Abstract
Quaternion moments are widely used in several applications, such as image classification, object recognition, and multimedia security. The computation of these moments requires a vast computational time, especially for big-size images. Several attempts to accelerate quaternion moments are not enough to process big-size color images with the desired speedup. In this work, we proposed a new parallel framework for fast computation of quaternion moments in Cartesian coordinates using multi-core CPUs and many-core graphics processing units (GPUs) with the Compute Unified Device Architecture (CUDA). We called the proposed unified computational framework “CUDAQuat.” This framework was tested by eleven sets of quaternion moments. Several applications executed using the proposed parallel framework where the CPU times, execution-time-improvement ratio, and speedup were reported. The evaluation outlined significant speedup over the single-core CPU implementation, where the proposed framework accelerated several sets of quaternion moments with speedup 600x.
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References
He, B., Cui, J.: Weighted spherical Bessel–Fourier image moments. Clust. Comput. 22, 12985–12996 (2019)
Papakostas, G.A.: Over 50 Years of Image Moments and Moment Invariants. Moments and Moment Invariants-Theory and Applications, pp. 3–32. Science Gate Publishing, Thrace (2014)
Flusser, J., Suk, T., Zitova, B.: 2D and 3D Image Analysis by Moments. Wiley, Hoboken (2016)
Ell, T.A., Sangwine, S.J.: Robust hand gesture recognition of color images. IEEE Trans. Image Process. 16, 22–35 (2007)
Hamilton, W.R.: Elements of Quaternions. Longmans Green, London (1866)
Guo, L., Zhu, M.: Quaternion Fourier–Mellin moments for color images. Pattern Recogn. 44(2), 187–195 (2011)
Chen, B.J., Shu, H.Z., Zhang, H., Chen, G., Toumoulin, C., Dillenseger, J.L., Luo, L.M.: Quaternion Zernike moments and their invariants for color image analysis and object recognition. Signal Process. 92(2), 308–318 (2012)
Chen, B., Xingming, S., Wang, D., Zhao, X.: Color face recognition using quaternion representation of color image. Acta Autom. Sin. 38(11), 1815–1823 (2012)
Wang, X., Li, W., Yang, H., Wang, P., Li, Y.: Quaternion polar complex exponential transform for invariant color image description. Appl. Math. Comput. 256, 951–967 (2015)
Wang, X., Li, W., Yang, H., Niu, P., Li, Y.: Invariant quaternion radial harmonic Fourier moments for color image retrieval. Opt. Laser Technol. 66, 78–88 (2015)
Yang, H.Y., Liang, L.L., Li, Y.W., Wang, X.Y.: Quaternion exponent moments and their invariants for color image. Fundamenta Informaticae 145(2), 189–205 (2016)
Hosny, K.M., Darwish, M.M.: New set of quaternion moments for color images representation and recognition. J. Math. Imaging Vision 60(5), 717–736 (2018)
Singh, C., Singh, J.: Quaternion generalized Chebyshev–Fourier and pseudo-Jacobi–Fourier moments. Opt. Laser Technol. 106, 234–250 (2018)
Hosny, K.M., Darwish, M.M.: Invariant color images representation using accurate quaternion Legendre–Fourier moments. Pattern Anal. Appl. 22(3), 1105–1122 (2019)
Darwish, M.M., Kamal, S.T., Hosny, K.M.: “Improved Color Image Watermarking using Logistic Maps and Quaternion Legendre-Fourier moments Studies in Computational Intelligence, pp. 137–158. Springer, New York (2020). https://doi.org/10.1007/978-3-030-38700-6_6
Hosny, K.M., Darwish, M.M.: Resilient color image watermarking using quaternion radial substituted Chebychev moments. ACM Trans. Multimedia Comput. Commun. Appl. 15(2), 46 (2019)
Chunpeng, W., Xingyuan, W., Zhiqiu, X., Chuan, Z.: Ternary radial harmonic Fourier moments based robust stereo image zero-watermarking algorithm. Inf. Sci. 470, 109–120 (2019)
Hosny, K.M., Darwish, M.M.: Robust color image watermarking using invariant quaternion Legendre-Fourier moments. Multimedia Tools Appl. 77, 24727–24750 (2018)
Xia, Z., Wang, X., Zhou, W., Li, R., Wang, C., Zhang, C.: Color medical image lossless watermarking using chaotic system and accurate quaternion polar harmonic transforms. Signal Process. 157, 108–118 (2019)
