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NETVC Working Group                                              N. Egge
Internet-Draft                                                L. Trudeau
Intended status: Informational                                   Mozilla
Expires: May 19, 2018                                            D. Barr
                                                     Xiph.Org Foundation
                                                       November 15, 2017


              Chroma From Luma Intra Prediction for NETVC
                        draft-egge-netvc-cfl-01

Abstract

   Chroma from luma (CfL) prediction is a new and promising chroma-only
   intra predictor that models chroma pixels as a linear function of the
   coincident reconstructed luma pixels.  In this document, we propose
   the CfL predictor adopted in Alliance Video 1 (AV1) to the NETVC
   working group.  The proposed CfL distinguishes itself from prior art
   not only by reducing decoder complexity, but also by producing more
   accurate predictions.  On average, CfL reduces the BD-rate, when
   measured with CIEDE2000, by 5% for still images and 2% for video
   sequences.

Status of This Memo

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   This document is subject to BCP 78 and the IETF Trust's Legal
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   (https://trustee.ietf.org/license-info) in effect on the date of



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   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  State of the Art in Chroma from Luma Prediction . . . . . . .   4
   3.  Model Fitting the "AC" Contribution . . . . . . . . . . . . .   5
   4.  Chroma "DC" Prediction for "DC" Contribution  . . . . . . . .   6
   5.  Parameter Signaling . . . . . . . . . . . . . . . . . . . . .   7
   6.  Experimental Results  . . . . . . . . . . . . . . . . . . . .   8
   7.  Conclusion  . . . . . . . . . . . . . . . . . . . . . . . . .  10
   8.  Informative References  . . . . . . . . . . . . . . . . . . .  10
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  12

1.  Introduction

   Still image and video compression is typically not performed using
   red, green, and blue (RGB) color primaries, but rather with a color
   space that separates luma from chroma.  There are many reasons for
   this, notably that luma and chroma are less correlated than RGB,
   which favors compression; and also that the human visual system is
   less sensitive to chroma allowing one to reduce the resolution in the
   chromatic planes, a technique know as chroma subsampling [Wang01].

   Another way to improve compression in still images and videos is to
   subtract a predictor from the pixels.  When this predictor is derived
   from previously reconstructed information inside the current frame,
   it is referred to as an intra prediction tool.  In contrast, an inter
   prediction tool uses information from previously reconstructed
   frames.  For example, "DC" prediction is an intra prediction tool
   that predicts the pixels values in a block by averaging the values of
   neighboring pixels adjacent to the above and left borders of the
   block [Li14].

   Chroma from luma (CfL) prediction is a new and promising chroma-only
   intra predictor that models chroma pixels as a linear function of the
   coincident reconstructed luma pixels [Kim10].  It was proposed for
   the HEVC video coding standard [Chen11b], but was ultimately
   rejected, as the decoder model fitting caused a considerable
   complexity increase.

   More recently, CfL prediction was implemented in the Thor
   codec [Midtskogen16] as well as in the Daala codec [Egge15].  The



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   inherent conceptual differences in the Daala codec, when compared to
   HEVC, led to multiple innovative contributions by Egge and
   Valin [Egge15] to CfL prediction.  Most notably a frequency domain
   implementation and the absence of decoder model fitting.

   As both Thor and Daala are part of NETVC working group, a research
   initiative was established regarding CfL, the results of which are
   presented in this draft.  The proposed CfL implementation not only
   builds on the innovations of [Egge15], but does so in a way that is
   compatible with the more conventional compression tools found in
   Alliance Video 1 (AV1).  The following table details the key
   differences between LM Mode [Chen11b], Thor CfL [Midtskogen16], and
   Daala CfL [Egge15] (the previous version of this draft):

