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Network Working Group                                          JM. Valin
Internet-Draft                                                   Mozilla
Intended status: Standards Track                          March 21, 2016
Expires: September 22, 2016


                      Directional Deringing Filter
                     draft-valin-netvc-deringing-01

Abstract

   This document describes a deringing filter that takes into account
   the direction of edges and patterns being filtered.  The filter works
   by identifying the direction of each block and then adaptively
   filtering along the identified direction.  In a second pass, the
   blocks are also filtered in a different direction, with more
   conservative thresholds to avoid blurring edges.  The proposed
   deringing filter is shown to improve the quality of both Daala and
   the Alliance for Open Media (AOM) video codec.

Status of This Memo

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   include Simplified BSD License text as described in Section 4.e of
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   This document may not be modified, and derivative works of it may not
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Direction Search  . . . . . . . . . . . . . . . . . . . . . .   2
   3.  Directional Filter  . . . . . . . . . . . . . . . . . . . . .   3
   4.  Second Stage Filter . . . . . . . . . . . . . . . . . . . . .   4
   5.  Setting Thresholds  . . . . . . . . . . . . . . . . . . . . .   5
   6.  Superblock Filtering  . . . . . . . . . . . . . . . . . . . .   6
   7.  Results . . . . . . . . . . . . . . . . . . . . . . . . . . .   6
   8.  Conclusion  . . . . . . . . . . . . . . . . . . . . . . . . .   7
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   7
   10. Security Considerations . . . . . . . . . . . . . . . . . . .   7
   11. Informative References  . . . . . . . . . . . . . . . . . . .   7
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .   8

1.  Introduction

   This document describes a deringing filter that takes into account
   the direction of edges and patterns being filtered.  The filter works
   by identifying the direction of each block and then adaptively
   filtering along the identified direction.  In a second pass, the
   blocks are also filtered in a different direction, with more
   conservative thresholds to avoid blurring edges.  The deringing
   filter is implemented for both Daala and the Alliance for Open Media
   (AOM) codec.

2.  Direction Search

   The first step is to divide the image into blocks of fixed or
   variable size.  Variable-size blocks make it possible to use large
   blocks on long, continuous edges and small blocks where edges
   intersect or change direction.  A fixed block size is easier to
   implement and does not require signaling the sizes on a block-by-
   block basis.  For this work, we consider a fixed block size of 8x8.

   Once the image is divided into blocks, we determine which direction
   best matches the pattern in each block.  One way to determine the
   direction is to minimize mean squared difference (MSD) between the
   input block and a perfectly directional block.  A perfectly
   directional block is a block for which each line along a certain




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   direction has a constant value.  For each direction, we assign a line
   number to each pixel, as shown below.

                     +---+---+---+---+---+---+---+---+
                     | 0 | 0 | 1 | 1 | 2 | 2 | 3 | 3 |
                     +---+---+---+---+---+---+---+---+
                     | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 |
                     +---+---+---+---+---+---+---+---+
                     | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 |
                     +---+---+---+---+---+---+---+---+
                     | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 6 |
                     +---+---+---+---+---+---+---+---+
                     | 4 | 4 | 5 | 5 | 6 | 6 | 7 | 7 |
                     +---+---+---+---+---+---+---+---+
                     | 5 | 5 | 6 | 6 | 7 | 7 | 8 | 8 |
                     +---+---+---+---+---+---+---+---+
                     | 6 | 6 | 7 | 7 | 8 | 8 | 9 | 9 |
                     +---+---+---+---+---+---+---+---+
                     | 7 | 7 | 8 | 8 | 9 | 9 |10 |10 |
                     +---+---+---+---+---+---+---+---+

   For each direction d, we compute the value s_d, which is equal to a
   direction-independent offset minus the MSD (see [Deringing-Note] for
   detauls) as:

                      __                      __           2
                      \          1      /     \           \
              s_d=    /_      ------- * |     /_      x_p | ,
                  k in block  N_(d,k)   \ p in P_(d,k)    /

   where x_p is the value of pixel p, P_(d,k) is the set of pixels in
   like k along direction d, and N_(d,k) is the cardinality of P_(d,k).
   From there, the direction is computed as the value of d that
   maximizes s_d.

