROM AUTHOR]
Copyright of Pattern Recognition is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 149761263
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  Data: Geometric moment invariants to spatial transform and N-fold symmetric blur.
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  Data: <searchLink fieldCode="AR" term="%22Mo%2C+Hanlin%22">Mo, Hanlin</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> mohanlin@ict.ac.cn</i><br /><searchLink fieldCode="AR" term="%22Hao%2C+Hongxiang%22">Hao, Hongxiang</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Hua%22">Li, Hua</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Pattern+Recognition%22">Pattern Recognition</searchLink>. Jul2021, Vol. 115, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Rotational+symmetry%22">Rotational symmetry</searchLink><br /><searchLink fieldCode="DE" term="%22Image+retrieval%22">Image retrieval</searchLink>
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  Group: Ab
  Data: • Suppose the PSF has N -fold rotational symmetry, we prove its geometric moments of the same order are linearly dependent. • A new method is proposed to determine whether an existing similarity or affine moment invariant also has invariance to N -fold symmetric blur. • We analyse classical moment invariants, and find that five of Hu moment invariants are naturally invariant to N -fold symmetric blur. • We first prove the existence of moment invariants to both affine transform and N -fold symmetric blur. • The experiments on synthetic and real images are conducted. We find Hu moment invariants outperform most of widely used blur moment invariants. In this paper, we focus on the derivation of blur moment invariants. Blur moment invariants are image moment-based features, which preserve their values when the image is convolved by a point-spread function (PSF). Suppose a PSF has N -fold rotational symmetry, we prove its geometric moments of the same order are linearly dependent. Depending on this property, a new approach is proposed to determine whether an existing similarity or affine moment invariant also has invariance to N -fold symmetric blur. Unlike earlier work, this method is not based on complicated operators and construction formulas. We use it to analyse classical moment-based features, and surprisingly find that five of Hu moment invariants are naturally invariant to N -fold symmetric blur. Meanwhile, we first prove the existence of moment invariants to both affine transform and N -fold symmetric blur. The experiments using synthetic and real blur image datasets are carried out to test these expectations. And the results show that five Hu moment invariants outperform some widely used blur moment invariants and non-moment image features in image retrieval, classification and template matching. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Pattern Recognition is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.patcog.2021.107887
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Rotational symmetry
        Type: general
      – SubjectFull: Image retrieval
        Type: general
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      – TitleFull: Geometric moment invariants to spatial transform and N-fold symmetric blur.
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            NameFull: Mo, Hanlin
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            NameFull: Hao, Hongxiang
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            – D: 01
              M: 07
              Text: Jul2021
              Type: published
              Y: 2021
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              Value: 115
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            – TitleFull: Pattern Recognition
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