   +-----------------------+---------+----------+-----------+---------+
   |                       | LM Mode | Thor CfL | Daala CfL | AV1 CfL |
   +-----------------------+---------+----------+-----------+---------+
   |     Prediction Domain | Spatial |  Spatial | Frequency | Spatial |
   |                       |         |          |           |         |
   |    Bitsream Signaling |      No |       No |  Sign bit |   Signs |
   |                       |         |          |           |         |
   |                       |         |          |  PVQ Gain | + Index |
   |                       |         |          |           |         |
   |          Requires PVQ |      No |       No |       Yes |      No |
   |                       |         |          |           |         |
   | Encoder Model Fitting |     Yes |      Yes |   Via PVQ |  Search |
   |                       |         |          |           |         |
   | Decoder Model Fitting |     Yes |      Yes |        No |      No |
   +-----------------------+---------+----------+-----------+---------+

   This new implementation is considerably different from its
   predecessors.  Its key contributions are:

   o  Parameter signaling, which avoids model fitting on the decoder
      and, as explained in Section 2, results in more precise
      predictions, as the chroma reference pixels are used for fitting
      (which is impossible when fitting on the decoder).  The actual
      signaling is described in Section 5.

   o  Model fitting the "AC" contribution of the reconstructed luma
      pixels, as shown in Section 3, which simplifies the model and
      allows for a more precise fit.

   o  Chroma "DC" prediction for "DC" contribution, which requires no
      signaling and, as described in Section 4, is more precise.

   Finally, Section 6 presents detailed results of the compression gains
   of the proposed CfL prediction implementation in AV1.



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2.  State of the Art in Chroma from Luma Prediction

   As described in [Kim10], CfL prediction models chroma pixels as a
   linear function of the coincident reconstructed luma pixels.  More
   precisely, Let L be an M X N matrix of pixels in the luma plane; we
   define C to be the chroma pixels spatially coincident to L.  Since L
   is not available to the decoder, the reconstructed luma pixels, L^r,
   corresponding to L are used instead.  The chroma pixel prediction,
   C^p, produced by CfL uses the following linear equation:

                         C^p = alpha * L^r + beta

   Some implementations of CfL [Kim10], [Chen11b] and [Midtskogen16]
   determine the linear model parameters alpha and beta using linear
   least-squares regression

               ___ ___                   ___ ___          ___ ___
               \   \                     \   \            \   \
 alpha = (M*N) /__ /__ L^r(i,j)*C(i,j) - /__ /__ L^r(i,j) /__ /__ C(i,j)
               i=0 j=0                   i=0 j=0          i=0 j=0
         ---------------------------------------------------------------
                     ___ ___                 ___ ___
                     \   \                   \   \
               (M*N) /__ /__ (L^r(i,j))^2 - (/__ /__ L^r(i,j))^2
                     i=0 j=0                 i=0 j=0

                     ___ ___                ___ ___
                     \   \                  \   \
              beta = /__ /__ C(i,j) - alpha /__ /__ L^r(i,j)
                     i=0 j=0                i=0 j=0
                     ---------------------------------------
                                   (M*N)

   We classify [Kim10], [Chen11b], and [Midtskogen16] as implicit
   implementations of CfL, since alpha and beta are not signaled in the
   bitstream, but are implied from the bitstream.  The main advantage of
   the implicit implementation is the absence of signaling.

   However, implicit implementations have numerous disadvantages.  As
   mentioned before, computing least squares considerably increases
   decoder complexity.  Another important disadvantage is that the
   chroma pixels, C, are not available when computing least squares on
   the decoder.  As such, prediction error increases since neighboring
   reconstructed chroma pixels must be used instead.

   In [Egge15], the authors argue that the advantages of explicit
   signaling considerably outweigh the signaling cost.  Based on these




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   findings, we propose a hybrid approach that signals alpha and implies
   beta.

3.  Model Fitting the "AC" Contribution

   In [Egge15], Egge and Valin demonstrate the merits of separating the
   "DC" and "AC" contributions of the frequency domain CfL prediction.
   In the pixel domain, the "AC" contribution of a block can be obtained
   by subtracting it by its average.