3.  Directional Filter

   The directional filter for pixel (i,j) is defined as the 7-tap non-
   linear filter












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                    3     _
                1  --    |  /                                          \
 y(i,j)=x(i,j)+---*\ w_k*| f| x(i,j)-x(i+floor(k*d_y),j+floor(k*d_x), T|
                W  /_    |_ \                                          /
                   k=1                                                _
                          /                                          \ |
                       + f| x(i,j)-x(i-floor(k*d_y),j-floor(k*d_x), T| |
                          \                                          /_|


   where d_x and d_y define the direction, W is a constant normalizing
   factor, T is the filtering threshold for the block, and f(d,T) is
   defined as

                                  /
                                  \  d    , |d| < T
                        f(d, T) = <
                                  /  0    , otherwise
                                  \

   The direction parameters are shown in the table below.  The weights
   w_k can be chosen so that W is a power of two.  For example, Daala
   currently uses w=[3 2 2] with W=16.  Since the direction is constant
   over 8x8 blocks, all operations in this filter are directly
   vectorizable over the blocks.

                        +-----------+------+------+
                        | Direction | d_x  | d_y  |
                        +-----------+------+------+
                        |     0     |  1   |  -1  |
                        |     1     |  1   | -1/2 |
                        |     2     |  1   |  0   |
                        |     3     |  1   | 1/2  |
                        |     4     |  1   |  1   |
                        |     5     | 1/2  |  1   |
                        |     6     |  0   |  1   |
                        |     7     | -1/2 |  1   |
                        +-----------+------+------+

                                  Table 1

4.  Second Stage Filter

   The 7-tap directional filter is sometimes not enough to eliminate all
   ringing, so we use an additional filtering step that operates across
   the direction lines used in the first filter.  Considering that the
   input of the second filter has considerably less ringing than the
   input of the second filter, and the fact that the second filter risks



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   blurring edges, the position-dependent threshold T_2(i,j) for the
   second filter is set lower than that of the first filter T.  The
   filter structure is the same as the one used for the directional
   filter.  The direction parameters for the second stage filter are
   shown in the table below and the filter weights are w=[1 1] with
   W=16/3.

                         +-----------+-----+-----+
                         | Direction | d_x | d_y |
                         +-----------+-----+-----+
                         |     0     |  1  |  0  |
                         |     1     |  0  |  1  |
                         |     2     |  0  |  1  |
                         |     3     |  0  |  1  |
                         |     4     |  1  |  0  |
                         |     5     |  1  |  0  |
                         |     6     |  1  |  0  |
                         |     7     |  1  |  0  |
                         +-----------+-----+-----+

                                  Table 2

5.  Setting Thresholds

   The thresholds T and T_2 must be set high enough to smooth out
   ringing artefacts, but low enough to avoid blurring important details
   in the image.  Although the ringing is roughly proportional to the
   quantization step size Q, as the quantizer increases the error grows
   slightly less than linearly because the unquantized coefficients
   become very small compared to Q.  As a starting point for determining
   the thresholds, Daala uses a power model of the form
   T_0=level*alpha_1*Q^beta, with beta=0.842, and where alpha_1 depends
   on the input scaling.  The level is a threshold adjustment coded for
   each superblock (64x64).  In the AOM codec, a global threshold is
   selected by the encoder instead of using a function of the quantizer,
   so T_0=level*global_level.

   Another factor that affects the optimal filtering threshold is the
   presence of strong directional edges/patterns.  These can be
   estimated from the s_d parameters computed in the direction search as
   delta=s_(d_opt)-s_(d_ortho), where d_ortho=d_opt+4 (mod 8).  We
   compute the direction filtering threshold for each block as

                       /  1      /                   1/6  \ \
            T = T_0*max| ---, min| 3, alpha_2*(delta)     | |,
                       \  2      \                        / /





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   where alpha_2 also depends on the input scaling.  For the second
   filter, we use a more conservative threshold that depends on the
   amount of change caused by the directional filter.

                              /     T                    \
                T_2(i,j) = min| T, --- + |y(i,j)-x(i,j)| |.
                              \     3                    /

   As a special case, when the pixels corresponding to the 8x8 block
   being filtered are all skipped, then T=T_2=0, so no deringing is
   performed.

