A novel unified method for the fast computation of discrete image moments on grayscale images
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ORIGINAL RESEARCH PAPER
A novel unified method for the fast computation of discrete image moments on grayscale images Xia Hua1 · Hanyu Hong1 · Jianguo Liu2 · Yu Shi1 Received: 13 December 2017 / Accepted: 27 April 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract We proposed a new method to compute the discrete image moments in this paper. By simple mathematical deduction, the discrete image moments can be transformed into first-order moments. Therefore, the fast algorithm for first-order moments’ calculation can be used to compute discrete image moments. We also design an efficient computation structure based on systolic array to implement this approach. Since our method does not use the moment kernel polynomials’ properties in the calculation process, the proposed method can be used to compute any discrete image moments in the same way. The presented algorithm has several advantages such as regular and simple computation structure, without multiplication, independent of the image’s intensity distribution, applicable to any discrete moment family. Various experiments demonstrate the effectiveness of the proposed algorithm in comparison with some state-of-the-art methods. Keywords Feature extraction · Discrete image moments · Moment calculation · Fast algorithms
1 Introduction First, introduced by Hu [1], the moment functions have received considerable attention from the scientific community. Because the image moments was able to fully describe an image by encoding its contents in a compact way, they have been widely used in image processing [2–5] and pattern recognition [6–9]. As the calculation is very simple, geometric moments were first applied to image processing. Hu [1] constructed seven moment invariants which are invariant to translation, scaling and rotation. However, the geometric moments suffer from high information redundancy, and that makes the image reconstruction difficult. This fact motivated the researchers to develop the orthogonal moments, which can be used to represent the image with a minimal amount of information redundancy. Teague [10] first used orthogonal moments for image analysis. These orthogonal moments are generated by continuous orthogonal polynomials. Apart from their usefulness, these * Xia Hua [email protected] 1
School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China
School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China
2
orthogonal moments present some approximation errors [11, 12]. This is because the kernel polynomials are defined in a continuous space. To eliminate the approximation errors of orthogonal moments, discrete orthogonal moments are proposed in the literature. The typical representatives of discrete orthogonal moments are the Discrete Tchebichef, Krawtchouk, dual Hahn and Racah moments (TMs, KMs, HMs, and RMs) [13–17]. Moments have been widely used in the field of pattern recognition and image analysis. As the computation of image’s moments
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