Abstract
Multimedia streaming of three-dimensional (3D) stereoscopic videos over last-generation networks subject to bandwidth limitations is an open problem. The development and spread of communication networks and devices that accept 3D videos is not supported by proper scheduling strategies. Namely the high variability of streams should be considered to reduce effects of network delays, packet losses, shortage of bandwidth resources, and shared use by multiple clients. Then, it is important to improve the characterization of 3D videos for more effective streaming. To this aim, this paper proposes a fractional exponential reduction moments approach based on the statistics of the so-called fractional moments. Each random sequence of frames in 3D videos can be analyzed and reduced to a finite set of parameters, that allow fitting to the sequence by exponential functions and then a characterization and classification of the video by a sort of fingerprint. The method does not depend on the format and the encoding technique of the video. Finally, the approach will allow comparing real streams and numerical data output from fractional dynamical models by means of the reduced parameters. Statistical proximity between time series and a fractional model or between different models simplifies formalization and classification of fractional models.
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Bashan, A., Bartsch, R., Kantelhardt, J.W., Havlin, S.: Comparison of detrending methods for fluctuation analysis. Phys. A Stat. Mech. Appl. 387(21), 5080–5090 (2008)
Beran, J.: Statistics for long-memory processes, vol. 61. Chapman & Hall, London (1994)
Buche, R.T., Ghosh, A., Pipiras, V., Zhang, J.X.: Heavy traffic methods in wireless systems: towards modeling heavy tails and long range dependence. Wirel. Commun. IMA Vol. Math. Appl. 143, 53–74 (2007)
Burr, R.L., Kirkness, C.J., Mitchell, P.H.: Detrended fluctuation analysis of the ICP predicts outcome following traumatic brain injury. IEEE Trans. Biomed. Eng. 55(11), 2509–2518 (2008)
Ceglie, C., Maione, G., Striccoli, D.: Periodic feedback control for streaming 3D videos in last-generation cellular networks. In: Giri, F., Van Assche, V. (eds.), 5th IFAC Int. Workshop on Periodic Control Systems (PSYCO 2013), Vol. 5, Part 1, pp. 23–28, Caen, France, July 3–5 (2013)
Ceglie, C., Maione, G., Striccoli, D.: Statistical analysis of long-range dependence in three-dimensional video traffic. In Proceedings of International Conference on Mathematical Methods in Engineering (MME 2013), Porto, Portugal, July 22–26 (2013)
Chong, S., Li, S.-Q., Ghosh, J.: Predictive dynamic bandwidth allocation for efficient transport of real-time vbr video over atm. IEEE J. Sel. Areas Commun. 13(1), 12–23 (1995)
Dahlman, E., Parkvall, S., Skold, S.: New Imaging Frontiers: 3D and Mixed Reality. Elsevier, Amsterdam (2011)
Feng, W.C., Rexford, J.: Performance evaluation of smoothing algorithms for transmitting prerecorded variable-bit-rate video. IEEE Trans. Multimed. 1(3), 302–313 (1999)
Garrett, M.W., Willinger, W.: Analysis, modeling and generation of self-similar VBR video traffic. In: Proceedings of ACM SIGCOMM ’94, pp. 269–280, London, UK, Aug. 31–Sept. 2 (1994)
Hausdorff, J.M., Peng, C.-K., Ladin, Z., Wei, J.Y., Goldberger, A.L.: Is walking a random walk? Evidence for long-range correlations in the stride interval of human gait. J. Appl. Physiol. 78, 349–358 (1995)
Hausdorff, J.M., Purdon, P., Peng, C.-K., Ladin, Z., Wei, J.Y., Goldberger, A.L.: Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations. J. Appl. Physiol. 80, 1448–1457 (1996)
