Patent Grant
11968367
The present disclosure relates to video processing techniques, devices and systems.
In spite of the advances in video compression, digital video still accounts for the largest bandwidth use on the internet and other digital communication networks. As the number of connected user devices capable of receiving and displaying video increases, it is expected that the bandwidth demand for digital video usage will continue to grow.
Devices, systems and methods related to digital video processing, and specifically, to context modeling for residual coding in video coding. The described methods may be applied to both the existing video coding standards (e.g., High Efficiency Video Coding (HEVC)) and future video coding standards or video codecs.
In one representative aspect, the disclosed technology may be used to provide a method for video processing. This method includes performing a conversion between a video region of a video and a coded representation of the video, wherein the performing of the conversion includes configuring, based on a partition type of the video region, a context model for coding a first bin, the first bin and a second bin included in a bin string corresponding to an index of a secondary transform tool applied to the video region, wherein the index indicates an applicability of the secondary transform tool and/or a kernel information of the secondary transform tool, and wherein the secondary transform tool includes applying, during encoding, a forward secondary transform to an output of a forward primary transform applied to a residual of a video block prior to quantization, or wherein the secondary transform tool includes applying, during decoding, an inverse secondary transform to an output of dequantization to the video block before applying an inverse primary transform.
In another representative aspect, the disclosed technology may be used to provide a method for video processing. This method includes determining, for a current video block of a video comprising sub-blocks, based on a coding condition of the current video block, a zero-out region in which coefficients are zeroed out; and performing a conversion between the current video block and a coded representation of the video based on the determining, wherein the conversion includes applying a secondary transform tool, and wherein the secondary transform tool includes applying, during encoding, a forward secondary transform to an output of a forward primary transform applied to a residual of a video block prior to quantization, or wherein the secondary transform tool includes applying, during decoding, an inverse secondary transform to an output of dequantization to the video block before applying an inverse primary transform.
In yet another representative aspect, the disclosed technology may be used to provide a method for video processing. This method includes determining, for a conversion between a current video block having a dimension N×N of a video and a coded representation of the video, to use a transform matrix and/or an inverse transform matrix with a reduced size that is smaller than N×N in an application of a secondary transform tool to the current video block of a video; and performing a conversion between the video and a coded representation of the video, wherein the secondary transform tool includes applying, during encoding, a forward secondary transform to an output of a forward primary transform applied to a residual of a video block prior to quantization, or wherein the secondary transform tool includes applying, during decoding, an inverse secondary transform to an output of dequantization to the video block before applying an inverse primary transform.
In yet another representative aspect, the disclosed technology may be used to provide a method for video processing. This method includes determining, for a conversion between a current video block of a video and a coded representation of the video, based on a rule, to use a residual pattern among one or more residual patterns, wherein each of the one or more residual patterns corresponds to a mask that provides information about positions of zeroed out samples; and performing a conversion between the video and a coded representation of the video based on the determining.
In yet another representative aspect, the disclosed technology may be used to provide a method for video processing. This method includes determining, based on a type of a primary transform, a secondary transform tool associated with a current video block of a video; and performing a conversion between the video and a coded representation of the video, wherein the secondary transform tool includes applying, during encoding, a forward secondary transform to an output of a forward primary transform applied to a residual of a video block prior to quantization, or wherein the secondary transform tool includes applying, during decoding, an inverse secondary transform to an output of dequantization to the video block before applying an inverse primary transform.
In yet another representative aspect, the disclosed technology may be used to provide a method for video processing. This method includes determining to use multiple sets of transform matrices to be used to process a video region of a video; and performing a conversion between the video and a coded representation of the video, and wherein the coded representation includes an indication of which set among the multiple sets is used for the video region.
In yet another example aspect, a method of video processing is disclosed. The method includes determining, based on a rule, a transform matrix or an inverse transform matrix to be used in an application of a secondary transform tool to a current video block of a video; and performing a conversion between the video and a coded representation of the video, wherein the secondary transform tool includes applying, during encoding, a forward secondary transform to an output of a forward primary transform applied to a residual of a video block prior to quantization, or wherein the secondary transform tool includes applying, during decoding, an inverse secondary transform to an output of dequantization to the video block before applying an inverse primary transform, wherein the rule specifies to determine coefficients of the transform matrix or the inverse transform matrix based on a variable specifying a transform output length.
In yet another example aspect, a method of video processing is disclosed. The method includes determining a transform matrix or an inverse transform matrix to be used in an application of a secondary transform tool to a current video block of a video based on a rule; and performing a conversion between the video and a coded representation of the video, wherein the secondary transform tool includes applying, during encoding, a forward secondary transform to an output of a forward primary transform applied to a residual of a video block prior to quantization, or wherein the secondary transform tool includes applying, during decoding, an inverse secondary transform to an output of dequantization to the video block before applying an inverse primary transform, wherein the rule specifies to determine the transform matrix or the inverse transform matrix by using a retraining process.
In yet another representative aspect, the above-described method is embodied in the form of processor-executable code and stored in a computer-readable program medium.
In yet another representative aspect, a device that is configured or operable to perform the above-described method is disclosed. The device may include a processor that is programmed to implement this method.
In yet another representative aspect, a video decoder apparatus may implement a method as described herein.
The above and other aspects and features of the disclosed technology are described in greater detail in the drawings, the description and the claims.
Embodiments of the disclosed technology may be applied to existing video coding standards (e.g., HEVC, H.265) and future standards to improve compression performance. Section headings are used in the present disclosure to improve readability of the description and do not in any way limit the discussion or the embodiments (and/or implementations) to the respective sections only.
2 Video Coding Introduction
Due to the increasing demand of higher resolution video, video coding methods and techniques are ubiquitous in modern technology. Video codecs typically include an electronic circuit or software that compresses or decompresses digital video, and are continually being improved to provide higher coding efficiency. A video codec converts uncompressed video to a compressed format or vice versa. There are complex relationships between the video quality, the amount of data used to represent the video (determined by the bit rate), the complexity of the encoding and decoding algorithms, sensitivity to data losses and errors, ease of editing, random access, and end-to-end delay (latency). The compressed format usually conforms to a standard video compression specification, e.g., the High Efficiency Video Coding (HEVC) standard (also known as H.265 or MPEG-H Part 2), the Versatile Video Coding (VVC) standard to be finalized, or other current and/or future video coding standards.
Video coding standards have evolved primarily through the development of the well-known International Telecommunication Union—Telecommunication Standardization Sector (ITU-T) and International Organization for Standardization (ISO)/International Electrotechnical Commission (IEC) standards. The ITU-T produced H.261 and H.263, ISO/IEC produced Moving Picture Experts Group (MPEG)-1 and MPEG-4 Visual, and the two organizations jointly produced the H.262/MPEG-2 Video and H.264/MPEG-4 Advanced Video Coding (AVC) and H.265/HEVC standards. Since H.262, the video coding standards are based on the hybrid video coding structure wherein temporal prediction plus transform coding are utilized. To explore the future video coding technologies beyond HEVC, Joint Video Exploration Team (JVET) was founded by Video Coding Experts Group (VCEG) and MPEG jointly in 2015. Since then, many new methods have been adopted by JVET and put into the reference software named Joint Exploration Model (JEM) [3][4]. In April 2018, the Joint Video Expert Team (JVET) between VCEG (Q6/16) and ISO/IEC JTC1 SC29/WG11 (MPEG) was created to work on the VVC standard targeting at 50% bitrate reduction compared to HEVC.
2.1 Coding Flow of a Typical Video Codec
2.2 Intra Coding in VVC
2.2.1 Intra Mode Coding with 67 Intra Prediction Modes
To capture the arbitrary edge directions presented in natural video, the number of directional intra modes is extended from 33, as used in HEVC, to 65. The additional directional modes are depicted as dotted arrows in
Conventional angular intra prediction directions are defined from 45 degrees to −135 degrees in clockwise direction as shown in
In the HEVC, every intra-coded block has a square shape and the length of each of its side is a power of 2. Thus, no division operations are required to generate an intra-predictor using DC mode. In VTM2, blocks can have a rectangular shape that necessitates the use of a division operation per block in the general case. To avoid division operations for DC prediction, only the longer side is used to compute the average for non-square blocks.
In addition to the 67 intra prediction modes, wide-angle intra prediction for non-square blocks (WAIP) and position dependent intra prediction combination (PDPC) methods are further enabled for certain blocks. PDPC is applied to the following intra modes without signalling: planar, DC, horizontal, vertical, bottom-left angular mode and its eight adjacent angular modes, and top-right angular mode and its eight adjacent angular modes.
2.2.2 Affine Linear Weighted Intra Prediction (ALWIP or Matrix-Based Intra Prediction)
Affine linear weighted intra prediction (ALWIP, a.k.a., Matrix based intra prediction (MIP)) is proposed in JVET-N0217.
2.2.2.1 Generation of the Reduced Prediction Signal by Matrix Vector Multiplication
The neighboring reference samples are firstly down-sampled via averaging to generate the reduced reference signal bdryred. Then, the reduced prediction signal predred is computed by calculating a matrix vector product and adding an offset:
predred=A·bdryred+b
Here, A is a matrix that has Wred·Hred rows and 4 columns if W=H=4 and 8 columns in all other cases. b is a vector of size Wred·Hred.
2.2.2.2 Illustration of the Entire ALWIP Process
The entire process of averaging, matrix vector multiplication and linear interpolation is illustrated for different shapes in
For larger shapes, the procedure is essentially the same and it is easy to check that the number of multiplications per sample is less than four.
For W×8 blocks with W>8, only horizontal interpolation is necessary as the samples are given at the odd horizontal and each vertical positions.
Finally for W×4 blocks with W>8, let A_kbe the matrix that arises by leaving out every row that corresponds to an odd entry along the horizontal axis of the downsampled block. Thus, the output size is 32 and again, only horizontal interpolation remains to be performed.
The transposed cases are treated accordingly.
