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Accurate quaternion radial harmonic Fourier moments for color image reconstruction and object recognition

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Abstract

Orthogonal moments have become a powerful tool for object representation and image analysis. Radial harmonic Fourier moments (RHFMs) are one of such image descriptors based on a set of orthogonal projection bases, which outperform other moments because of their computational efficiency. However, the conventional computational framework of RHFMs produces geometric error and numerical integration error, which will affect the accuracy of RHFMs, thus degrading the image reconstruction performance. To overcome this shortcoming, we propose a new computational framework of RHFMs, namely accurate quaternion radial harmonic Fourier moments (AQRHFMs), for color image processing, and also analyze the properties of AQRHFMs. Firstly, we propose a precise computation method of RHFMs to reduce the geometric and numerical errors. Secondly, by using the algebra of quaternions, we extend the accurate RHFMs to AQRHFMs in order to deal with the color images in a holistic manner. Experimental results show the proposed AQRHFMs achieve promising performance in image reconstruction and object recognition in both noise-free and noisy conditions.

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Acknowledgments

This work was partially supported by the National Science Fund of China under Grant Nos. 61702262, 61861136011, and U1713208; Program for Changjiang Scholars; Natural Science Foundation of Jiangsu Province under Grant No. BK20181299; CCF-Tencent Open Fund (RAGR20180113); Young Elite Scientists Sponsorship Program by GAST (2018QNRC001); Science and Technology on Parallel and Distributed Processing Laboratory (PDL) Open Fund (WDZC20195500106); Fundamental Research Funds for the Central Universities under Grant No. 30918011322.

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Authors and Affiliations

  1. PCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, and Jiangsu Key Laboratory of Image and Video Understanding for Social Security, School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Yunan Liu, Shanshan Zhang & Jian Yang

  2. National Ocean Technology Center, Tianjin, 300112, People’s Republic of China

    Houjun Wang

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  1. Yunan Liu
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  2. Shanshan Zhang
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  3. Guangyu Li
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  4. Houjun Wang
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  5. Jian Yang
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Correspondence to Shanshan Zhang.

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Liu, Y., Zhang, S., Li, G. et al. Accurate quaternion radial harmonic Fourier moments for color image reconstruction and object recognition. Pattern Anal Applic 23, 1551–1567 (2020). https://doi.org/10.1007/s10044-020-00877-6

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  • DOI: https://doi.org/10.1007/s10044-020-00877-6

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