Organisation internationale de normalisation

17.14.2Alternative transforms

17.14.2.1.1.1.1.1.1JCTVC-D048 Low-Complexity 4-point Integer Discrete Sine Transform [C. Yeo, Y. H. Tan, Z. Li (I2R)]

In this proposal, a method for performing a multiplier-less 4-point integer discrete sine transform is presented. In previous proposals, it has reportedly been shown that the mode-dependent directional transform can be carried out using an appropriate combination of discrete cosine transform and discrete sine transform. However, the discrete sine transform is carried out using fixed-point arithmetic. Here, an integer approximation of the discrete sine transform that is exactly orthogonal is presented. Furthermore, the resulting integer transform can reportedly be implemented without any multiplications. Experimental results reportedly show that the proposed integer transform has compression performance that is similar to the higher precision fixed-point arithmetic implementation.

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  Results similar to JCTVC-D286
  
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  DST type III (quarter of sine)
  
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  BR reduction for intra: 1.3% / 2% for HE and LC
  
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  Can be implemented by 15 adds and 6 shifts
  
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  Results reported are using 4-point and 8-point DST, 8-point does not have fast algorithm
  

17.14.2.1.1.1.1.1.2JCTVC-D286 Simplified multiplierless 4x4 DST for intra prediction residue [Xin Zhao, Li Zhang, Siwei Ma, Wen Gao]

In this contribution, a simplified 4x4 discrete sine transform (DST) scheme for intra prediction residuals is proposed. The proposed 4x4 pseudo DST is implemented integer transform matrix, multiplierless arithmetic and has low dynamic range of internal results. Also a mode-dependent coefficient scanning method is proposed together with the proposed DST.

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  4-point DST identical to JCTVC-D048 (except sign inversion)
  
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  8-point integer transform is a KLT computed from covariances of horizontal/vertical prediction errors
  
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  Mode-dependent coefficient scanning
  
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  HE intra results: 1.8% for luma with MD scanning, 1.0% without scanning
  

It was commented that, for this 8-point transform (KLT), no fast algorithm exists, but there could be chances to find one similar to a DST.

17.14.2.1.1.1.1.1.3JCTVC-D182 Performance report of adaptive DCT/DST selection [Atsuro Ichigaya, Shinichi Sakaida]

This document describes the coding performance of an adaptive DCT/DST selection method on HEVC test Model (HM) 0.9. In this proposed method, DST is used as an additional transform for intra and inter coding blocks in JCTVC-A122. DCT and DST are selected adaptively according to input signal characteristics without any training. Adaptive transform selection to the luma signal is implemented in HM0.9 and the performance is evaluated in this document. The coding results reportedly show BD BR reduction averaging 0.8% for low delay LC condition is achieved.

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  DCT and DST type II (half period of sine), symmetric basis can be implemented by fast algorithm
  
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  Almost same algorithm can be used for both transforms
  
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  Either 2D-DST or 2D-DCT is used for all block sizes; usage is signalled. No mode dependency.
  
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  Coding results: Intra/RA/LC HE 0.5/0.6/0.6%, LC -0.1/0.3/0.8%.
  
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  Encoding time significantly increased (60%) for intra, as both transforms need to be computed and compared for mode decision
  

17.14.2.1.1.1.1.1.4JCTVC-D180 (m18935) CE7: Hardware Friendly Rotational Transform [Xing Wen, Oscar C. Au, Lin Sun, Jiali Li, Feng Zou, Chao Pang, Jingjing Dai]

Notes below JCTVC-D222.

17.14.2.1.1.1.1.1.5JCTVC-D222 Performance of Rotational Transform (ROT) in TMuC 0.9 [Xing Wen, Oscar C. Au, Lin Sun, Jingjing Dai, Feng Zou, Chao Pang]

(Both contributions presented jointly; JCTVC-D222 is the result of TMuC ROT.)

The 8x8 Rotational Transform (ROT) is a secondary transform after DCT and is implemented in the HEVC Test Model (HM) software. Although ROT can reportedly achieve superior coding efficiency compared to only using a DCT-like transform, it was reported that the original ROT design cannot be efficiently implement by hardware. In this proposal, a different rotational transform (HF-ROT) is proposed which can reportedly achieve similar coding efficiency gain and also can be easily implemented by hardware. Four HF-ROT modes were proposed.

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  Results: 0.1-0.2% BR increase compared to original ROT from previous TMuC
  
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  BR reduction compared to anchor: Intra 2.4/3.2%, RA 1.1/1.2% for HE/LC
  
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  The contribution reports a very significant increase in encoding and significant increase in decoding time, but this is said to be unreliable.
  
