Fractional Orthogonal Fourier-Mellin Moments for Pattern Recognition
In this paper, we generalize the orthogonal Fourier-Mellin moments (OFMMs) to the fractional orthogonal Fourier-Mellin moments (FOFMMs), which are based on the fractional radial polynomials. We propose a new method to construct FOFMMs by using a continuou
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Abstract. In this paper, we generalize the orthogonal Fourier-Mellin moments (OFMMs) to the fractional orthogonal Fourier-Mellin moments (FOFMMs), which are based on the fractional radial polynomials. We propose a new method to construct FOFMMs by using a continuous parameter t ðt [ 0Þ. The fractional radial polynomials of FOFMMs have the same number of zeros as OFMMs with the same degree. But the zeros of FOFMMs polynomial are more uniformly distributed than which of OFMMs and the first zero is closer to the origin. A recursive method is also given to reduce computation time and improve numerical stability. Experimental results show that the proposed FOFMMs have better performance. Keywords: Fractional orthogonal Fourier-Mellin moments Orthogonal Fourier-Mellin moments Moment invariant Pattern recognition
1 Introduction Moment methods effectively describe an image in terms of form and shape and possess excellent invariant to image translation, rotation and scaling. They have been used in a multitude of applications in image analysis, such as object representation and recognition [1–5], image registration [6, 7], robot navigation [8], image retrieval [9, 10], medical imaging [11, 12] and watermarking [13–15]. Hu [16] introduced moment invariants in 1961, based on methods of algebraic invariants. However, higher order moments are vulnerable, and the recovery of the image from these moments is considered to be extremely difficult [17]. Teague [18] has proposed the concept of orthogonal moments to recover the image from moments based on the theory of orthogonal polynomials, and has introduced Zernike moments. The most remarkable quality of orthogonal moments, is their ability of full description of an object, with least redundancy [19, 20]. Consequently, the reconstruction of an object by a finite number of moments is possible. Furthermore, Teh and Chin [17] proved that the orthogonal moments perform better than non-orthogonal moments in image representation and are more robust to noise. Other families of orthogonal moments were proposed through the years, such as Lengendre [21], Chebyshev [11], Pseudo-Zernike [11] and orthogonal Fourier-Mellin moments [23–28]. © Springer Nature Singapore Pte Ltd. 2016 T. Tan et al. (Eds.): CCPR 2016, Part I, CCIS 662, pp. 766–778, 2016. DOI: 10.1007/978-981-10-3002-4_62
FOFMMs for Pattern Recognition
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The most frequently employed orthogonal families are the Zernike, Pseudo-Zernike and Fourier-Mellin moment. Ref. [17, 29–31] have shown that Zernike moments have outstanding performance as image descriptors. But, when they are used for scale-invariant pattern recognition, Zernike moments have difficulty in describing images of small size. Sheng and Shen [27] introduced the orthogonal Fourier-Mellin moments (OFMMs) as the generalized Zernike moments or the orthogonal complex moments, and demonstrated OFMMs have better performance than ZMs in regard to image reconstruction errors and signal-to-noise ratios, especially in describing images of small size. OFMMs have been widely us
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