   An important advantage of the "AC" contribution is that it is zero
   mean, which results in significant simplifications to the least
   squares model parameter equations.  More precisely, let L^AC$ be the
   zero-meaned reconstructed luma pixels.  Because

                           ___ ___
                           \   \
                           /__ /__ L_AC(i,j) = 0
                           i=0 j=0

   substituting L^r by L_AC yields the following simplified model
   parameters equations:

                               ___ ___
                               \   \
                    alpha_AC = /__ /__ L_AC(i,j)*C(i,j)
                               i=0 j=0
                               ------------------------
                               ___ ___
                               \   \
                               /__ /__ (L^r(i,j))^2
                               i=0 j=0

                                   ___ ___
                                   \   \
                         beta_AC = /__ /__ C(i,j)
                                   i=0 j=0
                                   --------------
                                        (M*N)

   We define the zero-mean chroma prediction, C_AC, like so

                     C_AC = alpha_AC * L_AC + beta_AC

   When computing the zero-mean reconstructed pixels, the resulting
   values are stored using 1/8th precision fixed-point values.  This
   ensures that even with 12-bit integer pixels, the average can be
   stored in a 16-bit signed integer.



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   By combining the luma subsampling step with the average subtraction
   step not only do the equations simplify, but the subsampling
   divisions and the corresponding rounding error are removed.  The
   equation corresponding to the combination of both steps simplifies
   to:

                               __sy-1__sx-1
                               \     \
             L_AC(i,j) =  8   (/__   /__L^r(sy*i+y,sx*j+x))
                        -----  y=0   x=0
                        sy*sx
                   ___ ___        __sy-1__sx-1
                   \   \          \     \
                 - /__ /__   8   (/__   /__L^r(sy*i+y,sx*j+x))
                   i=0 j=0 -----   y=0   x=0
                           sy*sx
                   -------------------------------------------
                                    (M*N)

   Note that this equation uses an integer division.

   In the previous equation, sx and sy are the subsampling steps for the
   x and y axes, respectively.  The proposed CfL only supports 4:2:0,
   4:2:2, 4:4:0 and 4:4:4 chroma subsamplings [Wang01], for which:

                            sy*sx in {1, 2, 4}.

   Also, because both M and N are powers of two, M * N is also a power
   of two.  It follows that the previous integer divisions can be
   replaced by bit shift operations.

4.  Chroma "DC" Prediction for "DC" Contribution

   Switching the linear model to use zero mean reconstructed luma pixels
   also changes beta_AC, to the extent that it now only depends on C.
   More precisely, beta_AC is the average of the chroma pixels.

   The chroma pixel average for a given block is not available in the
   decoder.  However, there already exists an intra prediction tool that
   predicts this average.  When applied to the chroma plane, the "DC"
   prediction predicts the pixel values in a block by averaging the
   values of neighboring pixels adjacent to the above and left borders
   of the block [Li14].

   Concretely, the output of the chroma "DC" predictor can be injected
   inside the proposed CfL implementation as an approximation for
   beta_AC.




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   The proposed CfL prediction is expressed as follows:

                   CfL(alpha) = alpha * L_AC + DC_PRED.

5.  Parameter Signaling

   Signaling the scaling parameters allows encoder-only fitting of the
   linear model.  This reduces decoder complexity and results in a more
   precise prediction, as the best scaling parameter can be determined
   based on the reference chroma pixels which are only available to the
   encoder.  The scaling parameters for both chromatic planes are
   jointly coded using the following scheme.

   First, we signal the joint sign of both scaling parameters.  A sign
   is either negative, zero, or positive.  In the proposed scheme,
   signaling (zero, zero) is not permitted as it results in "DC"
   prediction.  It follows that the joint sign requires an eight-value
   symbol.

   As for each scaling parameter, a 16-value symbol is used to represent
   values ranging from 0 to 2 with a step of 1/8th.  The entropy coding
   details are beyond the scope of this document; however, it is
   important to note that a 16-value symbol fully utilizes the
   capabilities of the multi-symbol entropy encoder [Valin16].  Finally,
   scaling parameters are signaled only if they are non-zero.

   Signaling the scaling parameters fundamentally changes their
   selection.  In this context, the least-squares regression used in
   [Kim10], [Chen11b], and [Midtskogen16] does not yield an RD-optimal
   solution as it ignores the trade-off between the rate and the
   distortion of the scaling parameters.

