Abstract
Color image representation using quaternion moments has gained more interest during the last few years. In this paper, invariant color image representation using quaternion Legendre–Fourier moments (QLFMs) is presented. A new method for exact, fast and stable computation of QLFMs in polar coordinates is proposed. Explicit rotation, scaling and translation (RST) invariants of quaternion Legendre–Fourier are derived. Numerical experiments are performed to compare the performance of QLFMs with the existing quaternion moments. The comparison clearly shows the superiority of the proposed method over all existing quaternion moments in terms of image reconstruction capability, RST invariances and numerical stability.
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References
Teague MR (1980) Image analysis via the general theory of moments. J Opt Soc Am 70(8):920–930
Chong CW, Raveendran P, Mukundan R (2004) Translation and scale invariants of Legendre moments. Pattern Recognit 37(1):119–129
Hosny KM (2010) Refined translation and scale Legendre moment invariants. Pattern Recognit Lett 31(7):533–538
Hosny KM (2010) New set of rotationally Legendre moment invariants. Int J Electr Electron Eng 4:176–180
Zhang H, Shu H, Coatrieux G, Zhu J, Wu QMJ, Zhang Y, Zhu H, Luo L (2011) Affine Legendre moment invariants for image watermarking robust to geometric distortions. IEEE Trans Image Process 20(8):2189–2199
Luo R, Lin Tusheng (2007) Finger crease pattern recognition using Legendre moments and principal component analysis. Chin Opt Lett 5(3):160–163
Rao CS, Srinivas Kumar S, Chandra Mohan B (2010) Content based image retrieval using exact Legendre moments and support vector machine. Int J Multimed Appl 2(2):69–79
Zhang H, Shu H, Han GN, Coatrieux G, Luo L, Coatrieux JL (2010) Blurred image recognition by Legendre moment invariants. IEEE Trans Image Process 19(3):596–611
Srivastava P, Khare Ashish (2017) Integration of wavelet transform, Local Binary Patterns and moments for content-based image retrieval. J Vis Commun Image Represent 42:78–103
Marengo E, Bobba M, Liparota MC, Robotti E, Righetti PG (2005) Use of Legendre moments for the fast comparison of two-dimensional polyacrylamide gel electrophoresis maps images. J Chromatogr A 1096(1–2):86–91
Bharathi VS, Ganesan L (2008) Orthogonal moments-based texture analysis of CT liver images. Pattern Recognit Lett 29(13):1868–1872
Vijayalakshmi B, Subbiah Bharathi V (2016) Classification of CT liver images using local binary pattern with Legendre moments. Curr Sci 110(4):687–691
Hosny KM (2010) Robust template matching using orthogonal Legendre moment invariants. J Comput Sci 6(10):1083–1087
Mirzapour F, Ghassemian Hassan (2016) Moment-based feature extraction from high spatial resolution hyperspectral images. Int J Remote Sens 37(6):1349–1361
Suna Q, Liua R, Yu F (2016) An extraction method of laser stripe centre based on Legendre moment. Opt Int J Light Electron Opt 127(2):912–915
Mustapha H, Dimitrakopoulos Roussos (2011) HOSIM: a high-order stochastic simulation algorithm for generating three-dimensional complex geological patterns. Comput Geosci 37(9):1242–1253
Dahdouha S, Angelinia ED, Grangéb G, Blocha I (2015) Segmentation of embryonic and fetal 3D ultrasound images based on pixel intensity distributions and shape priors. Med Image Anal 24(1):255–268
Nakib A, Schulze Y, Petit E (2012) Image thresholding framework based on two-dimensional digital fractional integration and Legendre moments. IET Image Process 6(8):717–727
Wojak J, Angelini ED, Bloch I (2010) Introducing shape constraint via Legendre moments in a variational framework for cardiac segmentation on non-contrast CT images. In: VISAPP 2010, Angers, France, pp 209–214
Hosny KM, Papakostas GA, Koulouriotis DE (2013) Accurate reconstruction of noisy medical images using orthogonal moments. In: 18th international conference on digital signal processing (DSP)
