Accurate quaternion radial harmonic Fourier moments for color image reconstruction and object recognition
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Accurate quaternion radial harmonic Fourier moments for color image reconstruction and object recognition Yunan Liu1 · Shanshan Zhang1 · Guangyu Li · Houjun Wang2 · Jian Yang1 Received: 20 September 2018 / Accepted: 30 March 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
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. Keywords Radial harmonic Fourier moments · Geometric error · Numerical error · Quaternion · Object recognition
1 Introduction Description of objects invariant to geometric transformation such as translation, scale, and rotation is useful in pattern recognition and other similar applications. A popular class of invariant features is based on the moment techniques including geometric moments, rotational moments, complex moments, and orthogonal moments [1, 2]. However, geometric moments and their extensions in the form of complex moments and rotational moments are not orthogonal. It has a certain degree of information redundancy and high sensitivity to noise. Consequently, reconstruction of images
* Shanshan Zhang [email protected] 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
National Ocean Technology Center, Tianjin 300112, People’s Republic of China
2
from these moments is quite difficult and computationally expensive. To overcome this shortcoming, Khotanzad et al. [3] proposed using orthogonal moments—Zernike moments (ZMs)—in object recognition task. Chong et al. [4] used a new set of translation and scale invariants of orthogonal Legendre moments to recognize English, Chinese, and Latin characters. Teh et al. [5] commented the description performance and noise sensibility of var
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