When constructing the most probable mode (MPM) list for an intra predicted block, if a neighboring block is coded in MIP mode, the MIP mode will be mapped to the intra prediction mode by using the following table. Here, assuming the width and height of the neighboring luma block are widthNeig and heightNeig respectively, MipSizeId is derived as follows:
2.2.2.3 Syntax and Semantics
7.3.6.5 Coding Unit Syntax
2.2.3 Multiple Reference Line (MRL)
Multiple reference line (MRL) intra prediction uses more reference lines for intra prediction. In
The index of selected reference line (mrl_idx) is signaled and used to generate intra predictor. For reference line index, which is greater than 0, only include additional reference line modes in MPM list and only signal MPM index without remaining mode. The reference line index is signaled before intra prediction modes, and Planar and DC modes are excluded from intra prediction modes in case a nonzero reference line index is signaled.
MRL is disabled for the first line of blocks inside a coding tree unit (CTU) to prevent using extended reference samples outside the current CTU line. Also, PDPC is disabled when additional line is used.
2.2.4 Intra Sub-Block Partitioning (ISP)
In JVET-M0102, ISP is proposed, which divides luma intra-predicted blocks vertically or horizontally into 2 or 4 sub-partitions depending on the block size dimensions, as shown in Table 1.
For each of these sub-partitions, a residual signal is generated by entropy decoding the coefficients sent by the encoder and then invert quantizing and invert transforming them. Then, the sub-partition is intra predicted and finally the corresponding reconstructed samples are obtained by adding the residual signal to the prediction signal. Therefore, the reconstructed values of each sub-partition will be available to generate the prediction of the next one, which will repeat the process and so on. All sub-partitions share the same intra mode.
2.2.4.1 Syntax and Semantics
7.3.7.5 Coding Unit Syntax
intra_subpartitions_mode_flag[x0][y0] equal to 1 specifies that the current intra coding unit is partitioned into NumIntraSubPartitions[x0][y0] rectangular transform block subpartitions. intra_subpartitions_mode_flag[x0][y0] equal to 0 specifies that the current intra coding unit is not partitioned into rectangular transform block subpartitions.
When intra_subpartitions_mode_flag[x0][y0] is not present, it is inferred to be equal to 0.
intra_subpartitions_split_flag[x0][y0] specifies whether the intra subpartitions split type is horizontal or vertical. When intra_subpartitions_split_flag[x0][y0] is not present, it is inferred as follows:
The variable NumIntraSubPartitions specifies the number of transform block subpartitions an intra luma coding block is divided into. NumIntraSubPartitions is derived as follows:
For chroma intra mode coding, a total of 8 or 5 intra modes are allowed for chroma intra mode coding depending on whether cross-component linear model (CCLM) is enabled or not. Those modes include five traditional intra modes and three cross-component linear model modes. Chroma DM mode use the corresponding luma intra prediction mode. Since separate block partitioning structure for luma and chroma components is enabled in I slices, one chroma block may correspond to multiple luma blocks. Therefore, for Chroma DM mode, the intra prediction mode of the corresponding luma block covering the center position of the current chroma block is directly inherited.
2.4 Transform Coding in VVC
2.4.1 Multiple Transform Set (MTS) in VVC
2.4.1.1 Explicit Multiple Transform Set (MTS)
In VTM4, large block-size transforms, up to 64×64 in size, are enabled, which is primarily useful for higher resolution video, e.g., 1080p and 4K sequences. High frequency transform coefficients are zeroed out for the transform blocks with size (width or height, or both width and height) equal to 64, so that only the lower-frequency coefficients are retained. For example, for an M×N transform block, with M as the block width and N as the block height, when M is equal to 64, only the left 32 columns of transform coefficients are kept. Similarly, when N is equal to 64, only the top 32 rows of transform coefficients are kept. When transform skip mode is used for a large block, the entire block is used without zeroing out any values.
In addition to Discrete Cosine Transform (DCT)-II which has been employed in HEVC, a Multiple Transform Selection (MTS) scheme is used for residual coding both inter and intra coded blocks. It uses multiple selected transforms from the DCT8/Discrete Sine Transform (DST)7. The newly introduced transform matrices are DST-VII and DCT-VIII. The Table 4 below shows the basis functions of the selected DST/DCT.
In order to keep the orthogonality of the transform matrix, the transform matrices are quantized more accurately than the transform matrices in HEVC. To keep the intermediate values of the transformed coefficients within the 16-bit range, after horizontal and after vertical transform, all the coefficients are to have 10-bit.
In order to control MTS scheme, separate enabling flags are specified at sequence parameter set (SPS) level for intra and inter, respectively. When MTS is enabled at SPS, a coding unit (CU) level flag is signalled to indicate whether MTS is applied or not. Here, MTS is applied only for luma. The MTS CU level flag is signalled when the following conditions are satisfied.
If MTS CU flag is equal to zero, then DCT2 is applied in both directions. However, if MTS CU flag is equal to one, then two other flags are additionally signalled to indicate the transform type for the horizontal and vertical directions, respectively. Transform and signalling mapping table as shown in Table 5. When it comes to transform matrix precision, 8-bit primary transform cores are used. Therefore, all the transform cores used in HEVC are kept as the same, including 4-point DCT-2 and DST-7, 8-point, 16-point and 32-point DCT-2. Also, other transform cores including 64-point DCT-2, 4-point DCT-8, 8-point, 16-point, 32-point DST-7 and DCT-8, use 8-bit primary transform cores.
To reduce the complexity of large size DST-7 and DCT-8, High frequency transform coefficients are zeroed out for the DST-7 and DCT-8 blocks with size (width or height, or both width and height) equal to 32. Only the coefficients within the 16×16 lower-frequency region are retained.
In addition to the cases wherein different transforms are applied, VVC also supports a mode called transform skip (TS) which is like the concept of TS in the HEVC. TS is treated as a special case of MTS.
2.4.2 Reduced Secondary Transform (RST) Proposed in JVET-N0193
2.4.2.1 Non-Separable Secondary Transform (NSST) in JEM
In Joint Exploration Model (JEM), secondary transform is applied between forward primary transform and quantization (at encoder) and between de-quantization and invert primary transform (at decoder side). As shown in
Application of a non-separable transform is described as follows using input as an example. To apply the non-separable transform, the 4×4 input block X
The non-separable transform is calculated as {right arrow over (F)}=T·{right arrow over (X)}, where {right arrow over (F)} indicates the transform coefficient vector, and T is a 16×16 transform matrix. The 16×1 coefficient vector F is subsequently re-organized as 4×4 block using the scanning order for that block (horizontal, vertical or diagonal). The coefficients with smaller index will be placed with the smaller scanning index in the 4×4 coefficient block. There are totally 35 transform sets and 3 non-separable transform matrices (kernels) per transform set are used. The mapping from the intra prediction mode to the transform set is pre-defined. For each transform set, the selected non-separable secondary transform (NSST) candidate is further specified by the explicitly signalled secondary transform index. The index is signalled in a bit-stream once per Intra CU after transform coefficients.
2.4.2.2 Reduced Secondary Transform (RST) in JVET-N0193
The RST (a.k.a., Low Frequency Non-Separable Transform (LFNST)) was introduced in JVET-K0099 and 4 transform set (instead of 35 transform sets) mapping introduced in JVET-L0133. In this JVET-N0193, 16×64 (further reduced to 16×48) and 16×16 matrices are employed. For notational convenience, the 16×64 (reduced to 16×48) transform is denoted as RST8×8 and the 16×16 one as RST4×4.
2.4.2.2.1 RST Computation
The main idea of a Reduced Transform (RT) is to map an N dimensional vector to an R dimensional vector in a different space, where R/N (R<N) is the reduction factor.
The RT matrix is an R×N matrix as follows:
In this contribution, the RST8×8 with a reduction factor of 4 (¼ size) is applied. Hence, instead of 64×64, which is conventional 8×8 non-separable transform matrix size, 16×64 direct matrix is used. In other words, the 64×16 invert RST matrix is used at the decoder side to generate core (primary) transform coefficients in 8×8 top-left regions. The forward RST8×8 uses 16×64 (or 8×64 for 8×8 block) matrices so that it produces non-zero coefficients only in the top-left 4×4 region within the given 8×8 region. In other words, if RST is applied then the 8×8 region except the top-left 4×4 region will have only zero coefficients. For RST4×4, 16×16 (or 8×16 for 4×4 block) direct matrix multiplication is applied.
An invert RST is conditionally applied when the following two conditions are satisfied:
If both width (W) and height (H) of a transform coefficient block is greater than 4, then the RST8×8 is applied to the top-left 8×8 region of the transform coefficient block. Otherwise, the RST4×4 is applied on the top-left min(8, W)×min(8, H) region of the transform coefficient block.
If RST index is equal to 0, RST is not applied. Otherwise, RST is applied, of which kernel is chosen with the RST index. The RST selection method and coding of the RST index are explained later.
Furthermore, RST is applied for intra CU in both intra and inter slices, and for both Luma and Chroma. If a dual tree is enabled, RST indices for Luma and Chroma are signaled separately. For inter slice (the dual tree is disabled), a single RST index is signaled and used for both Luma and Chroma.
2.4.2.2.2 Restriction of RST
When ISP mode is selected, RST is disabled, and RST index is not signaled, because performance improvement was marginal even if RST is applied to every feasible partition block. Furthermore, disabling RST for ISP-predicted residual could reduce encoding complexity.
2.4.2.2.3 RST Selection
A RST matrix is chosen from four transform sets, each of which consists of two transforms. Which transform set is applied is determined from intra prediction mode as the following:
The index to access the above table, denoted as IntraPredMode, have a range of [−14, 83], which is a transformed mode index used for wide angle intra prediction.
Later, the Low Frequency Non-Separable Transform (LFNST, a.k.a., RST) set selection for chroma blocks coded in CCLM modes is modified to be based on a variable IntraPredMode_CCLM, wherein the IntraPredMode_CCLM has a range of [−14, 80]. The IntraPredMode_CCLM is determined by the co-located luma intra prediction mode and the dimension of the current chroma block.
