Network Working Group JM. Valin Internet-Draft Mozilla Intended status: Standards Track October 15, 2012 Expires: April 18, 2013 Pyramid Vector Quantization for Video Coding draft-valin-videocodec-pvq-00 Abstract This proposes applying pyramid vector quantization (PVQ) to video coding. Status of this Memo This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79. This document may not be modified, and derivative works of it may not be created, and it may not be published except as an Internet-Draft. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet- Drafts is at http://datatracker.ietf.org/drafts/current/. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." This Internet-Draft will expire on April 18, 2013. Copyright Notice Copyright (c) 2012 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License. Valin Expires April 18, 2013 [Page 1]

Internet-Draft Video PVQ October 2012 Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. Gain-Shape Coding and Activity Masking . . . . . . . . . . . . 3 4. Householder Reflection . . . . . . . . . . . . . . . . . . . . 4 5. Angle-Based Encoding . . . . . . . . . . . . . . . . . . . . . 5 6. Pyramid-Based Encoding . . . . . . . . . . . . . . . . . . . . 7 7. Bi-prediction . . . . . . . . . . . . . . . . . . . . . . . . . 7 8. Development Repository . . . . . . . . . . . . . . . . . . . . 7 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . . 8 10. Security Considerations . . . . . . . . . . . . . . . . . . . . 8 11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 8 12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 8 12.1. Normative References . . . . . . . . . . . . . . . . . . . 8 12.2. Informative References . . . . . . . . . . . . . . . . . . 8 Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . 8 Valin Expires April 18, 2013 [Page 2]

Internet-Draft Video PVQ October 2012 1. Introduction This draft describes a proposal for adapting the Opus RFC 6716 [RFC6716] energy conservation principle to video coding based on a pyramid vector quantizer (PVQ) [PVQ]. One potential advantage of conserving energy of the AC coefficients in video coding is preserving textures rather than low-passing them. Also, by introducing a fixed-resolution PVQ-type quantizer, we automatically gain a simple activity masking model. The main challenge of adapting this scheme to video is that we have a good prediction (the reference frame), so we are essentially starting from a point that is already on the PVQ hyper-sphere, rather than at the origin like in CELT. Other challenges are the introduction of a quantization matrix and the fact that we want the reference (motion predicted) data to perfectly correspond to one of the entries in our codebook. 2. Terminology The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119 [RFC2119]. 3. Gain-Shape Coding and Activity Masking The main idea behind the proposed video coding scheme is to code groups of DCT coefficient as a scalar gain and a unit-norm "shape" vector. A block's AC coefficients may all be part of the same group, or may be divided by frequency (e.g. by octave) and/or by directionality (horizontal vs vertical). It is desirable for a single quality parameter to control the resolution of both the gain and the shape. Ideally, that quality parameter should also take into account activity masking, that is, the fact that the eye is less sensitive to regions of an image that have more details. According to Jason Garrett-Glaser, the perceptual analysis in the x264 encoder uses a resolution proportional to the variance of the AC coefficients raised to the power a, with a=0.173. For gain-shape quantization, this is equivalent to using a resolution of g^(2a), where g is the gain. We can derive a scalar quantizer that follows this resolution: 1+2a g=Q_g gamma , Valin Expires April 18, 2013 [Page 3]

Internet-Draft Video PVQ October 2012 where gamma is the gain quantization index and Q_g is the gain resolution and main quality parameter. An important aspect of the current proposal is the use of prediction. In the case of the gain, there is usually a significant correlation with the gain of neighboring blocks. One way to predict the gain of a block is to compute the gain of the coefficients obtained through intra or inter prediction. Another way is to use the encoded gain of the neighboring blocks to explicitly predict the gain of the current block. 4. Householder Reflection Let vector x_d denote the (pre-normalization) DCT band to be coded in the current block and vector r_d denote the corresponding reference (based on intra prediction or motion compensation), the encoder computes and encodes the "band gain" g = sqrt(x_d^T x_d). The normalized band is computed as x_d x = --------- , || x_d || with the normalized reference r similarly computed based on r_d. The encoder then finds the position and sign of the maximum value in r: m = argmax_i | r_i | s = sign(r_m) and computes the Householder reflection that reflects r to -s e_m. The reflection vector is given by v = r + s e_m . The encoder reflects the normalized band to find the unit-norm vector v^T x z = x - 2 ----- v . v^T v The closer the current band is from the reference band, the closer z is from -s e_m. This can be represented either as an angle, or as a coordinate on a projected pyramid. Valin Expires April 18, 2013 [Page 4]