Zhiqiu, X., Xingyuan, W., Xiaoxiao, L., Chunpeng, W., Unar, S., Mingxu, W., Tingting, Z.: Efficient copyright protection for three CT images based on quaternion polar harmonic Fourier moments. Signal Process. 164, 368–379 (2019)
Ouyang, J., Wen, X., Liu, J., Chen, J.: Robust Hashing Based on Quaternion Zernike Moments for Image Authentication. ACM Trans. Multimedia Comput. Commun. Appl. 12(45), 1–13 (2016). https://doi.org/10.1145/2978572
Hosny, K.M., Khedr, Y.M., Khedr, W.I., Mohamed, E.R.: Robust color image hashing using quaternion polar complex exponential transform for image robust copy-move forgery detection authentication. J. Circ. Syst. Signal Process. 37(12), 5441–5462 (2018)
Wang, X.Y., Liu, Y.N., Xu, H., Wang, P., Yang, H.Y.: Robust copy-move forgery detection using quaternion exponent moments. Pattern Anal. Appl. 21(2), 451–467 (2018)
Hosny, K.M., Hamza, H.M., Lashin, N.A.: Copy-for-duplication forgery detection in colour images using QPCETMs and sub-image approach. IET Image Proc. 13(9), 1437–1446 (2019)
Thajeel, S.A., Mahmood, A.S., Humood, W.R., Sulong, G.: Detection copy-move forgery in image via quaternion polar harmonic transforms. TIIS 13(8), 4005–4025 (2019)
Su, L., Li, C., Lai, Y., Yang, J.: A fast forgery detection algorithm based on exponential-Fourier moments for video region duplication. IEEE Trans. Multimedia 20(4), 825–840 (2018)
Chen, B., Qi, X., Sun, X., Shi, Y.-Q.: Quaternion pseudo-Zernike moments combining both of RGB information and depth information for color image splicing detection. J. Vis. Commun. Image Represent. 49, 283–290 (2017)
Camacho-Bello, C., Padilla-Vivanco, A., Toxqui-Quitl, C., Báez-Rojas, J.J.: Reconstruction of color biomedical images by means of quaternion generic Jacobi-Fourier moments in the framework of polar pixels. J. Med. Imaging 3(1), (2016)
Hua, L., Qiang, Y., Gu, J., Chen, L., Zhang, X., Zhu, H.: Mechanical fault diagnosis using color image recognition of vibration spectrogram based on quaternion invariable moment. Math. Probl. Eng. 15, 1–11 (2015). https://doi.org/10.1155/2015/702760
Guo, L., Dai, M., Zhu, M.: Quaternion moment and its invariants for color object classification. Inf. Sci. 273, 132–143 (2014)
Dad, N., En-Nahnahi, N., El El Alaoui Ouatik, S.: Quaternion Harmonic moments and extreme learning machine for color object recognition. Multimedia Tools Appl. 78, 20935–20959 (2019)
Dad, N., En-Nahnahi, N., El Alaoui Ouatik, S.: Combining minutiae triplets and quaternion orthogonal moments for fingerprint verification. J. Electron. Imaging 26(3), (2017). https://doi.org/10.1117/1.JEI.26.3.033012
Wang, X.-Y., Zhi-Fang, W., Chen, L., Zheng, H.-L., Yang, H.-Y.: Pixel classification based color image segmentation using quaternion exponent moments. Neural Netw. 74, 1–13 (2016)
Wang, X.Y., Wang, Q., Wang, X.B., Yang, H.Y., Wu, Z.F., Niu, P.P.: Color image segmentation using proximal classifier and quaternion radial harmonic Fourier moments. Pattern Anal. Appl. (2019). https://doi.org/10.1007/s10044-019-00826-y
Wang, X.-Y., Liang, L.-L., Li, Y.-W., Yang, H.-Y.: Image retrieval based on exponent moments descriptor and localized angular phase histogram. Multimedia Tools Appl. 76, 7633–7659 (2017)
Hassan, G., Hosny, K.M., Farouk, R.M., AlZohairy, A.M.: An efficient retrieval system for biomedical images based on Radial Associated Laguerre Moments. IEEE Access 8, 175669–175687 (2020)
Hassan, G., Hosny, K.M., Farouk, R.M., AlZohairy, A.M.: Efficient Quaternion Moments for Representation and Retrieval of Biomedical Color Images. Biomed. Eng. 32(5), 16 (2020)
Elouariachi, I., Benouini, R., Zenkouar, K., Zarghili, A.: Robust hand gesture recognition system based on a new set of quaternion Tchebichef moment invariants. Pattern Anal. Appl. (2020). https://doi.org/10.1007/s10044-020-00866-9
Karakasis, E.G., Papakostas, G.A., Koulouriotis, D.E., Tourassis, V.D.: A unified methodology for computing accurate quaternion color moments and moment invariants. IEEE Trans. Image Process. 23(2), 596–611 (2014)