Sastry SS, Mallika K, Gowri B, Rao S, Ha ST, Lakshminarayana S (2012) Novel approach to study liquid crystal phase transitions using Legendre moments. Phase Trans 85(8):735–749
Bahaoui Z, Zenkouar K, Fadili H, Qjidaa H, Zarghili A (2018) Blocking artifact removal using partial overlapping based on exact Legendre moments computation. J Real-Time Image Process 14(2):433–451
Hosny KM (2007) Exact Legendre moment computation for gray level images. Pattern Recognit 40(12):3597–3605
Hosny KM (2011) Fast and low-complexity method for exact computation of 3D Legendre moments. Pattern Recognit Lett 32(9):1305–1314
Papakostas GA, Karakasis EG, Koulouriotis DE (2010) Accurate and speedy computation of image Legendre moments for computer vision applications. Image Vision Comput 29(3):414–423
Yap P-T, Paramesran R (2005) An efficient method for the computation of Legendre moments. IEEE Trans Pattern Anal Mach Intell 27(12):1996–2002
Xiao B, Wang G, Li W (2014) Radial shifted Legendre moments for image analysis and invariant image recognition. Image Vis Comput 32(12):994–1006
Guo L, Zhu M (2011) Quaternion Fourier-Mellin moments for color images. Pattern Recognit 44(2):187–195
Chen BJ, Shu HZ, Zhang H, Chen G, Toumoulin C, Dillenseger JL, Luo LM (2012) Quaternion Zernike moments and their invariants for color image analysis and object recognition. Sig Process 92(2):308–318
Chen BJ, Sun XM, Wang DC, Zhao XP (2012) Color face recognition using quaternion representation of color image. ACTA Autom Sin 38(11):1815–1823
Wang XY, Li WY, Yang HY, Niu PP, Li YW (2015) Invariant quaternion radial harmonic Fourier moments for color image retrieval. Opt Laser Technol 66:78–88
Wang X-Y, Li W-Y, Yang H-Y, Wang P, Li Y-W (2015) Quaternion polar complex exponential transform for invariant color image description. Appl Math Comput 256:951–967
Yang H-Y, Liang L, Li Y, Wang X (2016) Quaternion exponent moments and their invariants for color image. Fundam Inf 145:189–205
Camacho-Bello C, Báez-Rojas JJ, Toxqui-Quitl C, Padilla-Vivanco A (2014) Color image reconstruction using quaternion Legendre–Fourier moments in polar pixels. In: 2014 international conference on mechatronics, electronics and automotive engineering
Hamilton WR (1866) Elements of quaternions. Longmans Green, London
Ell TA, Sangwine SJ (2007) Hypercomplex Fourier transforms of color images. IEEE Trans Image Process 16:22–35
Zhang H, Wang S, Xu X, Chow TWS, Wu QMJ (2018) Tree2Vector: learning a vectorial representation for tree-structured data. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/tnnls.2018.2797060
Hosny KM, Shouman MA, Abdel-Salam HM (2011) Fast computation of orthogonal Fourier-Mellin moments in polar coordinates. J Real-Time Image Process 6(2):73–80
Hosny KM (2011) Accurate orthogonal circular moment invariants of gray-level images. J Comput Sci 7(5):715–722
Liu C, Huang X-H, Wang M (2012) Fast computation of Zernike moments in polar coordinates. IET Image Process 6(7):996–1004
Xin Y, Pawlak M, Liao S (2007) Accurate computation of Zernike moments in polar coordinates. IEEE Trans Image Process 16(2):581–587
Suk T, Flusser J (2009) Affine moment invariants of color images. In: The 13th international conference on computer analysis of images and patterns, lecture notes computer science, vol 5702, Münste, Germany. pp 334–341
Wang JZ, Li J, Wiederhold G (2001) SIMPLIcity: semantics-sensitive Integrated Matching for Picture LIbraries. IEEE Trans. on Pattern Analysis and Machine Intelligence, vol 23, no 9, pp 947–963
Nene SA, Nayar SK, Murase H (1996) Columbia object image library (COIL-100), Technical Report CUCS-006-96
Nilsback M-E, Zisserman A (2010) Delving deeper into the whorl of flower segmentation. Image Vis Comput 28(6):1049–1062
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Hosny, K.M., Darwish, M.M. Invariant color images representation using accurate quaternion Legendre–Fourier moments. Pattern Anal Applic 22, 1105–1122 (2019). https://doi.org/10.1007/s10044-018-0740-1
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DOI: https://doi.org/10.1007/s10044-018-0740-1