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Polar radius moment with application for affine invariants

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Abstract

Image moment is an important technique for pattern recognition. But, invariants constructed with high-order moments are sensitive to noise. Only a few invariants with low-order moments can be used in practice. In this paper, the definition of traditional moment is reviewed in polar coordinate system. Polar radius moment (PRM), which is defined by a linear combination of integrals on the symmetrical polar radiuses in an image, is proposed. Traditional moment is only a special case of PRM. Algorithm is developed to construct affine invariants with PRMs. In particular, the first-degree PRM is considered as the generalization of the zero-order moment. It can be used to construct affine invariants directly. The third-degree PRM can be viewed as the generalization of the second-order moment. Consequently, more invariants can be constructed with low-order (degree) moments. The experimental results also show that invariants with low-degree PRMs are more robust to noise.

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Acknowledgements

This work was supported in part by the National Science Foundation Under Grants 42275160, 61572015.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Jianwei Yang & Chunyan Liu

  2. Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen Key Laboratory of Media Security, Shenzhen, 518060, China

    Jianwei Yang

  3. School of Economics, Beijing Technology and Business University, Beijing, 100048, China

    Fei Li

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  1. Jianwei Yang
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  2. Chunyan Liu
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  3. Fei Li
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Correspondence to Fei Li.

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Yang, J., Liu, C. & Li, F. Polar radius moment with application for affine invariants. Pattern Anal Applic 26, 529–542 (2023). https://doi.org/10.1007/s10044-022-01128-6

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