Abstract
This paper introduces four classes of orthogonal transforms by modifying the generic polar harmonic transforms. Then, the rotation invariant feature of the proposed transforms is investigated. Compared with the traditional generic polar harmonic transforms, the proposed transforms have the ability to describe the central region of the image with a parameter controlling the area of the region. Experimental results verified the image representation capability of the proposed transforms and showed better performance of the proposed transform in terms of rotation invariant pattern recognition.
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References
Flusser J, Suk T (2006) Rotation moment invariants for recognition of symmetric objects. IEEE Trans Image Process 15(12):3784–3790
J. Flusser, T. Suk, B. Zitova (2009) Moments and moments invariants in pattern recognition. Wiley, Hoboken
Flusser J, Suk T (1993) Pattern recognition by affine moment invariants. Pattern Recogn 26(1):167–174
Shu HZ, Luo LM, Coatrieux JL (2007) Moment-based approaches in imaging part 1, basic features. IEEE Eng Med Biol Mag 26(5):70–74
Mukundan R, Ramakrishnan KR (1998) Moment functions in image analysis-theory and applications. World Scientific, Singapore
Fu B, Zhou JZ, Li YH, Zhang GJ, Wang C (2007) Image analysis by modified Legendre moments 40(2):691–704
Mukundan R, Ong SH, Lee PA (2001) Image analysis by Tchebichef moments. IEEE Trans Image Process 10(9):1357–1364
Teague MR (1980) Image analysis via the general theory of moments. J Opt Soc Am 70(8):920–930
Khotanzad A, Hong YH (1990) Invariant image recognition by Zernike moments. IEEE Trans Pattern Anal Mach Intell 12(5):489–497
Sheng YL, Shen LX (1994) Orthogonal Fourier–Mellin moments for invariant pattern recognition. JOSA A 11(6):1748–1757
Bailey RR, Srinath M (1996) Orthogonal moment features for use with parametric and non-parametric classifiers. IEEE Trans Pattern Anal Mach Intell 18(4):389–399
Ananthraj P, Venkataramana A (2007) Radial Krawtchouk moments for rotational invariant pattern recognition. In: 6th International conference on information, communications and signal processing, pp 1–5
Xiao B, Ma JF, Cui JT (2012) Radial Tchebichef moment invariants for image recognition. J Vis Commun Image Represent 23(2):381–386
Xiao B, Wang GY, Li WS (2014) Radial shifted Legendre moments for image analysis and invariant image recognition. Image Vis Comput 32(12):994–1006
Xiao B, Ma JF, Wang X (2010) Image analysis by Bessel–Fourier moments. Pattern Recogn 43(8):2620–2629
Ping ZL, Wu RG, Sheng YL (2002) Image description with Chebyshev–Fourier moments. J Opt Soc Am A Opt Image Sci Vis 19(9):1748–1754
Ping ZL, Ren HP, Zou J, Sheng YL, Bo W (2007) Generic orthogonal moments: Jacobi–Fourier moments for invariant image description. Pattern Recogn 40(4):1245–1254
Zhu HQ, Yang Y, Gui ZG, Zhu Y, Chen ZH (2016) Image analysis by generalized Chebyshev–Fourier and generalized pseudo-Jacobi–Fourier moments. Pattern Recogn 51:1–11
Xia T, Zhu HQ, Shu HS, Haigron P, Luo LM (2007) Image description with generalized pseudo-Zernike moments. J Opt Soc Am A Opt Image Sci Vis 24(1):50–59
Zhu HQ, Yang Y, Zhu XL, Gui ZG, Shu HZ (2014) General form for obtaining unit disc-based generalized orthogonal moments. IEEE Trans Image Process 23(12):5455–5469
Xiao B, Wang GY (2013) Generic radial orthogonal moment invariants for invariant image recognition. J Vis Commun Image Represent 24(7):1002–1008
Dai XB, Liu TL, Shu HZ, Luo LM (2013) Pseudo-Zernike moments invariants to blur degradation and their use in image recognition. Lect Notes Comput Sci 7751:90–97