When dual tree is enabled, the block (e.g., picture unit (PU)) covering the corresponding luma sample of the top-left chroma sample in the current chroma block is defined as the co-located luma block. An example was shown in
2.4.2.2.4 RST Matrices of Reduced Dimension
As a further simplification, 16×48 matrices are applied instead of 16×64 with the same transform set configuration, each of which takes 48 input data from three 4×4 blocks in a top-left 8×8 block excluding right-bottom 4×4 block (as shown in
2.4.2.2.5 RST Signaling
The forward RST8×8 uses 16×48 matrices so that it produces non-zero coefficients only in the top-left 4×4 region within the first 3 4×4 region. In other words, if RST8×8 is applied, only the top-left 4×4 (due to RST8×8) and bottom right 4×4 region (due to primary transform) may have non-zero coefficients. As a result, RST index is not coded when any non-zero element is detected within the top-right 4×4 and bottom-left 4×4 block region (shown in
2.4.2.2.6 Zero-Out Region within One CG
Usually, before applying the invert RST on a 4×4 sub-block, any coefficient in the 4×4 sub-block may be non-zero. However, it is constrained that in some cases, some coefficients in the 4×4 sub-block must be zero before invert RST is applied on the sub-block.
Let nonZeroSize be a variable. It is required that any coefficient with the index no smaller than nonZeroSize when it is rearranged into a one dimensional (1-D) array before the invert RST must be zero.
When nonZeroSize is equal to 16, there is no zero-out constrain on the coefficients in the top-left 4×4 sub-block.
In JVET-N0193, when the current block size is 4×4 or 8×8, nonZeroSize is set equal to 8 (that is, coefficients with the scanning index in the range [8, 15] as show in
2.4.2.2.7 Description of RST in Working Draft
7.3.2.3 Sequence Parameter Set RBSP Syntax
7.3.7.11 Residual Coding Syntax
7.3.7.5 Coding Unit Syntax
sps_st_enabled_flag equal to 1 specifies that st_idx may be present in the residual coding syntax for intra coding units. sps_st_enabled_flag equal to 0 specifies that st_idx is not present in the residual coding syntax for intra coding units. st_idx[x0][y0] specifies which secondary transform kernel is applied between two candidate kernels in a selected transform set. st_idx[x0][y0] equal to 0 specifies that the secondary transform is not applied. The array indices x0, y0 specify the location (x0, y0) of the top-left sample of the considered transform block relative to the top-left sample of the picture.
When st_idx[x0][y0] is not present, st_idx[x0][y0] is inferred to be equal to 0.
It is noted that whether to send the st_idx is dependent on number of non-zero coefficients in all TUs within a CU (e.g., for single tree, number of non-zero coefficients in 3 blocks (i.e., Y, Cb, Cr); for dual tree and luma is coded, number of non-zero coefficients in the luma block; for dual tree and chroma is coded, number of non-zero coefficients in the two chroma blocks). In addition, the threshold is dependent on the partitioning structure, (treeType==SINGLE_TREE)?2:1).
Bins of st_idx are context-coded. More specifically, the following applies:
9.5.4.2.8 Derivation Process of ctxInc for the Syntax Element St_Idx
Inputs to this process are the colour component index cIdx, the luma or chroma location (x0, y0) specifying the top-left sample of the current luma or chroma coding block relative to the top-left sample of the current picture depending on cIdx, the tree type treeType, the luma intra prediction mode IntraPredModeY[x0][y0] as specified in clause 8.4.2, the syntax element intra_chroma_pred_mode[x0][y0] specifying the intra prediction mode for chroma samples as specified in clause 7.4.7.5, and the multiple transform selection index tu_mts_idx[x0][y0].
Output of this process is the variable ctxInc.
The variable intraModeCtx is derived as follows:
If cIdx is equal to 0, intraModeCtx is derived as follows:
intraModeCtx=(IntraPredModeY[x0][y0]<=1)?1:0
Otherwise (cIdx is greater than 0), intraModeCtx is derived as follows:
intraModeCtx=(intra_chroma_pred_mode[x0][y0]>=4)?1:0
The variable mtsCtx is derived as follows:
mtsCtx=(tu_mts_idx[x0][y0]=0&& treeType!=SINGLE_TREE)?1:0
The variable ctxInc is derived as follows:
ctxInc=(binIdx<<1)+intraModeCtx+(mtsCtx<<2)
2.4.2.2.8 Summary of RST Usage
RST may be enabled only when the number of non-zero coefficients in one block is greater than 2 and 1 for single and separate tree, respectively. In addition, the following restrictions of locations of non-zero coefficients for RST applied Coding Groups (CGs) is also required when RST is enabled.
2.4.3 Sub-Block Transform
For an inter-predicted CU with cu_cbf equal to 1, cu_sbt_flag may be signaled to indicate whether the whole residual block or a sub-part of the residual block is decoded. In the former case, inter MITS information is further parsed to determine the transform type of the CU. In the latter case, a part of the residual block is coded with inferred adaptive transform and the other part of the residual block is zeroed out. The SBT is not applied to the combined inter-intra mode.
In sub-block transform, position-dependent transform is applied on luma transform blocks in SBT-V and SBT-H (chroma transform block (TB) always using DCT-2). The two positions of SBT-H and SBT-V are associated with different core transforms. More specifically, the horizontal and vertical transforms for each SBT position is specified in
2.4.3.1 Syntax Elements
7.3.7.5 Coding Unit Syntax
cu_sbt_flag equal to 1 specifies that for the current coding unit, subblock transform is used. cu_sbt_flag equal to 0 specifies that for the current coding unit, subblock transform is not used.
When cu_sbt_flag is not present, its value is inferred to be equal to 0.
In JVET-N0413, quantized residual domain BDPCM (denoted as RBDPCM hereinafter) is proposed. The intra prediction is done on the entire block by sample copying in prediction direction (horizontal or vertical prediction) similar to intra prediction. The residual is quantized and the delta between the quantized residual and its predictor (horizontal or vertical) quantized value is coded.
For a block of size M (rows)×N (cols), let ri,j, 0≤i≤M−1, 0≤j≤N−1. be the prediction residual after performing intra prediction horizontally (copying left neighbor pixel value across the predicted block line by line) or vertically (copying top neighbor line to each line in the predicted block) using unfiltered samples from above or left block boundary samples. Let Q(ri,j), 0≤i≤M−1, 0≤j≤N−1 denote the quantized version of the residual ri,j, where residual is difference between original block and the predicted block values. Then the block DPCM is applied to the quantized residual samples, resulting in modified M×N array {tilde over (R)} with elements {tilde over (r)}i,j. When vertical BDPCM is signaled:
For horizontal prediction, similar rules apply, and the residual quantized samples are obtained by
The residual quantized samples {tilde over (r)}i,j are sent to the decoder.
On the decoder side, the above calculations are reversed to produce Q(ri,j), 0≤i≤M−1, 0≤j≤N−1. For vertical prediction case,
Q(ri,j)=Σk=0i{tilde over (r)}k,j,0≤i≤(M−1),0≤j≤(N−1)
For horizontal case,
Q(ri,j)=Σk=0j{tilde over (r)}i,k,0≤i≤(M−1),0≤j≤(N−1)
The invert quantized residuals, Q−1 (Q(ri,j)), are added to the intra block prediction values to produce the reconstructed sample values.
When quantized residual BDPCM (QR-BDPCM) is selected, there is no transform applied.
2.5 Entropy Coding of Coefficients
2.5.1 Coefficients Coding of Transform-Applied Blocks
In HEVC, transform coefficients of a coding block are coded using non-overlapped coefficient groups (or subblocks), and each coefficient group (CG) contains the coefficients of a 4×4 block of a coding block. The CGs inside a coding block, and the transform coefficients within a CG, are coded according to pre-defined scan orders.
The CGs inside a coding block, and the transform coefficients within a CG, are coded according to pre-defined scan orders. Both CG and coefficients within a CG follows the diagonal up-right scan order. An example for 4×4 block and 8×8 scanning order is depicted in
Note that the coding order is the reversed scanning order (i.e., decoding from CG3 to CG0 in
The coding of transform coefficient levels of a CG with at least one non-zero transform coefficient may be separated into multiple scan passes. In the first pass, the first bin (denoted by bin0, also referred as significant_coeff_flag, which indicates the magnitude of the coefficient is larger than 0) is coded. Next, two scan passes for context coding the second/third bins (denoted by bin1 and bin2, respectively, also referred as coeff_abs_greater1_flag and coeff_abs_greater2_flag) may be applied. Finally, two more scan passes for coding the sign information and the remaining values (also referred as coeff_abs_level_remaining) of coefficient levels are invoked, ifnecessary. Note that only bins in the first three scan passes are coded in a regular mode and those bins are termed regular bins in the following descriptions.
In the VTM 3, for each CG, the regular coded bins and the bypass coded bins are separated in coding order; first all regular coded bins for a subblock are transmitted and, thereafter, the bypass coded bins are transmitted. The transform coefficient levels of a subblock are coded in five passes over the scan positions as follows:
It is guaranteed that no more than 32 regular-coded bins (sig_flag, par_flag, gt1_flag and gt2_flag) are encoded or decoded for a 4×4 subblock. For 2×2 chroma subblocks, the number of regular-coded bins is limited to 8.
The Rice parameter (ricePar) for coding the non-binary syntax element remainder (in Pass 3) is derived similar to HEVC. At the start of each subblock, ricePar is set equal to 0. After coding a syntax element remainder, the Rice parameter is modified according to predefined equation. For coding the non-binary syntax element absLevel (in Pass 4), the sum of absolute values sumAbs in a local template is determined. The variables ricePar and posZero are determined based on dependent quantization and sumAbs by a table look-up. The intermediate variable codeValue is derived as follows:
The value of codeValue is coded using a Golomb-Rice code with Rice parameter ricePar.
2.5.1.1 Context Modeling for Coefficient Coding
The selection of probability models for the syntax elements related to absolute values of transform coefficient levels depends on the values of the absolute levels or partially reconstructed absolute levels in a local neighbourhood. The template used is illustrated in
The selected probability models depend on the sum of the absolute levels (or partially reconstructed absolute levels) in a local neighborhood and the number of absolute levels greater than 0 (given by the number of sig_coeff_flags equal to 1) in the local neighborhood. The context modelling and binarization depends on the following measures for the local neighborhood:
Based on the values of numSig, sumAbs1, and d, the probability models for coding sig_flag, par_flag, gt1_flag, and gt2_flag are selected. The Rice parameter for binarizing abs_remainder is selected based on the values of sumAbs and numSig.