6.  Superblock Filtering

   The filtering is applied one superblock at a time, in a way that
   depends on the level.  In Daala, the level can take one of 6 values:
   0, 0.5, 0.7, 1.0, 1.4, 2.0, where a level of zero disables the
   deringing filter for the current superblock.  The level is the only
   information coded in the bitstream by the deringing filter.  On
   keyframes, it is entropy-coded based on the neighbor values.  On
   inter-predicted frames, the level is only coded for superblocks that
   are not skipped and is entropy-coded based on a single adapted
   probability distribution (no context from the neighbors).
   Superblocks where no level is coded have deringing disabled.
   Similarly, any skipped block within a superblock has deringing
   disabled, even if it is signaled enabled for the superblock.

   The level of the deringing filter in AOM is handled similarly, except
   that only four levels are currently available and there is no entropy
   coding yet.

   The deringing process sometimes reads pixels that lie outside of the
   superblock being processed.  When these pixels belong to another
   superblock, the filtering always uses the unfiltered pixel values --
   even for the second stage filter -- so that no dependency is added
   between the superblocks.  This makes it possible -- in theory -- to
   filter all superblocks in parallel.  When the pixels used for a
   filter lie outside of the viewable image, we set f(d,T)=0.

7.  Results

   The deringing filter described here has been implemented for the
   Daala [Daala-website] codec.  It is available from the Daala Git
   repository [Daala-Git].  We tested the deringing filter on the Are We
   Compressed Yet [AWCY] ntt-short1 set over the 0.025 bit/pixel to 0.1
   bit/pixel range, corresponding to a 1080p30 bitrate of 1.5 Mbit/s to
   6 Mbit/s.  The Bjontegaard-delta [I-D.daede-netvc-testing] rate
   reduction over that range was 6.5% for PSNR, 4.7% for PSNR-HVS, 5.6%



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   for SSIM and -6.0% (regression) for FAST-SSIM.  Visual inspection
   confirmed that the quality is indeed improved, despite the regression
   in the FAST-SSIM result.

   In AOM for the ntt-short1 set, the medium bitrate (0.02 to 0.06 bit/
   pixel) Bjontegaard-delta improvement is 2.5% for PSNR, 1.5% for PSNR-
   HVS, 1.5% for SSIM, and -3.8% (regression) on FAST-SSIM.  The high
   bitrate (0.06 to 0.2 bit/pixel) Bjontegaard-delta improvement is 2.0%
   for PSNR, 0.8% for PSNR-HVS, 1.3% for SSIM, and -3.1% (regression) on
   FAST-SSIM.

   The smaller improvement for AOM compared to Daala may be due to the
   newly integrated code not being mature, but also to the fact that
   some features in Daala tend to cause more ringing.  These features
   include lapped transforms, quantization matrices, perceptual vector
   quantization, overlapped block motion compensation (OBMC), and
   activity masking.

8.  Conclusion

   We have demonstrated an effective algorithm to remove ringing
   artefacts from coded images and videos.  The proposed filter takes
   into account the directionality of the patterns it is filtering to
   reduce the risk of blurring.

9.  IANA Considerations

   This document makes no request of IANA.

10.  Security Considerations

   This draft has no security considerations.

11.  Informative References

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

   [Daala-Git]
              "Daala Git repository", Xiph.Org Foundation ,
              <http://git.xiph.org/?p=daala.git;a=summary>.

   [Daala-website]
              "Daala website", Xiph.Org Foundation , <https://xiph.org/
              daala/>.






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   [Deringing-Note]
              Valin, JM., "The Daala Directional Deringing Filter",
              arXiv:1602.05975 [cs.MM] ,
              <http://arxiv.org/abs/1602.05975>.

   [I-D.daede-netvc-testing]
              Daede, T. and J. Jack, "Video Codec Testing and Quality
              Measurement", draft-daede-netvc-testing-02 (work in
              progress), October 2015.

Author's Address

   Jean-Marc Valin
   Mozilla
   331 E. Evelyn Avenue
   Mountain View, CA  94041
   USA

   Email: jmvalin@jmvalin.ca
































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