Shao ZH, Shang YY, Zhang Y, Liu X, Guo G (2016) Robust watermarking using orthogonal Fourier–Mellin moments and chaotic map for double images. Sig Process 120:522–531
Chen BJ, Shu HZ, Zhang H, Goatrieux G, Luo LM, Coatrieux JL (2011) Combined invariants to similarity transformation and to blur using orthogonal Zernike moments. IEEE Trans Image Process 20(2):345–360
Ren HP, Ping ZL, Bo W, Wu WK, Sheng YL (2003) Multidistortion-invariant image recognition with radial harmonic Fourier moments. J Opt Soc Am A Opt Image Sci Vis 20(4):631–637
Yap PT, Jiang XD, Kot AC (2010) Two-dimensional polar harmonic transforms for invariant image representation. IEEE Trans Pattern Anal Mach Intell 32(7):1259–1270
Hu HT, Zhang YD, Shao C, Ju Q (2014) Orthogonal moments based on exponent functions: exponent–Fourier moments. Pattern Recogn 47(8):2596–2606
Hoang TV, Tabbone S (2011) Generic polar harmonic transform for invariant image description. In: Proceedings of 18th IEEE international conference on image processing, pp 829–832
Wang CP, Wang XY, Xia ZQ (2016) Geometrically invariant image watermarking based on fast radial harmonic Fourier moments. Signal Process Image Commun 45:10–23
Wang XY, Liu YN, Li S, Yang HY, Niu PP (2016) Robust image watermarking approach using polar harmonic transforms based geometric correction. Neurocomputing 174:627–642
Li LD, Li SS, Abraham A, Pan JS (2012) Geometrically invariant image watermarking using polar harmonic transforms. Inf Sci 199:1–19
Gan YF (2015) Research on copy-move image forgery detection using features of discrete polar complex exponent transform. Int J Bifurc Chaos 25(14):1540018-1–1540018-15
Li YN (2013) Image copy-move forgery detection based on polar cosine transform and approximate nearest neighbor searching. Forensic Sci Int 224:59–67
Hoang TV, Tabbone S (2014) Generic polar harmonic transforms for invariant image representation. Image Vis Comput 32(8):497–509
Abu-Mostafa YS, Psaltis D (1984) Recognitive aspects of moment invariants. IEEE Trans Pattern Anal Mach Intell 6(6):698–706
Hu HT, Ju Q, Shao C (2016) Errata and comments on “Errata and Comments on orthogonal moments based on exponent functions: exponent–Fourier moments”. Pattern Recogn 52:471–476
Xiao B, Li WS, Wang GY (2015) Errata and comments on “Orthogonal moments based on exponent functions: exponent–Fourier moments”. Pattern Recogn 48(4):1571–1573
https://www1.cs.columbia.edu/CAVE//software/softlib/coil-20.php
Dai XB, Zhang H, Liu TL, Shu HZ, Luo LM (2014) Legendre moment invariants to blur and affine transformation and their use in image recognition. Pattern Anal Appl 17(2):311–326
Vedaldi A, Lenc K (2015) MatConvNet—convolutional neural networks for MATLAB. In: Proceedings of the ACM international conference on multimedia
Teh CH, Chin RT (1988) On image analysis by the methods of moments. IEEE Trans Pattern Anal Mach Intell 20(4):496–513
Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grant Nos. 61601311 and 61876037, Project of Beijing Excellent Talents (No. 2016000020124G088), Beijing Municipal Education Research Plan Project (SQKM201810028018), Project supported by the Natural Science Foundation of Shanxi Province, China (No. 201801D221186), Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (No. 2017141), and School Foundation of Taiyuan University of Technology (Nos. 2017QN11 and 2017QN12).
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Liu, X., Wu, Y., Shao, Z. et al. The modified generic polar harmonic transforms for image representation. Pattern Anal Applic 23, 785–795 (2020). https://doi.org/10.1007/s10044-019-00840-0
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DOI: https://doi.org/10.1007/s10044-019-00840-0