2.5.1.2 Dependent Quantization (DQ)
In addition, the same HEVC scalar quantization is used with a new concept called dependent scale quantization. Dependent scalar quantization refers to an approach in which the set of admissible reconstruction values for a transform coefficient depends on the values of the transform coefficient levels that precede the current transform coefficient level in reconstruction order. The main effect of this approach is that, in comparison to conventional independent scalar quantization as used in HEVC, the admissible reconstruction vectors are packed denser in the N-dimensional vector space (N represents the number of transform coefficients in a transform block). That means, for a given average number of admissible reconstruction vectors per N-dimensional unit volume, the average distortion between an input vector and the closest reconstruction vector is reduced. The approach of dependent scalar quantization is realized by: (a) defining two scalar quantizers with different reconstruction levels and (b) defining a process for switching between the two scalar quantizers.
The two scalar quantizers used, denoted by Q0 and Q1, are illustrated in
As illustrated in
2.5.1.3 Syntax and Semantics
7.3.7.11 Residual Coding Syntax
2.5.2 Coefficients coding of TS-coded blocks and QR-BDPCM coded blocks
QR-BDPCM follows the context modeling method for TS-coded blocks.
A modified transform coefficient level coding for the TS residual. Relative to the regular residual coding case, the residual coding for TS includes the following changes:
The number of context coded bins is restricted to be no larger than 2 bins per sample for each CG.
2.5 Chroma Direct Mode
In Direct Mode (DM), prediction mode of co-located luma block is used for deriving the chroma intra prediction mode.
Firstly, an intra prediction mode lumaIntraPredMode is derived:
Secondly, the intra chroma prediction mode (denoted as IntraPredModeC) is derived according to lumaIntraPredMode in the following table. Note that intra_chroma_pred_mode equal to 4 refers to the DM mode.
Finally, if the color format of the picture is 4:2:2, IntraPredModeC is further modified according to the following table for the DM mode.
The detailed draft is specified as follows.
8.4.3 Derivation Process for Chroma Intra Prediction Mode
Input to this Process are:
When chroma_format_idc is equal to 2, the chroma intra prediction mode Y is derived using the chroma intra prediction mode X in Table 8-2 as specified in Table 8-3, and the chroma intra prediction mode X is set equal to the chroma intra prediction mode Y afterwards.
3 Drawbacks of Existing Implementations
The current design has the following problems:
Embodiments of the presently disclosed technology overcome the drawbacks of existing implementations, thereby providing video coding with higher coding efficiencies. The methods for context modeling for residual coding, based on the disclosed technology, may enhance both existing and future video coding standards, is elucidated in the following examples described for various implementations. The examples of the disclosed technology provided below explain general concepts, and are not meant to be interpreted as limiting. In an example, unless explicitly indicated to the contrary, the various features described in these examples may be combined.
In the following description, a “block” may refer to coding unit (CU) or a transform unit (TU) or any rectangle region of video data. a “current block” may refer to a current being decoded/coded coding unit (CU) or a current being decoded/coded transform unit (TU) or any being decoded/coded coding rectangle region of video data. “CU” or “TU” may be also known as “coding block” and“transform block”.
In these examples, the RST may be any variation of the design in JVET-N0193. RST could be any technology that may apply a secondary transform to one block or apply a transform to the transform skip (TS)-coded block (e.g., the RST proposed in JVET-N0193 applied to the TS-coded block).
Hereinafter, “normal intra prediction mode” is used to refer to the conventional intra prediction method wherein the prediction signal is generated by extrapolating neighbouring pixels from a certain direction. such as DC mode, Planar mode and Angular intra prediction modes (e.g., may further include wide angle intra prediction modes). For a block coded without using normal intra prediction mode, the block may be coded with at least one of the coding methods, e.g., IBC, MIP, palette, BDPCM intra-prediction modes.
In addition, the ‘zero-out region’ or ‘zero-out CG’ may indicate those regions/CGs which always have zero coefficients due the reduced transform size used in the secondary transform process. For example, if the secondary transform size is 16×32, and CG size is 4×4, it will be applied to the first two CGs, but only the first CG may have non-zero coefficients, the second 4×4 CG is also called zero-out CG.
Selection of Transform Matrices in RST
The examples described above may be incorporated in the context of the methods described below, e.g., methods 2200, 2210, 2220, 2230, 2240 and 2250, which may be implemented at a video decoder or a video encoder.
The method 2200 includes, at step 2204, applying, as part of a conversion between the current video block and a bitstream representation of a video comprising the current video block, the selected transform set or transform matrix to a portion of the current video block.
In some embodiments, the portion of the current video block is a top-right sub-region, bottom-right sub-region, bottom-left sub-region or center sub-region of the current video block.
In some embodiments, the characteristic of the current video block is an intra prediction mode or a primary transform matrix of the current video block.
In some embodiments, the characteristic is a color component of the current video block. In an example, a first transform set is selected for a luma component of the current video block, and wherein a second transform set different from the first transform set is selected for one or more chroma components of the current video block.
In some embodiments, the characteristic is an intra prediction mode or an intra coding method of the current video block. In an example, the intra prediction method comprises a multiple reference line (MRL)-based prediction method or a matrix-based intra prediction method. In another example, a first transform set is selected when the current video block is a cross-component linear model (CCLM) coded block, and wherein a second transform set different from the first transform set is selected when the current video block is a non-CCLM coded block. In yet another example, a first transform set is selected when the current video block is coded with a joint chroma residual coding method, and wherein a second transform set different from the first transform set is selected when the current video block is not coded with the joint chroma residual coding method.
In some embodiments, the characteristic is a primary transform of the current video block.
The method 2210 includes, at step 2214, performing, based on the decision, a conversion between the current video block and a video comprising the bitstream representation of the current video block.
In some embodiments, the one or more coefficients comprises a last non-zero coefficient in a scanning order of the current video block.
In some embodiments, the one or more coefficients comprises a plurality of coefficients within a partial region of the current video block. In an example, the partial region comprises one or more coding groups that the RST could be applied to. In another example, the partial region comprises a first M coding groups or a last M coding groups in a scanning order of the current video block. In yet another example, the partial region comprises a first M coding groups or a last M coding groups in a reverse scanning order of the current video block. In yet another example, making the decision is further based on an energy of one or more non-zero coefficients of the plurality of coefficients.
The method 2220 includes, at step 2224, performing, based on the configuring, a conversion between the current video block and the bitstream representation of the current video block.
In some embodiments, signaling the syntax element related to the RST is based on at least one coded block flag or a usage of a transform selection mode.
In some embodiments, the bitstream representation excludes the coding residual information corresponding to coding groups with all zero coefficients.
In some embodiments, the coding residual information is based on the application of the RST.
The method 2230 includes, at step 2234, performing, based on the configuring, a conversion between the current video block and the bitstream representation of the current video block.
In some embodiments, the transform skip indication or the MTS index is based on the syntax element related to the RST.
The method 2240 includes, at step 2244, performing, based on the configuring, a conversion between the current video block and a bitstream representation of a video comprising the current video block.
In some embodiments, the characteristic is an explicit or implicit enablement of a multiple transform selection (MTS) process.
In some embodiments, the characteristic is an enablement of a cross-component linear model (CCLM) coding mode in the current video block.
In some embodiments, the characteristic is a size of the current video block.
In some embodiments, the characteristic is a splitting depth of a partitioning process applied to the current video block. In an example, the partitioning process is a quadtree (QT) partitioning process, a binary tree (BT) partitioning process or a ternary tree (TT) partitioning process.
In some embodiments, the characteristic is a color format or a color component of the current video block.
In some embodiments, the characteristic excludes an intra prediction mode of the current video block and an index of a multiple transform selection (MTS) process.
The method 2250 includes, at step 2254, performing, based on the decision, a conversion between the current video block and a bitstream representation of a video comprising the current video block.
In some embodiments, the characteristic is a coded block flag of a coding group of the current video block. In an example, the inverse RST process is not applied, and wherein the coded block flag of a top-left coding group is zero. In another example, the inverse RST process is not applied, and wherein coded block flags for a first and a second coding group in a scanning order of the current video block are zero.
In some embodiments, the characteristic is a height (M) or a width (N) of the current video block. In an example, the inverse RST process is not applied, and wherein (i) M=8 and N=4, or (ii) M=4 and N=8.
As further described in the listing in the previous section (e.g., items 27 to 29), in some embodiments, a method of video processing includes determining, for a conversion between a coded representation of a current video block comprising sub-blocks and the current video block, a zero-out region applied for the conversion of the sub-blocks based on a coding condition; and performing the conversion based on the determining.
In this method, the coding condition comprises a size of the sub-blocks (see, e.g., item 27).
In this method, the coding condition includes a size of a secondary transform used during the conversion (see, e.g., item 28).
In some embodiments, the conversion may be performed using reduced size transform matrices (see, e.g., item 29).
5 Example Implementations of the Disclosed Technology
In the following exemplary embodiments, the changes are on top of JVET-N0193. Deleted texts are marked with double brackets (e.g., [[a]] denotes the deletion of the character “a”).
5.1 Embodiment #1
Signaling of RST index is dependent on number of non-zero coefficients within a sub-region of the block, instead of the whole block.
7.3.6.11 Residual Coding Syntax
Alternatively, the condition may be replaced by:
5.2 Embodiment #2
RST may not be invoked according to coded block flags of certain CGs.
8.7.4. Transformation Process for Scaled Transform Coefficients
8.7.4.1 General
Inputs to this Process are:
Context modeling of RST index is revised.
5.3.1 Alternative #1
9.5.4.2.8 Derivation Process of ctxInc for the Syntax Element St_Idx
Inputs to this process are the colour component index cIdx, the luma or chroma location (x0, y0) specifying the top-left sample of the current luma or chroma coding block relative to the top-left sample of the current picture depending on cIdx, the tree type treeType, the luma intra prediction mode IntraPredModeY[x0][y0] as specified in clause 8.4.2, the syntax element intra_chroma_pred_mode[x0][y0] specifying the intra prediction mode for chroma samples as specified in clause 7.4.7.5, the block width nTbW and height nTbH, and the multiple transform selection index tu_mts_idx[x0][y0].
Output of this process is the variable ctxInc.