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  Some concerns were expressed whether the analysis of clock cycles necessary for ROT is correct.
  
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  It was questioned why the compression performance is reduced, while other proposals for fast ROT do not report such degradations.
  

17.14.2.1.1.1.1.1.6JCTVC-D276 Rate-Distortion Optimized Transforms for Intra Block Coding [F. Zou, O. C. Au, C. Pang, J. Dai, X. Zhang, X. Wen (HKUST)]

This contribution proposes a rate-distortion (RD) optimized transform scheme for NxN TU in HM0.9. The transform pairs are trained off-line and implemented using matrix multiplication in HM0.9 based software. This technique reportedly achieves 3.2% BD BR improvement in Intra Low Complexity (LC) conditions and 2.0% BDBR improvement in Intra High Efficiency (HE) conditions.

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  The algorithm to optimize transform is a kind of least-squares optimization plus lambda-penalty for transform coefficient energy for RD term (for lambda=0 this would be SVD)
  
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  A very significant increase in encoding time and a significant increase in decoding time (25%) were reported.
  

As it appears that this scheme must be directly inplemented as a 2D transform, it seems too complex.

17.14.2.1.1.1.1.1.7JCTVC-D425 Cross-check report of HKUST's proposal JCTVC-D276 by ZJU [X. Zhu, S. Li, (ZJU)] (late registration Thursday 20th after start of meeting, uploaded Thursday 20th, first day of meeting)

17.14.2.1.1.1.1.1.8JCTVC-D151 Mode Dependent 2-step Transform for Intra Coding [Youji Shibahara, Takahiro Nishi]

This contribution proposes a unification of MDDT and ROT, in which a mode dependent 1-step transform is used for 4x4 transform blocks and mode dependent 2-step transforms are used for larger ones. The same 4x4 mode dependent KLT as MDDT is used for 4x4 transform blocks. The first one of the 2-step transform is either the AVC transform or a Chen-DCT in the TMuC0.9-hm, and the second one is 4x4 KLT which is partially applied only for the lower frequency components. Application of the second transform is depending on the intra prediction mode of the corresponding prediction unit. An experimental result reportedly shows that the proposed method provides 1.3% and 0.6% gain for Intra HE and Random Access HE, respectively, over the TMuC0.9-hm anchors. The encoding time (and decoding time) is 103% (101%) for Intra HE and no major difference was reportedly observed for Random Access HE.

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  A second transform is applied to a subset of coefficients, applied to all block sizes up to 32x32, always with a 4x4 size of second transform
  
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  Quantization was not changed
  
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  This approach could give a way to define a mode-dependent ROT
  
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  It was recommendation to include this in a CE (along with ROT) to find commonalities (also in terms of complexity reduction)
  

17.14.2.1.1.1.1.1.9JCTVC-D049 Mode-Dependent Coefficient Scanning for Intra Prediction Residual Coding [C. Yeo, Y. H. Tan, Z. Li (I2R)]

In this proposal, a method for the scanning of intra prediction residual coefficients is presented to improve rate-distortion performance of intra coding. While prior work in mode-dependent coefficient scanning has shown similar gains, they reportedly greatly increase the decoding complexity, since the scans are adaptive and residual coefficients statistics have to be update as each block is decoded. Furthermore, due to the arbitrary scan orders that are used, parallelization of the coding process may be difficult. The method in this contribution attempts to overcome these difficulties by using a simplified set of scans that lend themselves well to parallelization, and requires no statistics updating. Experimental results reportedly show that the proposed method has similar compression performance to adaptive scans while requiring much less decoding complexity.

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  Result: -0.9% Intra HE, +0.1% Intra LC
  
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  Four scans (2 different diagonal)
  
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  Otherwise same as JCTVC-D360/JCTVC-D393
  

17.14.2.1.1.1.1.1.10JCTVC-D447 BoG Report on Alternative Transforms [R. Cohen, C. Yeo, R. Joshi, F. Fernandes] (BoG report registered Monday 24th after start of meeting, uploaded Monday 24th, fifth day of meeting)

A BoG on alternative transforms met on the afternoon of Monday, Jan. 24 to discuss what should be done in the CE that follows from the work done in CE7: Alternative Transforms. Approximately 20 people attended the meeting. The goals of the upcoming CE are to investigate the compression efficiency and the additional complexity associated with each alternative transform. The main topics of discussion during this BoG meeting were the list of tools to include in the CE and which complexity metrics to use. A draft of the CE description that includes notes from the BoG meeting was appended in the document and was presented in the Track B session Wednesday afternoon.