Internet-Draft Video PVQ October 2012 5. Angle-Based Encoding Assuming no quantization, the similarity can be represented by the angle theta = arccos(-s z_m) . If theta is quantized and transmitted to the decoder, then z can be reconstructed as z = -s cos(theta) e_m + sin(theta) z_r , where z_r is a unit vector based on z that excludes dimension m. The vector z_r can be quantized using PVQ. Let y be a vector of integers that satisfies sum_i(|y[i]|) = K , with K determined in advance, then the PVQ search finds the vector y that maximizes y^T z_r / (y^T y) . The quantized version of z_r is y z_rq = ------- . || y || If we assume that MSE is a good criterion for optimizing the resolution, then the angle quantization resolution should be (roughly) dg 1 1+2a Q_theta = ---------*----- = ------ . d(gamma) g gamma To derive the optimal K we need to consider the cosine distance between adjacent codevectors y_1 and y_2 for two cases: K<N and K>N. For K<N, the worst resolution occurs when no value in y is larger than one. In that case, the two closest codevectors have a cosine distance 1 cos(tau) = 1 - --- . K (derivation left as an exercise for the reader) By approximating cos(tau) as 1 - tau^2, we get Valin Expires April 18, 2013 [Page 5]

Internet-Draft Video PVQ October 2012 2 K = --- . tau For K>N the worst resolution happens when all values are equal to K/N in y_1, and y_2 differs by one pulse. In that case N cos(tau) = 1 - --- . K^2 (also left as an exercise for the reader) which gives the approximation _____ \/ 2 N ' K = ------- . tau By combining the two cases, we have _____ / \/ 2 N ' 2 \ K = min| ------- , ----- | . \ tau tau^2 / To achieve uniform resolution in all dimensions, Q_theta tau = ---------- . sin(theta) The value of K does not need to be coded because all the variables it depends on are known to the decoder. However, because Q_theta depends on the gain, this can lead to unacceptable loss propagation behavior in the case where inter prediction is used for the gain. This problem can be worked around by making the approximation sin(theta)~=theta. With this approximation, then tau is equal to the inverse of the theta quantization index, with no dependency on the gain. Alternatively, instead of quantizing theta, we can quantize sin(theta) which also removes the dependency on the gain. In the general case, we quantize f(theta) and then assume that sin(theta)~=f(theta). A possible choice of f(theta) is a quadratic function of the form: 2 f(theta) = a1 theta - a2 theta. Valin Expires April 18, 2013 [Page 6]

Internet-Draft Video PVQ October 2012 where a1 and a2 are two constants satisfying the constraint that f(pi/2)=pi/2. The value of f(theta) can also be predicted, but in case where we care about error propagation, it should only be predicted from information coded in the current frame. 6. Pyramid-Based Encoding Instead of explicitly encoding an angle, it is also possible to apply PVQ directly on z. In that case, the angle is replaced by v = K + s y[m], with 0 <= v <= 2K, with smaller values more likely (assuming the predictor is good). Based on calculations similar to those for the angle-based encoding, the value of K is set to ___ K = min( c1 gamma \/ N ' , c2 gamma^2 ) , where c1 and c2 are empirical constants. As is the case for angle-based encoding, K does not need to be coded. However, if the gain parameter gamma is predicted from a different frame, then this would lead to unacceptable error propagation behavior. To reduce the error propagation, instead of coding v we can code v'=K-|y[m]|, along with the sign of s*y[m]. In this way, any error in the gain will lead to the wrong value of K, but will not cause a desynchronization of the range coder as would happen when decoding the wrong number of symbols. 7. Bi-prediction We can use this scheme for bi-prediction by introducing a second theta parameter. For the case of two (normalized) reference frames r1 and r2, we introduce s1=(r1+r2)/2 and s2=(r1-r2)/2. We start by using s1 as a reference, apply the Householder reflection to both x and s2, and evaluate theta1. From there, we derive a second Householder reflection from the reflected version of s2 and apply it to z. The result is that the theta2 parameter controls how the current image compares to the two reference images. It should even be possible to use this in the case of fades, using two references that are before the frame being encoded. 8. Development Repository The algorithms in this proposal are being developed as part of Xiph.Org's Daala project. The code is available in the Daala git repository at <https://git.xiph.org/daala.git>. See Valin Expires April 18, 2013 [Page 7]

Internet-Draft Video PVQ October 2012 <https://xiph.org/daala/> for more information. 9. IANA Considerations This document makes no request of IANA. 10. Security Considerations This draft has no security considerations. 11. Acknowledgements Thanks to Jason Garrett-Glaser, Timothy Terriberry, Greg Maxwell, and Nathan Egge for their contribution to this document. 12. References 12.1. Normative References [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997. 12.2. Informative References [PVQ] Fischer, T., "A Pyramid Vector Quantizer", IEEE Trans. on Information Theory, Vol. 32 pp. 568-583, July 1986. [RFC6716] Valin, JM., Vos, K., and T. Terriberry, "Definition of the Opus Audio Codec", RFC 6716, September 2012. Author's Address Jean-Marc Valin Mozilla 650 Castro Street Mountain View, CA 94041 USA Email: jmvalin@jmvalin.ca Valin Expires April 18, 2013 [Page 8]