The variable intraModeCtx is derived as follows:
If cIdx is equal to 0, intraModeCtx is derived as follows:
intraModeCtx=(IntraPredModeY[x0][y0]<=1)?1:0
Otherwise(cIdx is greater than 0),intraModeCtx is derived as follows:
intraModeCtx=(intra_chroma_pred_mode[x0][y0]>=4)?1:0
The variable mtsCtx is derived as follows:
mtsCtx=((sps_explicit_mts_intra_enabled_flag?tu_mts_idx[x0][y0]==0:nTbW==nTbH) && treeType!=SINGLE_TREE)?1:0
The variable ctxInc is derived as follows:
ctxInc=(binIdx<<1)+intraModeCtx+(mtsCtx<<2)
5.3.2 Alternative #2
[[9.5.4.2.8 Derivation Process of ctxInc for the Syntax Element St_Idx
Inputs to this process are the colour component index cIdx, the luma or chroma location (x0, y0) specifying the top-left sample of the current luma or chroma coding block relative to the top-left sample of the current picture depending on cIdx, the tree type treeType, the luma intra prediction mode IntraPredModeY[x0][y0] as specified in clause 8.4.2, the syntax element intra_chroma_pred_mode[x0][y0] specifying the intra prediction mode for chroma samples as specified in clause 7.4.7.5, and the multiple transform selection index tu_mts_idx[x0][y0].
Output of this process is the variable ctxInc.
The variable intraModeCtx is derived as follows:
If cIdx is equal to 0, intraModeCtx is derived as follows:
intraModeCtx=(IntraPredModeY[x0][y0]<=1)?1:0
Otherwise (cdx is greater than 0), intraModeCtx is derived as follows:
intraModeCtx=(intra_chroma_pred_mode[x][y0]>4)?1:0
The variable mtsCtx is derived as follows:
mtsCtx=(tu_mts_idx[x0][y0]==0&& treeType!=SINGLE_TREE)?1:0
The variable ctxInc is derived as follows:
ctxInc=(binIdx<<1)+intraModeCtx+(mtsCtx<<2)]]
5.4 Embodiment #4
Corresponding to bullets 7.c and 7.d.
7.3.7.11 Residual Coding Syntax
In an alternative example, the following may apply:
In one example, the following may apply:
SigRangeX is equal to 8 if log 2TbWidth>3 && log 2TbHeight==2. Otherwise, it is equal to 4.
SigRangeY is equal to 8 if log 2TbHeight>3 && log 2TbWidth==2. Otherwise, it is equal to 4.
5.5 Embodiment #5
Corresponding to bullet 19.
7.3.6.5 Coding Unit Syntax
5.6 Embodiment #6
Corresponding to bullet 20.
7.3.6.5 Coding Unit Syntax
5.7 Embodiment #17
Corresponding to bullet 21.
7.3.7.11 Residual Coding Syntax
(CbX[x0][y0], CbY[x0][y0]) specifies the top-left position of the coding unit covering the position (x0, y0).
5.8 Embodiment #8
The RST transform set index is derived from default modes assigned to non-normal intra prediction modes. The deleted parts are marked with double brackets (e.g., [[a]] denotes the deletion of the character “a”).
8.7.4.1 General
Inputs to this Process are:
The RST transform set index is derived from default modes assigned to non-normal intra prediction modes, and dependent on color format. The deleted parts are marked with double brackets (e.g., [[a]] denotes the deletion of the character “a”).
8.7.4.2 General
Inputs to this Process are:
Specification
of
the
4:2:2
mapping
process
from
chroma
intra
prediction
mode
X
to
mode
Y
when
chroma_format_idc isequalto2
mode X
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Alternatively, the followings may apply:
In this embodiment, the center luma sample of corresponding luma region of current chroma block is checked whether it is coded with MIP or IBC or palette mode; and the setting of DM is also based on the center luma sample.
The deleted parts are marked with double brackets (e.g., [[a]] denotes the deletion of the character “a”).
8.4.3 Derivation Process for Chroma Intra Prediction Mode
Input to this Process are:
When chroma_format_idc is equal to 2, the chroma intra prediction mode Y is derived using the chroma intra prediction mode X in Table 8-2 as specified in Table 8-3, and the chroma intra prediction mode X is is set equal to the chroma intra prediction mode Y afterwards.
5.11 Embodiment #11
In this embodiment, the top-left luma sample of corresponding luma region of current chroma block is checked whether it also based on the center luma sample.
The deleted parts are marked with double brackets (e.g., [[a]] denotes the deletion of the character “a”).
8.4.3 Derivation Process for Chroma Intra Prediction Mode
Input to this Process are:
When chroma_format_idc is equal to 2, the chroma intra prediction mode Y is derived using the chroma intra prediction mode X in Table 8-2 as specified in Table 8-3, and the chroma intra prediction mode X is is set equal to the chroma intra prediction mode Y afterwards.
Embodiment #12
This embodiment shows an example on the context modeling of RST (a.k.a., LFNST) index. The deleted parts are highlighted and are marked with double brackets (e.g., [[a]] denotes the deletion of the character “a”).
Alternatively, the Following May Apply:
Embodiment #13
The zero-out range is revised for RST4×4. The newly added parts are on top of JVET-O2001 and the deleted parts are marked with double brackets (e.g., [[a]] denotes the deletion of the character “a”).
7.3.8.11 Residual Coding Syntax
Alternatively, the Following May Apply:
8.7.4.1 General
Inputs to this Process are:
The transformation matrix lowFreqTransMatrix is derived based on nTrS, lfnstTrSetIdx, and lfnstIdx as follows:
Otherwise, if nTrS is equal to 16, lfnstTrSetIdx is equal to 2, and lfnstIdx is equal to 2, the following applies:
8.7.4.2 General
Inputs to this Process are:
The transformation matrix lowFreqTransMatrix is derived based on nTrS, lfnstTrSetIdx, and lfnstIdx as follows:
Embodiment #15
This embodiment gives an example for 16×16 RST (a.k.a., LFNST) and 16×48 RST matrices.
The newly added parts are on top of JVET-P2001 and Deleted texts are marked with double brackets (e.g., [[a]] denotes the deletion of the character “a”).
Low frequency non-separable transformation matrix derivation process
Inputs to this Process are:
The transformation matrix lowFreqTransMatrix is derived based on nTrS, lfnstTrSetIdx, and lfnst_idx as follows:
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}
{
−2
0
23
−5
1
2
−1
−11
−2
3
1
−1
1
1
−1
−3
}
{
−8
17
−7
−42
2
−4
−12
1
0
−1
−3
−2
0
−3
−3
1
}
{
−23
−12
20
1
4
12
1
−5
−4
4
−4
−1
1
2
−1
0
}
{
6
9
0
−6
−2
−5
−2
−4
1
−1
1
0
−1
−2
0
0
}
{
16
40
12
−22
−2
−5
−17
−2
−3
−1
−1
6
−1
−2
−3
1
}
},
{
{
106
−50
−4
−4
−1
−1
0
0
−46
4
11
1
2
0
1
0
}
{
47
13
−19
1
−4
0
−2
0
88
−53
−10
2
−2
1
−1
0
}
{
25
−8
0
−2
0
−1
0
0
33
54
−37
−2
−5
−1
−2
0
}
{
34
99
−49
−4
−8
−1
−3
−1
−28
9
−13
3
1
1
0
0
}
{
6
−18
4
−1
1
0
0
0
56
9
13
−13
0
−3
0
−1
}
{
−4
−4
−22
10
−3
3
−1
1
−15
−77
35
14
2
4
1
1
}
{
−16
−16
−16
13
0
3
0
1
−11
−11
10
−2
2
−1
1
0
}
{
−8
−37
−12
12
3
2
1
1
−5
−18
−56
26
0
4
0
2
}
{
5
16
71
−33
6
−7
2
−3
−22
−40
−25
−1
7
2
2
1
}
{
−21
−27
−65
21
1
6
1
2
−10
13
−24
21
1
2
0
0
}
{
3
4
18
2
−6
1
−2
0
9
39
52
−5
−10
−2
−3
−1
}
{
−4
−14
−27
10
0
4
0
2
−4
−10
49
−32
2
−3
1
−1
}
{
5
−1
−8
−2
1
0
0
0
9
0
4
14
−4
1
−2
0
}
{
−6
−14
−10
−27
7
0
2
0
−7
−7
−38
−4
7
3
1
1
}
{
5
5
28
15
−6
−1
−2
−1
5
−1
10
64
−18
3
−5
0
}
{