Hwang, C.-L., Li, S.-Q.: On input state space reduction and buffer noneffective region. In: Proceedings of IEEE INFOCOM, pp. 1018–1028 (1994)
ITU-T and ISO/IEC JTC 1: Advanced video coding for generic audiovisual services. In: ITU-T Recommendation H.264 and ISO/IEC 14496–10 (MPEG-4 AVC) (2010)
Jenkins, M.A., Traub, J.F.: Algorithm 419: zeros of a complex polynomial. Commun. ACM 15, 97–99 (1972)
Jospin, M., Caminal, P., Jensen, E.W., Litvan, H., Vallverdu, M., Struys, M.R., Vereecke, H.E.M., Kaplan, D.T.: Detrended fluctuation analysis of EEG as a measure of depth of anesthesia. IEEE Trans. Biomed. Eng. 54(5), 840–846 (2007)
Li, S.-Q., Chong, S., Hwang, C.-L.: Link capacity allocation and network control by filtered input rate in high-speed networks. IEEE/ACM Trans. Netw. 3(1), 10–25 (1995)
Maione, G., Striccoli, D.: Transmission control of variable-bit-rate video streaming in UMTS networks. Control Eng. Pract. 20(12), 1366–1373 (2012)
Nigmatullin, R.R.: The statistics of the fractional moments: is there any chance to read “quantitatively” any randomness? J. Signal Process. 86, 2529–2547 (2006)
Nigmatullin, R.R.: Universal distribution function for the strongly-correlated fluctuations: general way for description of random sequences. Commun. Nonlinear Sci. Numer. Simul. 15, 637–647 (2010)
Nigmatullin, R.R., Ionescu, C., Baleanu, D.: NIMRAD: novel technique for respiratory data treatment. J. Signal Image Video Process 15, 637–647 (2012)
Nigmatullin, R.R., Ionescu, C.M., Osokin, S.I., Baleanu, D., Toboev, V.A.: Non-invasive methods applied for complex signals. Rom. Rep. Phys. 64(4), 1032–1045 (2012)
Nigmatullin, R.R., Baleanu, D., Al-Zhrani, A.A., Alhamed, Y.A., Zahid, A.H., Youssef, T.E.: Spectral analysis of HIV drugs for acquired immunodeficiency syndrome within modified non-invasive methods. Rev. Chim. 64(9), 987–993 (2013)
Nigmatullin, R.R., Baleanu, D., Povarova, D., Salah, N., Habib, S.S., Memic, A.: Raman spectra of nanodiamonds: new treatment procedure directed for improved Raman signal marker detection. Math. Probl. Eng. 847076 (2013)
Ossadnik, S.M., Buldyrev, S.V., Goldberger, A.L., Havlin, S., Mantegna, R.N., Peng, C.-K., Simons, M., Stanley, H.E.: Correlation approach to identify coding regions in DNA sequences. Biophys. J. 67, 64–70 (1994)
Peng, C.-K., Havlin, S., Stanley, H.E., Goldberger, A.L.: Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5, 82–87 (1995)
Penzel, T., Kantelhardt, J.W., Grote, L., Peter, J.-H., Bunder, A.: Comparison of detrended fluctuation analysis and spectral analysis for heart rate variability in sleep and sleep apnea. IEEE Trans. Biomed. Eng. 50(10), 1143–1151 (2003)
Pulipaka, A., Seeling, P., Reisslein, M., Karam, L.J.: Traffic and statistical multiplexing characterization of 3D video representation formats. IEEE Trans. Broadcast. 59(2), 382–389 (2013)
Scott, L.: Numerical Analysis. Princeton University Press, Princeton (2011)
Seeling, P., Reisslein, M.: Video transport evaluation with H.264 video traces. IEEE Commun. Surv. Tutor. 14(4), 1142–1165 (2012)
Wolf, A., Swift, B., Swinney, H., Vastano, J.: Determining Lyapunov exponents from a time series. Phys. D 16, 285–317 (1985)
Zhang, Z.-L., Kurose, J., Salehi, J., Towsley, D.: Smoothing, statistical multiplexing, and call admission control for stored video. IEEE J. Sel. Areas Commun. 15(6), 1148–1166 (1997)
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Nigmatullin, R.R., Ceglie, C., Maione, G. et al. Reduced fractional modeling of 3D video streams: the FERMA approach. Nonlinear Dyn 80, 1869–1882 (2015). https://doi.org/10.1007/s11071-014-1792-4
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DOI: https://doi.org/10.1007/s11071-014-1792-4