   For the proposed CfL prediction, the scaling parameter is determined
   using the same rate-distortion optimization mechanics as other coding
   tools and parameters of AV1.  Concretely, given a set of scaling
   parameters A, the selected scaling parameter is the one that
   minimizes the trade-off between the rate and the distortion

                alpha = argmin ( D(CfL(a)) + lambda R(a) ).
                        a in A

   In the previous equation, the distortion, D, is the sum of the
   squared error between the reconstructed chroma pixels and the
   reference chroma pixels.  Whereas, the rate, R, is the number of bits
   required to encode the scaling parameter and the residual
   coefficients.  Furthermore, lambda is the weighing coefficient
   between rate and distortion used by AV1.




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6.  Experimental Results

   To ensure a valid evaluation of coding efficiency gains, our testing
   methodology conforms to that of [Daede17].  All simulation parameters
   and a detailed sequence-by-sequence breakdown for all the results
   presented in this paper are available online at [AWCY].  Furthermore,
   the bitstreams generated in these simulations can be retrieved and
   analyzed online at [Analyzer].

   The following tables show the average percent rate difference
   measured using the Bjontegaard rate difference, also known as BD-
   rate [Bjontegaard01].  The BD-rate is measured using the following
   objective metrics: PSNR, PSNR-HVS [Egiazarian2006], SSIM [Wang04],
   CIEDE2000 [Yang12] and MSSIM [Wang03].  Of all the previous metrics,
   only the CIEDE2000 considers both luma and chroma planes.  It is also
   important to note that the distance measured by this metric is
   perceptually uniform [Yang12].

   As required in [Daede17], for individual feature changes in libaom,
   we use quantizers: 20, 32, 43, and 55.  We present results for three
   test sets: Objective-1-fast [Daede17], Subset1 [Testset] and
   Twitch [Testset].

   In the following table, we present the results for the Subset1 test
   set[AWCYSubset1].  This test set contains still images, which are
   ideal to evaluate the chroma intra prediction gains of CfL when
   compared to other intra prediction tools in AV1.

   +---------+-------+--------+--------+-------+-------+-------+-------+
   |         |  PSNR |   PSNR |   PSNR |  PSNR |  SSIM |    MS | CIEDE |
   |         |       |     Cb |     Cr |   HVS |       |  SSIM |  2000 |
   +---------+-------+--------+--------+-------+-------+-------+-------+
   | Average | -0.53 | -12.87 | -10.75 | -0.31 | -0.34 | -0.34 | -4.87 |
   +---------+-------+--------+--------+-------+-------+-------+-------+

   For still images, when compared to all of the other intra prediction
   tools of AV1 combined, CfL prediction reduces the rate by an average
   of 5% for the same level of visual quality measured by CIEDE2000.

   For video sequences, next table breaks down the results obtained over
   the objective-1-fast test set [AWCYObjective1].










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   +---------+-------+--------+--------+-------+-------+-------+-------+
   |         |  PSNR |   PSNR |   PSNR |  PSNR |  SSIM |    MS | CIEDE |
   |         |       |     Cb |     Cr |   HVS |       |  SSIM |  2000 |
   +---------+-------+--------+--------+-------+-------+-------+-------+
   | Average | -0.43 |  -5.85 |  -5.51 | -0.42 | -0.38 | -0.40 | -2.41 |
   |         |       |        |        |       |       |       |       |
   |   1080p | -0.32 |  -6.80 |  -5.31 | -0.37 | -0.28 | -0.31 | -2.52 |
   |         |       |        |        |       |       |       |       |
   | 1080psc | -1.82 | -17.76 | -12.00 | -1.72 | -1.71 | -1.75 | -8.22 |
   |         |       |        |        |       |       |       |       |
   |    360p | -0.15 |  -2.17 |  -6.45 | -0.05 | -0.10 | -0.04 | -0.80 |
   |         |       |        |        |       |       |       |       |
   |    720p | -0.12 |  -1.08 |  -1.23 | -0.11 | -0.07 | -0.12 | -0.52 |
   +---------+-------+--------+--------+-------+-------+-------+-------+

   Not only does CfL yield better intra frames, which produces a better
   reference for inter prediction tools, but it also improves chroma
   intra prediction in inter frames.  We observed CfL predictions in
   inter frames when the predicted content was not available in the
   reference frames.  As such, CfL prediction reduces the rate of video
   sequences by an average of 2% for the same level of visual quality
   when measured with CIEDE2000.