10
10
25
87
−25
7
−7
1
−2
−3
−17
−3
−8
0
0
0
}
},
−9
−2
−4
−3
−15
−3
−2
−1
−1
−7
−9
−72
−9
−2
−1
−18
−10
−2
−1
−1
−7
−1
−13
−4
−1
−32
−21
−4
−1
−1
−26
−57
−6
−5
−4
−1
−1
−24
−9
−1
−15
−4
−2
−1
−1
−28
−42
−6
−2
−11
−34
−4
−1
−80
−7
−6
−3
−12
−7
−2
−1
−1
−23
−4
−12
−12
−30
−9
−56
−9
−47
−58
−10
−7
−1
−14
−2
−36
−8
−13
−23
−3
−14
−9
−1
−1
−15
−16
−15
−29
−11
−2
−45
−19
−22
−1
−23
−11
−13
−3
−3
−20
−9
−2
{
{
−8
15
0
−2
0
0
0
0
−4
1
−4
0
0
0
0
0
}
{
−37
21
21
3
2
1
1
0
−13
12
10
−4
0
−1
0
0
}
{
57
−54
−30
14
−2
3
−1
1
−19
−36
28
12
−1
2
0
1
}
{
−2
5
−9
4
0
0
0
0
20
−19
−15
7
−2
2
−1
1
}
{
17
63
−40
−21
0
−3
0
−1
20
−31
−52
16
6
3
1
1
}
{
76
−4
10
−9
−6
−2
−2
0
−1
−32
6
−3
2
1
1
0
}
{
−63
6
−40
19
5
3
1
1
2
−48
33
42
−7
5
−1
1
}
{
−1
−9
19
31
−6
2
−2
1
70
1
3
−5
−17
0
−3
0
}
{
−10
−31
−18
5
8
2
2
1
−29
−4
−27
16
13
1
2
0
}
{
−11
−5
23
−15
−1
−2
0
−1
−66
2
−30
5
18
2
4
0
}
{
−18
−34
60
−25
−9
1
−1
0
22
−28
−11
−17
7
3
1
1
}
{
−10
−68
−36
−6
18
4
4
1
22
8
−11
16
12
−2
1
0
}
{
15
−13
−8
−15
5
−1
1
0
12
51
−20
38
6
−1
0
−1
}
{
−13
−24
13
−38
6
3
1
1
29
−35
−30
−7
33
1
3
0
}
{
−14
−2
9
−14
−24
2
−2
0
−16
−44
−2
−4
1
10
1
2
}
{
0
−4
−19
−12
−2
5
0
1
24
0
2
−21
18
0
2
0
}
},
{
{
−2
2
0
1
−1
0
0
0
−1
1
0
0
0
0
0
0
}
{
−10
6
0
−3
−4
4
−1
0
−4
1
0
0
−1
1
0
0
}
{
−5
3
16
−6
−7
1
3
−4
−2
1
1
−1
−3
0
1
−1
}
{
0
−20
8
8
2
−6
8
1
−1
−3
4
−1
1
−1
1
−1
}
{
−8
−29
7
26
−1
−6
14
5
−4
−1
6
−2
−2
−1
1
−1
}
{
−11
7
24
−3
−4
11
1
−10
−3
5
−1
−4
−1
4
−2
−1
}
{
−3
16
52
−14
6
12
1
−20
0
6
−1
−7
3
2
−2
−1
}
{
10
−48
3
1
−2
−7
33
0
−2
4
10
−12
−2
3
2
−6
}
{
−4
−18
17
40
3
13
30
0
3
5
3
−9
0
4
2
−4
}
{
−5
−4
8
43
4
8
24
5
6
3
6
−6
1
1
3
−4
}
{
−6
−23
29
6
−1
20
25
−26
−4
11
−14
−22
−2
4
−11
−2
}
{
12
−13
−32
11
−5
−24
11
37
3
5
24
6
0
1
5
−4
}
{
76
9
34
6
8
−10
−12
−51
−1
−16
−19
−6
−3
−3
0
7
}
{
−11
27
4
6
−3
9
−51
0
−8
−13
−12
44
5
1
11
18
}
{
41
−2
−7
−7
6
−45
−15
16
6
−14
43
17
3
3
15
−19
}
{
−7
43
−11
33
33
9
11
−2
−1
−9
−16
−17
3
−7
1
3
}
},
{
{
76
−49
4
−3
1
−1
0
0
−74
38
5
0
1
0
0
0
}
{
−55
−4
19
1
3
0
1
0
−6
56
−28
1
−4
0
−2
0
}
{
−60
28
−9
4
0
1
0
0
−44
10
22
−2
2
−1
1
0
}
{
−35
−14
25
−5
3
−1
2
0
−46
17
−11
7
1
1
0
0
}
{
26
69
−29
−8
−5
−2
−2
−1
−26
−34
−9
22
−1
5
−1
1
}
{
−22
12
−17
8
−2
2
−1
1
−56
−32
37
−5
5
0
2
0
}
{
24
39
−27
11
−7
1
−2
0
16
26
0
−19
2
−3
0
−1
}
{
−14
−52
−3
7
3
2
1
1
34
−24
45
−5
−1
−2
0
−1
}
{
13
31
−10
−15
5
−3
1
−1
16
50
−2
4
−10
−1
−2
0
}
{
−7
7
−36
11
2
2
0
1
−21
−1
22
2
−8
1
−1
0
}
{
−7
−29
−5
−5
9
0
2
0
−8
−34
−15
33
−12
6
−3
2
}
{
−5
9
25
−18
1
−3
1
−1
−14
−1
−38
7
9
0
1
0
}
{
15
29
80
−27
2
−7
0
−3
−4
−37
−14
−9
4
1
2
0
}
{
7
20
21
−11
3
−3
1
−1
12
44
31
11
−16
0
−4
0
}
{
2
16
29
−7
5
−3
0
−1
−12
−10
29
−41
−1
−2
1
0
}
{
7
9
41
−3
−9
1
−2
0
1
−2
56
−15
2
−3
0
−1
}
},
{
{
27
2
−14
2
−2
1
−1
0
−6
−12
8
1
0
0
0
0
}
{
53
−61
5
8
−1
2
0
0
−27
17
21
−12
3
−2
1
−1
}
{
30
38
−39
1
−3
0
−1
0
28
−57
8
15
−3
3
−1
1
}
{
−17
28
23
−10
0
−2
1
−1
18
33
−57
3
0
0
−1
0
}
{
55
−19
32
−21
0
−3
0
−1
−30
1
−27
5
8
−1
2
0
}
{
−19
13
13
0
2
−1
1
0
−14
44
14
−22
3
−4
1
−1
}
{
15
6
−31
18
−5
2
−2
1
24
−13
−6
−13
0
0
0
0
}
{
52
27
−23
−23
3
−4
0
−1
−51
4
−24
21
2
2
1
0
}
{
−9
20
−25
−24
12
−4
3
−1
−9
27
−26
30
−11
1
−2
0
}
{
−42
−41
−19
7
14
1
3
1
−25
9
33
39
−18
4
−3
1
}
{
17
−23
17
−8
8
0
1
0
35
−15
−1
13
−10
0
−2
0
}
{
−45
−2
−21
6
−4
2
0
1
−59
−35
−14
22
17
4
3
1
}
{
21
21
−18
28
−2
0
−1
0
0
12
27
−2
−22
3
−4
1
}
{
−3
18
33
−32
3
−3
0
−1
−2
9
3
1
−2
−3
0
0
}
{
−3
−25
−31
−6
23
−3
4
0
−26
5
−22
3
−5
−1
1
0
}
{
−5
−59
−3
−25
2
4
1
1
46
−3
−12
18
21
−3
2
−1
}
},
{
{
2
7
0
−3
−2
−3
−2
1
1
1
1
0
−1
−1
0
0
}
{
9
5
−20
3
−3
−6
7
4
3
1
−2
−3
−1
−1
1
1
}
{
−8
12
22
−15
4
1
−15
1
0
−2
5
3
2
−1
−2
−2
}
{
21
−52
16
24
−2
13
20
−22
2
−1
−14
3
1
1
4
2
}
{
6
−4
21
10
−4
5
−6
−14
1
−3
0
9
−1
1
2
−4
}
{
6
29
−58
7
14
−30
8
23
3
6
9
−12
2
−3
−5
3
}
{
−1
−35
−27
36
9
−25
63
−5
−10
16
−11
−29
−1
−5
−4
14
}
{
22
−3
4
11
−3
−15
17
−8
−2
11
−1
−9
−3
−1
−5
4
}
{
27
−17
−20
−27
−13
−23
−29
44
13
−16
38
4
−4
1
−3
−12
}
{
37
−22
36
−28
−14
16
22
−14
4
18
−16
−19
−3
−1
−8
9
}
{
−19
−26
2
−7
2
1
26
46
10
−3
47
−51
−11
15
−23
−8
}
{
−5
26
16
40
23
−25
20
−1
0
2
30
−11
1
9
−6
−11
}
{
36
−12
−2
−28
−10
−6
6
−3
−1
10
−6
−17
−4
−1
−13
5
}
{
−18
38
16
−8
29
17
5
−19
−3
−4
−16
−59
−9
7
−38
20
}
{
−60
−21
−10
10
−5
52
1
35
10
−15
−13
0
0
0
12
13
}
{
14
5
8
11
11
−37
0
−20
−6
6
22
17
4
2
5
−27
}
},
lowFreqTransMatrix
[
m
]
[
n
]
= lowFreqTransMatrixCol0to15
[
m
]
[
n
]
with m = 0 . . . 15, n = 0 . . . 15
lowFreqTransMatrixCol0to15 =
[
[
{
{
80
−49
6
−4
1
−1
1
−1
−72
36
4
0
1
0
0
0
}
{
−72
−6
17
0
3
0
1
0
−23
58
−21
2
−3
1
−1
0
}
{
−50
19
−15
4
−1
1
−1
1
−58
−2
30
−3
4
−1
2
0
}
{
−33
−43
28
−7
4
−2
2
−1
−38
11
−8
4
1
1
0
0
}
{
10
66
−21
−3
−3
0
−1
0
−53
−41
−2
16
−1
4
−1
1
}
{
18
14
13
−9
2
−2
1
−1
34
32
−31
12
−5
2
−2
1
}
{
21
66
−1
9
−4
2
−1
1
−21
41
−30
−10
0
−2
0
−1
}
{
1
−6
−24
17
−5
3
−2
1
24
10
39
−21
5
−4
2
−1
}
{
9
33
−24
1
4
0
1
0
6
50
26
1
−10
0
−2
0
}
{
−7
−9
−32
14
−3
3
−1
1
−23
−28
0
−5
−1
0
0
0
}
{
6
30
69
−18
5
−4
3
−1
−3
−11
−34
−16
9
−4
2
−1
}
{
1
−8
24
−3
7
−2
2
−1
−6
−51
−6
−4
−5
0
−1
0
}
{
4
10
4
17
−9
4
−2
1
5
14
32
−15
9
−3
2
−1
}
{
−3
−9
−23
10
−10
3
−3
1
−5
−14
−16
−27
13
−5
2
−1
}
{
2
11
22
2
9
−2
2
0
−6
−7
20
−32
−3
−4
0
−1
}
{
2
−3
8
14
−5
3
−1
1
−2
−11
5
−18
8
−3
2
−1
}
},
]
]
{
{
76
−49
4
−3
1
−1
0
0
−74
38
5
0
1
0
0
0
}
{
−55
−4
19
1
3
0
1
0
−6
56
−28
1
−4
0
−2
0
}
{
−60
28
−9
4
0
1
0
0
−44
10
22
−2
2
−1
1
0
}
{
−35
−14
25
−5
3
−1
2
0
−46
17
−11
7
1
1
0
0
}
{
26
69
−29
−8
−5
−2
−2
−1
−26
−34
−9
22
−1
5
−1
1
}
{
−22
12
−17
8
−2
2
−1
1
−56
−32
37
−5
5
0
2
0
}
{
24
39
−27
11
−7
1
−2
0
16
26
0
−19
2
−3
0
−1
}
{
−14
−52
−3
7
3
2
1
1
34
−24
45
−5
−1
−2
0
−1
}
{
13
31
−10
−15
5
−3
1
−1
16
50
−2
4
−10
−1
−2
0
}
{
−7
7
−36
11
2
2
0
1
−21
−1
22
2
−8
1
−1
0
}
{
−7
−29
−5
−5
9
0
2
0
−8
−34
−15
33
−12
6
−3
2
}
{
−5
9
25
−18
1
−3
1
−1
−14
−1
−38
7
9
0
1
0
}
{
15
29
80
−27
2
−7
0
−3
−4
−37
−14
−9
4
1
2
0
}
{
7
20
21
−11
3
−3
1
−1
12
44
31
11
−16
0
−4
0
}
{
2
16
29
−7
5
−3
0
−1
−12
−10
29
−41
−1
−2
1
0
}
{
7
9
41
−3
−9
1
−2
0
1
−2
56
−15
2
−3
0
−1
}
},
lowFreqTransMatrix
[
m
]
[
n
]
= lowFreqTransMatrixCol16to31
[
m − 16
]
[
n
]
with m = 16 . . . 31, n = 0 . . . 15
lowFreqTransMatrixCol16to31 =
[
[
{
{
26
0
−12
2
−2
1
−1
0
−7
−9
6
1
0
0
0
0
}
{
55
−46
−1
6
−2
1
−1
0
−22
7
17
−7
2
−1
1
0
}
{
6
57
−34
0
−2
0
−1
0
34
−48
−2
14
−4
3
−1
1
}
{
−55
24
26
−5
2
−1
1
0
15
46
−40
−1
−1
0
−1
0
}
{
36
−5
41
−20
3
−3
1
−1
−30
26
−32
−3
7
−2
2
−1
}
{
40
4
−4
−9
−3
−2
−1
−1
27
−31
−43
19
−2
3
−1
1
}
{
−35
−17
−3
26
−6
5
−2
2
56
3
18
−25
−1
−2
−1
−1
}
{
33
32
−30
4
−3
−1
−1
0
−4
13
−16
−10
0
−1
0
0
}
{
−27
1
−28
−21
16
−5
3
−2
−23
36
−2
40
−17
4
−3
1
}
{
−36
−59
−24
14
4
2
1
1
−23
−26
23
26
−3
5
0
2
}
{
−16
35
−35
30
−9
3
−2
1
−57
−13
6
4
−5
5
−1
1
}
{
38
−1
0
25
6
2
1
1
47
20
35
1
−27
1
−5
0
}
{
7
13
19
15
−8
1
−1
0
3
25
30
−18
1
−2
0
−1
}
{
−1
−13
−30
11
−5
2
−1
0
−5
−8
−22
−16
10
0
1
0
}
{
13
−5
−28
6
18
−4
3
−1
−26
27
−14
6
−20
0
−2
0
}
{
12
−23
−19
22
2
0
1
0
23
