Novel Quaternion Orthogonal Mountain Fourier Moments for Pattern Recognition Applications

Abstract

Recent advances have been made in a wide range of imaging and pattern recognition applications, including picture categorization and object identification systems. These systems necessitate a robust feature extraction method. This study proposes a new class of orthogonal functions known as orthogonal mountain functions (OMFs). Using these functions, a novel set of orthogonal moments and associated scaling, rotation, and translation (SRT) invariants are presented for building a color image’s feature vector components. These orthogonal moments are presented as quaternion orthogonal mountain Fourier moments (QOMFMs). To demonstrate the validity of our theoretically recommended technique, we conduct a number of image analysis and pattern recognition experiments, including a comparison of the performance of the feature vectors proposed above to preexisting orthogonal invariant moments. The result of this study experimentally proves the effectiveness and quality of our QOMFMs.

References

[1] Assefa D, Mansinha L, Tiampo KF, Rasmussen H, Abdella K. Local quaternion Fourier transform and color image texture analysis. Signal Process., 2010, 90(6): 1825-1835.

[2] Chen B, et al. . Fractional quaternion Zernike moments for robust color image copy-move forgery detection. IEEE Access, 2018, 6: 56637-56646.

[3] Choi M-S, Kim W-Y. A novel two stage template matching method for rotation and illumination invariance. Pattern Recogn., 2002, 35(1): 119-129.

[4] El Ogri O, Daoui A, Yamni M, Karmouni H, Sayyouri M, Qjidaa H. 2D and 3D medical image analysis by discrete orthogonal moments. Procedia Comput. Sci., 2019, 148: 428-437.

[5] Farida, Caraka, R.E., Cenggoro, T.W., Pardamean, B.: Batik Parang Rusak detection using geometric invariant moment. In: 2018 Indonesian Association for Pattern Recognition International Conference (INAPR). IEEE, pp. 71–74 (2018)

[6] Hjouji A, Bouikhalene B, EL-Mekkaoui J, Qjidaa H. New set of adapted Gegenbauer-Chebyshev invariant moments for image recognition and classification. J. Supercomput., 2021, 77: 5637-5667.

[7] Hjouji A, Chakid R, El-Mekkaoui J, Qjidaa H, et al. . Adapted Jacobi orthogonal invariant moments for image representation and recognition. Circuits Syst Signal Process, 2021, 40: 2855-2882.

[8] Hjouji, A., El-Mekkaoui, J., Qjidaa, H.: New set of non-separable 2D and 3D invariant moments for image representation and recognition. Multimedia Tools Appl. 80(8), 12309–12333 (2021)

[9] Hmimid A, Sayyouri M, Qjidaa H. Fast computation of separable two-dimensional discrete invariant moments for image classification. Pattern Recognit., 2015, 48: 509-521.

[10] Hosny KM, et al. . Resilient color image watermarking using accurate quaternion radial substituted Chebyshev moments. ACM Trans. Multimed. Comput. Commun. Appl., 2019, 15(2): 1-25.

[11] Hosny KM, et al. . New fractional-order Legendre-Fourier moments for pattern recognition applications. Pattern Recognit., 2020, 103,

[12] Hosny KM. Robust template matching using orthogonal legendre moment invariants. J. Comput. Sci., 2010, 6(10): 1083.

[13] Hosny KM, Shouman MA, Abdel-Salam HM. Fast computation of orthogonal Fourier-Mellin moments in polar coordinates. J. Real-Time Image Proc., 2011, 6: 73-80.

[14] http://www1.cs.columbia.edu/CAVE/software/softlib/coil-100.php

[15] http://www.dabi.temple.edu/~shape/MPEG7/dataset.html

[16] https://data.caltech.edu/records/mzrjq-6wc02

[17] Hu M-K. Visual pattern recognition by moment invariants. IRE Trans. Inf. Theory, 1962, 8: 179-187.

[18] Kanaya N, Liguni Y, Maeda H. 2-D DOA estimation method using Zernike moments. Signal Process., 2002, 82: 521-526.

[19] Kantor IL, Solodovnikov AS, Shenitzer A Hypercomplex Numbers: an Elementary Introduction to Algebras, 1989 New York Springer,

[20] Karmouni H, Jahid T, Sayyouri M, Hmimid A, Qjidaa H. Fast reconstruction of 3D images using Charlier discrete orthogonal moments. Circuits Syst. Signal Process., 2019, 38(8): 3715-3742.

[21] Kim WY, Kim YS. A region-based shape descriptor using Zernike moments. Signal Process: Image Commun., 2000, 16: 95-102

[22] Lahouli I, Karakasis E, Haelterman R, Chtourou Z, Cubber GD, Gasteratos A, Attia R. Hot spot method for pedestrian detection using saliency maps, discrete Chebyshev moments and support vector machine. IET Image Process., 2018, 12: 1284-1291.

[23] Liu Z, Wang H. A novel speech content authentication algorithm based on Bessel-Fourier moments. Digit. Signal Process., 2014, 24: 197-208,

[24] Luo LM, Xie XH, Bao XD. A modified moment-based edge operator for rectangular pixel image. IEEE Trans. Circuits Syst. Video Technol., 1994, 4: 552-554.

[25] Mandal MK, Aboulnasr T, Panchanathan S. Image indexing using moments and wavelets. IEEE Trans. Consum. Electron., 1996, 42(3): 557-565.

[26] Singh C, Pooja N. Local and global features based image retrieval system using orthogonal radial moments. Opt. Lasers Eng., 2012, 50: 655-667.

[27] Singh C, Singh J. Quaternion generalized Chebyshev-Fourier and pseudo-Jacobi-Fourier moments for color object recognition. Optics Laser Technol., 2018, 106: 234-250.

[28] Suk, T., Flusser, J.: Refine moment invariants of color images. In: International Conference on Computer Analysis of Images and Patterns. Springer, Berlin, Heidelberg (2009)

[29] Teague MR. Image analysis via the general theory of moments. J. Opt. Soc. Am., 1980, 70: 920-930,

[30] Wang C, Wang X, Xia Z, Ma B, Shi Y-Q. Image description with polar harmonic Fourier moments. IEEE Trans. Circuits Syst. Video Technol., 2019, 30(12): 4440-4452.

[31] Wang X-Y, Li W-Y, Yang H-Y, Wang P, Li Y-W. Quaternion polar complex exponential transform for invariant color image description. Appl. Math. Comput., 2015, 256: 951-967

[32] Xiao B, Lu G, Zhang Y, Li W, Wang G. Lossless image compression based on integer Discrete Tchebichef Transform. Neurocomputing, 2016, 214: 587-593.

[33] Xiao B, Li L, Li Y, Li W, Wang G. Image analysis by fractional-order orthogonal moments. Inf. Sci., 2017, 382/383: 135-149.

[34] Xin Y, Pawlak M, Liao S. Accurate computation of Zernike moments in polar coordinates. IEEE Trans. Image Process., 2007, 16: 581-587,

[35] Yang F, Ding M, Zhang X. Non-rigid multi-modal 3D medical image registration based on foveated modality independent neighborhood descriptor. Sensors, 2019, 19(21): 4675.