   The average rate reductions for 1080psc are considerably higher than
   those of other types of content.  This indicates that CfL prediction
   considerably outperforms other AV1 predictors for screen content
   coding.  As shown in the following table, the results on the Twitch
   test set [AWCYTwitch], which contains only gaming-based screen
   content, corroborates this finding.

   +---------+-------+--------+-------+-------+-------+-------+--------+
   |         |  PSNR |   PSNR |  PSNR |  PSNR |  SSIM |    MS |  CIEDE |
   |         |       |     Cb |    Cr |   HVS |       |  SSIM |   2000 |
   +---------+-------+--------+-------+-------+-------+-------+--------+
   | Average | -1.01 | -15.58 | -9.96 | -0.93 | -0.90 | -0.81 |  -5.74 |
   +---------+-------+--------+-------+-------+-------+-------+--------+

   Furthermore, individual sequences in the Twitch test set show
   considerable gains.  We present the results for Minecraft_10_120f
   (Mine), GTAV_0_120F (GTAV), and Starcraft_10_120f (Star) in the
   following table.  It would appear that CfL prediction is particularly
   efficient for sequences of the game Minecraft both sequences reduces
   the average rate by 20% for the same level of visual quality measured
   by CIEDE2000.







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   +------+-------+--------+--------+-------+-------+--------+---------+
   |      |  PSNR |   PSNR |   PSNR |  PSNR |  SSIM |     MS |   CIEDE |
   |      |       |     Cb |     Cr |   HVS |       |   SSIM |    2000 |
   +------+-------+--------+--------+-------+-------+--------+---------+
   | Mine | -3.76 | -31.44 | -25.54 | -3.13 | -3.68 |  -3.28 |  -20.69 |
   |      |       |        |        |       |       |        |         |
   | GTAV | -1.11 | -15.39 |  -5.57 | -1.11 | -1.01 |  -1.04 |   -5.88 |
   |      |       |        |        |       |       |        |         |
   | Star | -1.41 |  -6.18 |  -6.21 | -1.43 | -1.38 |  -1.43 |   -4.15 |
   +------+-------+--------+--------+-------+-------+--------+---------+

7.  Conclusion

   In this document, we presented the chroma from luma prediction tool
   adopted in AV1 that we proposed for NETVC.  This new implementation
   is considerably different from its predecessors.  Its key
   contributions are: parameter signaling, model fitting the "AC"
   contribution of the reconstructed luma pixels, and chroma "DC"
   prediction for "DC" contribution.  Not only do these contributions
   reduce decoder complexity, but they also reduce prediction error;
   resulting in a 5% average reduction in BD-rate, when measured with
   CIEDE2000, for still images, and 2% for video sequences.

   Possible improvements to CfL for AV2 include non-linear prediction
   models and motion-compensated CfL.

8.  Informative References

   [Analyzer]
              Bebenita, M., "AV1 Bitstream Analyzer",
              Mozilla https://arewecompressedyet.com/analyzer/, n.d..

   [AWCY]     "Are We Compressed Yet?", Xiph.Org
              Foundation https://arewecompressedyet.com, n.d..

   [AWCYObjective1]
              Trudeau, L., "Results of Chroma from Luma over the
              Objective-1-fast test set", Are We Compressed
              Yet? https://doi.org/10.6084/m9.figshare.5577778.v1,
              November 2017.

   [AWCYSubset1]
              Trudeau, L., "Results of Chroma from Luma over the Subset1
              test set", Are We Compressed
              Yet? https://doi.org/10.6084/m9.figshare.5577661.v2,
              November 2017.





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   [AWCYTwitch]
              Trudeau, L., "Results of Chroma from Luma over the twitch
              test set", Are We Compressed
              Yet? https://doi.org/10.6084/m9.figshare.5577946.v1,
              November 2017.

   [Bjontegaard01]
              Bjontegaard, G., "Calculation of average PSNR differences
              between RD-curves", Video Coding Experts Group (VCEG) of
              ITU-T VCEG-M33, 2001.