41
−7
35
−10
4
−1
1
}
},
]
]
{
{
27
2
−14
2
−2
1
−1
0
−6
−12
8
1
0
0
0
0
}
{
53
−61
5
8
−1
2
0
0
−27
17
21
−12
3
−2
1
−1
}
{
30
38
−39
1
−3
0
−1
0
28
−57
8
15
−3
3
−1
1
}
{
−17
28
23
−10
0
−2
1
−1
18
33
−57
3
0
0
−1
0
}
{
55
−19
32
−21
0
−3
0
−1
−30
1
−27
5
8
−1
2
0
}
{
−19
13
13
0
2
−1
1
0
−14
44
14
−22
3
−4
1
−1
}
{
15
6
−31
18
−5
2
−2
1
24
−13
−6
−13
0
0
0
0
}
{
52
27
−23
−23
3
−4
0
−1
−51
4
−24
21
2
2
1
0
}
{
−9
20
−25
−24
12
−4
3
−1
−9
27
−26
30
−11
1
−2
0
}
{
−42
−41
−19
7
14
1
3
1
−25
9
33
39
−18
4
−3
1
}
{
17
−23
17
−8
8
0
1
0
35
−15
−1
13
−10
0
−2
0
}
{
−45
−2
−21
6
−4
2
0
1
−59
−35
−14
22
17
4
3
1
}
{
21
21
−18
28
−2
0
−1
0
0
12
27
−2
−22
3
−4
1
}
{
−3
18
33
−32
3
−3
0
−1
−2
9
3
1
−2
−3
0
0
}
{
−3
−25
−31
−6
23
−3
4
0
−26
5
−22
3
−5
−1
1
0
}
{
−5
−59
−3
−25
2
4
1
1
46
−3
−12
18
21
−3
2
−1
},
lowFreqTransMatrix
[
m
]
[
n
]
= lowFreqTransMatrixCol32to47
[
m − 32
]
[
n
]
with m = 32 . . . 47, n = 0 . . . 15
lowFreqTransMatrixCol32to47 =
{
3
5
−1
−2
−2
−2
−1
1
1
1
0
0
−1
−1
0
0
}
{
9
5
−12
1
−3
−4
4
2
4
1
−2
−1
−1
−1
1
0
}
{
−10
7
21
−10
6
1
−11
0
−1
−1
4
2
3
0
−2
−1
}
{
17
−38
1
17
−3
11
15
−11
3
−1
−10
1
0
1
3
2
}
{
15
−8
1
17
−1
−2
4
−8
2
0
−1
3
0
0
0
−1
}
{
7
−49
52
10
−11
22
7
−26
−1
−6
−9
6
−2
2
4
−2
}
{
−15
−13
−27
9
9
−6
20
5
−3
2
−6
−9
3
−3
1
5
}
{
24
−26
−37
33
5
−32
55
−5
−7
22
−14
−22
1
−9
−3
13
}
{
43
−13
4
−41
−19
−2
−24
17
11
−4
8
4
−3
−3
−3
−3
}
{
10
−26
38
7
−12
11
42
−22
−5
20
−14
−15
−1
−2
1
6
}
{
28
10
4
7
0
−15
7
−10
−1
7
−2
2
1
−3
0
0
}
{
37
−37
−9
−47
−28
5
0
18
8
6
0
−8
−4
−3
−3
1
}
{
11
24
22
−11
−3
37
−13
−58
−5
12
−63
26
9
−15
11
8
}
{
0
−29
−27
6
−27
−10
−30
9
−3
−10
−7
77
9
−13
45
−8
}
{
−76
−26
−4
−7
12
51
5
24
7
−17
−16
−12
−5
4
2
13
}
{
5
7
23
5
69
−38
−8
−32
−15
−31
24
11
2
18
11
−15
}
},
]
]
{
{
2
7
0
−3
−2
−3
−2
1
1
1
1
0
−1
−1
0
0
}
{
9
5
−20
3
−3
−6
7
4
3
1
−2
−3
−1
−1
1
1
}
{
−8
12
22
−15
4
1
−15
1
0
−2
5
3
2
−1
−2
−2
}
{
21
−52
16
2 4
−2
13
20
−22
2
−1
−14
3
1
1
4
2
}
{
6
−4
21
10
−4
5
−6
−14
1
−3
0
9
−1
1
2
−4
}
{
6
29
−58
7
14
−30
8
23
3
6
9
−12
2
−3
−5
3
}
{
−1
−35
−27
36
9
−25
63
−5
−10
16
−11
−29
−1
−5
−4
14
}
{
22
−3
4
11
−3
−15
17
−8
−2
11
−1
−9
−3
−1
−5
4
}
{
27
−17
−20
−27
−13
−23
−29
44
13
−16
38
4
−4
1
−3
−12
}
{
37
−22
36
−28
−14
16
22
−14
4
18
−16
−19
−3
−1
−8
9
}
{
−19
−26
2
−7
2
1
26
46
10
−3
47
−51
−11
15
−23
−8
}
{
−5
26
16
40
23
−25
20
−1
0
2
30
−11
1
9
−6
−11
}
{
36
−12
−2
−28
−10
−6
6
−3
−1
10
−6
−17
−4
−1
−13
5
}
{
−18
38
16
−8
29
17
5
−19
−3
−4
−16
−59
−9
7
−38
20
}
{
−60
−21
−10
10
−5
52
1
35
10
−15
−13
0
0
0
12
13
}
{
14
5
8
11
11
−37
0
−20
−6
6
22
17
4
2
5
−27
}
},
{
{
120
−37
−5
−5
−2
−2
−1
−1
4
0
−1
0
0
0
0
0
}
{
−2
−2
1
0
0
0
0
0
118
−26
−8
−3
−3
−1
−1
0
}
{
18
−22
6
−2
2
−1
0
0
−22
−2
4
1
1
0
0
0
}
{
32
101
−46
8
−11
1
−4
0
0
28
−10
1
−2
0
−1
0
}
{
−8
−15
7
−1
2
0
1
0
−32
9
0
1
0
0
0
0
}
{
−5
−13
−1
2
0
1
0
0
19
94
−36
5
−8
0
−3
−1
}
{
−7
−2
−1
1
0
0
0
0
−5
−7
4
0
1
0
0
0
}
{
10
37
−17
4
−4
0
−2
0
−11
−45
6
0
2
1
1
0
}
{
5
4
6
−2
0
−1
0
0
6
−14
7
−2
1
0
0
0
}
{
−1
−3
−11
4
−2
1
0
0
−10
−44
9
2
2
1
1
0
}
{
−16
−44
−93
33
−10
10
−2
4
−6
−17
−47
14
−4
4
−1
2
}
{
−5
−8
−18
4
−1
1
0
1
7
19
55
−18
5
−5
1
−2
}
{
−3
−12
−31
6
−3
3
0
0
10
23
71
−20
5
−5
1
−2
}
{
−2
−11
3
0
2
0
1
0
3
10
−9
2
−1
1
0
0
}
{
−5
−10
−38
9
−3
3
−1
1
2
7
17
1
−1
0
−1
0
}
{
0
−1
−5
−1
1
0
0
0
−2
−13
5
−1
2
−1
1
0
}
},
{
{
−23
5
1
1
0
0
0
0
−6
2
0
0
0
0
0
0
}
{
25
0
4
0
1
0
0
0
28
6
2
0
0
0
0
0
}
{
117
−16
−10
−2
−4
−1
−2
0
24
2
−5
0
−1
0
0
0
}
{
15
−31
10
−3
2
−1
1
0
−15
−9
5
0
1
0
1
0
}
{
13
14
−4
0
−1
0
−1
0
−111
16
11
2
4
1
2
0
}
{
10
60
−12
−1
−2
−1
−1
−1
14
−26
10
−4
2
−1
0
0
}
{
−25
5
1
1
0
0
0
0
34
12
−7
−1
−2
−1
−1
0
}
{
13
92
−22
−1
−4
−1
−2
−1
10
50
−5
−2
−2
−2
−1
−1
}
{
−1
−1
0
0
0
0
0
0
24
−26
3
0
0
0
0
0
}
{
2
10
8
−2
1
−1
0
0
−12
−82
21
1
3
2
1
1
}
{
1
−3
23
−7
4
−2
1
−1
4
11
15
−4
2
−2
0
−1
}
{
2
12
35
−8
2
−2
0
−1
−1
1
−11
5
−2
1
−1
0
}
{
8
12
46
−9
3
−3
1
−1
−2
8
−19
4
−2
1
−1
0
}
{
−6
−45
1
3
0
2
0
1
5
55
−1
−3
−1
−2
−1
−1
}
{
−8
−12
−77
26
−8
7
−2
2
−11
−18
−79
16
−4
4
0
1
}
{
2
11
−6
1
−1
0
0
0
−3
−37
3
0
1
0
1
0
}
},
{
{
−3
1
0
0
−2
1
0
0
−2
1
0
0
−1
0
0
0
}
{
−15
2
1
0
−5
1
0
0
−1
0
0
0
−1
1
0
0
}
{
−16
4
1
0
−7
2
1
0
−2
1
0
0
−2
0
0
0
}
{
−15
−1
3
0
−2
−1
1
0
−1
−3
1
0
0
0
0
0
}
{
−38
−3
6
1
14
−3
−1
0
11
0
−1
0
3
0
0
0
}
{
−7
−24
6
0
−5
−8
2
0
0
0
0
−1
0
−2
0
0
}
{
−111
16
11
1
−38
0
7
0
2
−1
1
0
4
−1
−1
0
}
{
9
−22
6
−2
1
−8
1
0
−4
−1
1
−1
−1
0
0
0
}
{
−33
−32
7
2
100
−10
−16
0
46
8
−10
−1
4
3
−1
0
}
{
−5
−66
7
4
−42
6
1
2
−13
13
0
−1
1
4
−1
0
}
{
1
11
5
−1
14
4
−1
−1
2
2
2
−1
1
0
1
0
}
{
−16
−5
−8
3
34
7
−11
0
−81
8
14
0
−44
−1
9
0
}
{
11
−8
−11
2
−27
−16
0
2
60
−6
−10
0
33
2
−8
−1
}
{
1
−78
23
1
−10
−62
7
6
−16
2
1
1
−4
3
0
0
}
{
0
−9
−3
−3
3
5
13
−4
0
7
5
−2
0
3
0
−1
}
{
1
35
4
−5
8
−85
20
4
−11
−72
11
8
−6
−10
1
1
}
},
{
{
80
−43
3
−4
1
−1
0
−1
−75
34
2
1
1
1
0
0
}
{
73
−8
−11
−1
−3
0
−1
0
26
−35
11
−3
2
−1
1
0
}
{
37
−40
19
−6
3
−1
1
−1
73
17
−25
1
−5
0
−2
0
}
{
43
62
−41
6
−8
1
−3
0
5
−60
25
0
3
1
1
0
}
{
−10
26
−5
0
−1
0
−1
0
−55
1
−5
6
0
2
0
1
}
{
−23
−40
10
1
4
0
2
0
−9
−19
27
−8
3
−2
1
−1
}
{
−4
14
−12
7
−3
2
−1
1
−23
15
5
−5
0
−1
1
0
}
{
1
5
63
−36
10
−8
3
−3
−21
−45
−52
31
−1
5
0
2
}
{
22
61
11
−13
−1
−3
−1
−1
10
38
−42
14
−5
2
−1
1
}
{
2
14
−17
5
−2
2
−1
0
3
39
0
1
−4
1
−1
0
}
{
5
19
35
−8
5
−4
1
−1
−8
−20
1
−14
4
−1
1
−1
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}
},
The system 2320 may include a coding component 2324 that may implement the various coding or encoding methods described in the present disclosure. The coding component 2324 may reduce the average bitrate of video from the input 2322 to the output of the coding component 2324 to produce a coded representation of the video. The coding techniques are therefore sometimes called video compression or video transcoding techniques. The output of the coding component 2324 may be either stored, or transmitted via a communication connected, as represented by the component 2326. The stored or communicated bitstream (or coded) representation of the video received at the input 2322 may be used by the component 2328 for generating pixel values or displayable video that is sent to a display interface 2340. The process of generating user-viewable video from the bitstream representation is sometimes called video decompression. Furthermore, while certain video processing operations are referred to as “coding” operations or tools, it will be appreciated that the coding tools or operations are used at an encoder and corresponding decoding tools or operations that reverse the results of the coding will be performed by a decoder.
Examples of a peripheral bus interface or a display interface may include universal serial bus (USB) or high definition multimedia interface (HDMI) or Displayport, and so on. Examples of storage interfaces include serial advanced technology attachment (SATA), peripheral component interconnect (PCI), integrated drive electronics (IDE) interface, and the like. The techniques described in the present disclosure may be embodied in various electronic devices such as mobile phones, laptops, smartphones or other devices that are capable of performing digital data processing and/or video display.