Hosny, K.M., Darwish, M.M.: Accurate computation of quaternion polar complex exponential transform for color images in different coordinate systems. J. Electron. Imaging 26(2), (2017)
Hosny, K.M., Darwish, M.M.: Highly accurate and numerically stable higher-order QPCET moments for color image representation. Pattern Recogn. Lett. 97, 29–36 (2017)
Singh, S.P., Urooj, S.: A new computational framework for fast computation of a class of polar harmonic transforms. J. Signal Process. Syst. 91, 915–922 (2019)
Çavuşoğlu, Ü., Kaçar, S.: A novel parallel image encryption algorithm based on chaos. Clust. Comput. 22, 1211–1223 (2019)
Magid, S.A., Petrini, F., Dezfouli, B.: Image classification on IoT edge devices: profiling and modeling. Clust. Comput. 23, 1025–1043 (2020)
Tariq, S.A., Iqbal, S., Ghafoor, M., Taj, I.A., Jafri, N.M., Razzaq, S., Zia, T.: Massively parallel palmprint identification system using GPU. Clust. Comput. 22, 7201–7216 (2019)
Alawneh, L., Shehab, M.A., Al-Ayyoub, M., Jararweh, Y., Al-Sharif, Z.A.: A scalable multiple pairwise protein sequence alignment acceleration using hybrid CPU–GPU approach. Clust. Comput. 23, 2677–2688 (2020)
Afif, M., Said, Y., Atri, M.: Computer vision algorithms acceleration using graphic processors NVIDIA CUDA. Clust. Comput. 23, 3335–3347 (2020)
Toharia, P., Robles, O.D., SuáRez, R., Bosque, J.L., Pastor, L.: Shot boundary detection using Zernike moments in multi-GPU multi-CPU architectures. J. Parallel Distrib. Comput. 72(9), 1127–1133 (2012)
Requena, M.J.M., Moscato, P., Ujaldón, M.: Efficient data partitioning for the GPU computation of moment functions. J. Parallel Distrib. Comput. 74(1), 1994–2004 (2014)
Lachiondo, J.A., Ujaldón, M., Berretta, R., Moscato, P.: Legendre moments as high performance bone biomarkers: computational methods and GPU acceleration. Comput. Methods Biomech. Biomed. Eng. 4(3–4), 146–163 (2016)
Xuan, Y., Li, D., Han, W.: Efficient optimization approach for fast GPU computation of Zernike moments. J. Parallel Distrib. Comput. 111, 104–114 (2018)
Zhao, Z., Kuang, X., Zhu, Y., Liang, Y., Xuan, Y.: Combined kernel for fast GPU computation of Zernike moments. J. Real-Time Image Process. 1, 11 (2020). https://doi.org/10.1007/s11554-020-00979-8
Hosny, K.M., Salah, A., Saleh, H.I., Sayed, M.: Fast computation of 2D and 3D Legendre moments using multi-core CPUs and GPU parallel architectures. J. Real-Time Image Proc. 16(6), 2027–2041 (2019)
Yang, Zhuo, Tang, Mingkai, Li, Zhuozhang, Ren, Ziliang, Zhang, Qieshi: GPU Accelerated Polar Harmonic Transforms for Feature Extraction in ITS Applications. IEEE Access 8, 95099–95108 (2020)
Heidari, H., Chalechale, A. and Mohammadabadi, A.A.: Accelerating of color moments and texture features extraction using GPU based parallel computing. In 2013 8th Iranian Conference on Machine Vision and Image Processing (MVIP) (pp. 430–435). IEEE (2013)
Hosny, K.M., Darwish, M.M., Li, K., Salah, A.: Parallel multi-core CPU and GPU for fast and robust medical image watermarking. IEEE Access 6, 77212–77225 (2018)
Salah, A., Li, K., Hosny, K.M., Darwish, M.M., Tian, Q.: Accelerated CPU–GPUs implementations for quaternion polar harmonic transform of color images. Fut. Gener. Comput. Syst. 107, 368–382 (2020)
Wen-mei, W.H.: GPU Computing Gems, Emerald edn. Elsevier, Amsterdam (2011)
Di Carlo S., Gambardella G., Indaco M. et al.: A software-based self test of CUDA Fermi GPUs. pp. 1–6 (2013)
Lazebnik, S., Schmid, C., Ponce, J.: A maximum entropy framework for part-based texture and object recognition. Proc. IEEE Int. Conf. Comput. Vis. Beijing China 1, 832–838 (2005)
Navin, G., George, B., Nefian, A.V.: Face recognition experiments with random projections. In: SPIE Conference on Biometric Technology for Human Identification (2005)
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Hosny, K.M., Darwish, M.M., Salah, A. et al. CUDAQuat: new parallel framework for fast computation of quaternion moments for color images applications. Cluster Comput 24, 2385–2406 (2021). https://doi.org/10.1007/s10586-021-03271-x
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DOI: https://doi.org/10.1007/s10586-021-03271-x