   [Chen11b]  Chen, J., Seregin, V., Han, W., Kim, J., and B. Jeon,
              "CE6.a.4: Chroma intra prediction by reconstructed luma
              samples", Joint Collaborative Team on Video Coding (JCT-
              VC) of ITU-T SG16 WP3 and ISO/IEC JTC1/SC29/WG11, JCTVC-
              E266, March 2011.

   [Daede17]  Daede, T., Norkin, A., and I. Brailovsky, "Video Codec
              Testing and Quality Measurement", IETF NETVC Internet-
              Draft draft-ietf-netvc-testing-05, March 2017.

   [Egge15]   Egge, N. and J. Valin, "Predicting chroma from luma with
              frequency domain intra prediction", Proceedings of SPIE
              9410, Visual Information Processing and Communication VI,
              March 2015.

   [Egiazarian2006]
              Egiazarian, K., Astola, J., Ponomarenko, N., Lukin, V.,
              Battisti, F., and M. Carli, "Two new full-reference
              quality metrics based on HVS", Proceedings of the Second
              International Workshop on Video Processing and Quality
              Metrics for Consumer Electronics VPQM, January 2006.

   [Kim10]    Kim, J., Park, S., Choi, Y., Jeon, Y., and B. Jeon, "New
              intra chroma prediction using inter-channel correlation",
              Joint Collaborative Team on Video Coding (JCT-VC) of ITU-T
              SG16 WP3 and ISO/IEC JTC1/SC29/WG11, JCTVC-B021, January
              2010.

   [Li14]     Ze-Nian, L., Drew, M., and J. Liu, "Fundamentals of
              Multimedia", ISBN 3319052896, org Springer Publishing
              Company, Incorporated, edition 2nd, 2014.

   [Midtskogen16]
              Midtskogen, S., "Improved chroma prediction", draft-
              midtskogen-netvc-chromapred-02 IETF NETVC Internet-Draft,
              October 2016.




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   [Testset]  Daede, T., "Test Sets", Hosted by the Xiph.org
              Foundation https://people.xiph.org/~tdaede/sets/, n.d..

   [Valin16]  Valin, J., Terriberry, T., Egge, N., Daede, T., Cho, Y.,
              Montgomery, C., and M. Bebenita, "Daala: Building A Next-
              Generation Video Codec From Unconventional Technology",
              Multimedia signal processing (MMSP)
              workshop arXiv:1608.01947, September 2016.

   [Wang01]   Wang, Y., Zhang, Y., and J. Ostermann, "Video Processing
              and Communications", ISBN 23132985, Prentice Hall
              PTR, Upper Saddle River, NJ, USA, edition 1st, 2001.

   [Wang03]   Wang, Z., Simoncelli, E., and A. Bovik, "Multiscale
              structural similarity for image quality assessment", The
              37th Asilomar Conference on Signals, Systems
              Computers Volume 2, November 2003.

   [Wang04]   Wang, Z., Bovik, A., Sheikh, H., and E. Simoncelli, "Image
              Quality Assessment: From Error Visibility to Structural
              Similarity", issn 1057-7149, IEEE transactions on image
              processing Volume 13, number 4, April 2004.

   [Yang12]   Yang, Y., Ming, J., and N. Yu, "Color Image Quality
              Assessment Based on CIEDE2000", Advances in
              multimedia Article ID 273723, 2012.

Authors' Addresses

   Nathan E. Egge
   Mozilla
   331 E Evelyn Ave
   Mountain View  94041
   USA

   Email: negge@mozilla.com


   Luc N. Trudeau
   Mozilla
   331 E Evelyn Ave
   Mountain View  94041
   USA

   Email: luc@trud.ca






Egge, et al.              Expires May 19, 2018                 [Page 12]


Internet-Draft                     cfl                     November 2017


   David M. Barr
   Xiph.Org Foundation
   21 College Hill Road
   Somerville, MA  1124
   USA

   Email: b@rr-dav.id.au












































Egge, et al.              Expires May 19, 2018                 [Page 13]


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