Some embodiments of the disclosed technology include making a decision or determination to enable a video processing tool or mode. In an example, when the video processing tool or mode is enabled, the encoder will use or implement the tool or mode in the processing of a block of video, but may not necessarily modify the resulting bitstream based on the usage of the tool or mode. That is, a conversion from the block of video to the bitstream representation of the video will use the video processing tool or mode when it is enabled based on the decision or determination. In another example, when the video processing tool or mode is enabled, the decoder will process the bitstream with the knowledge that the bitstream has been modified based on the video processing tool or mode. That is, a conversion from the bitstream representation of the video to the block of video will be performed using the video processing tool or mode that was enabled based on the decision or determination.
Some embodiments of the disclosed technology include making a decision or determination to disable a video processing tool or mode. In an example, when the video processing tool or mode is disabled, the encoder will not use the tool or mode in the conversion of the block of video to the bitstream representation of the video. In another example, when the video processing tool or mode is disabled, the decoder will process the bitstream with the knowledge that the bitstream has not been modified using the video processing tool or mode that was disabled based on the decision or determination.
In the present disclosure, the term “video processing” may refer to video encoding, video decoding, video compression or video decompression. For example, video compression algorithms may be applied during conversion from pixel representation of a video to a corresponding bitstream representation or vice versa. The bitstream representation of a current video block may, for example, correspond to bits that are either co-located or spread in different places within the bitstream, as is defined by the syntax. For example, a macroblock may be encoded in terms of transformed and coded error residual values and also using bits in headers and other fields in the bitstream.
In some embodiments, the video coding methods may be implemented using an apparatus that is implemented on a hardware platform as described with respect to
Various techniques and embodiments may be described using the following clause-based format. The first set of clauses describe certain features and aspects of the disclosed techniques in the previous section.
The second set of clauses describe certain features and aspects of the disclosed techniques in the previous section (e.g., example items 7-9, 22, and 29-34).
From the foregoing, it will be appreciated that specific embodiments of the presently disclosed technology have been described herein for purposes of illustration, but that various modifications may be made without deviating from the scope of the invention. Accordingly, the presently disclosed technology is not limited except as by the appended claims.
Implementations of the subject matter and the functional operations described in the present disclosure can be implemented in various systems, digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Implementations of the subject matter described in this specification can be implemented as one or more computer program products, i.e., one or more modules of computer program instructions encoded on a tangible and non-transitory computer readable medium for execution by, or to control the operation of, data processing apparatus. The computer readable medium can be a machine-readable storage device, a machine-readable storage substrate, a memory device, a composition of matter effecting a machine-readable propagated signal, or a combination of one or more of them. The term “data processing unit” or “data processing apparatus” encompasses all apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.
A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.
The processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., a field programmable gate array (FPGA) or an application specific integrated circuit (ASIC).
Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read only memory or a random access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Computer readable media suitable for storing computer program instructions and data include all forms of nonvolatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and compact disc, read-only memory (CD ROM) and digital versatile disc read-only memory (DVD-ROM) disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.
It is intended that the specification, together with the drawings, be considered exemplary only, where exemplary means an example. As used herein, the use of “or” is intended to include “and/or”, unless the context clearly indicates otherwise.
While the present disclosure contains many specifics, these should not be construed as limitations on the scope of any invention or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in the present disclosure in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.
Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. Moreover, the separation of various system components in the embodiments described in the present disclosure should not be understood as requiring such separation in all embodiments.
Only a few implementations and examples are described and other implementations, enhancements and variations can be made based on what is described and illustrated in the present disclosure.
| Number | Date | Country | Kind |
|---|---|---|---|
| PCT/CN2019/101230 | Aug 2019 | WO | international |
| PCT/CN2019/107904 | Sep 2019 | WO | international |
| PCT/CN2019/127829 | Dec 2019 | WO | international |
This application is a continuation of U.S. patent application Ser. No. 17/585,788 filed on Jan. 27, 2022, which is a continuation of International Patent Application No. PCT/CN2020/109476 filed on Aug. 17, 2020, which claims the priority to and benefits of International Patent Application Nos. PCT/CN2019/101230 filed on Aug. 17, 2019, PCT/CN2019/107904 filed on Sep. 25, 2019, and PCT/CN2019/127829 filed on Dec. 24, 2019. All the aforementioned patent applications are hereby incorporated by reference in their entireties.
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| Number | Date | Country | |
|---|---|---|---|
| 20230145133 A1 | May 2023 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 17585788 | Jan 2022 | US |
| Child | 18089672 | US | |
| Parent | PCT/CN2020/109476 | Aug 2020 | US |
| Child | 17585788 | US |
