Patent ID: 12200250

DETAILED DESCRIPTION OF EMBODIMENTS

The present disclosure includes embodiments directed to unified secondary transform. The embodiments include methods, apparatuses, and non-transitory computer-readable storage mediums for improving secondary transform process. In addition, a block may refer to a prediction block, a coding block, or a coding unit.

I. Video Encoder and Decoder

FIG.2illustrates a simplified block diagram of a communication system (200) according to an embodiment of the present disclosure. The communication system (200) includes a plurality of terminal devices that can communicate with each other, via, for example, a network (250). For example, the communication system (200) includes a first pair of terminal devices (210) and (220) interconnected via the network (250). In theFIG.2example, the first pair of terminal devices (210) and (220) performs unidirectional transmission of data. For example, the terminal device (210) may code video data (e.g., a stream of video pictures that are captured by the terminal device (210)) for transmission to the other terminal device (220) via the network (250). The encoded video data can be transmitted in the form of one or more coded video bitstreams. The terminal device (220) may receive the coded video data from the network (250), decode the coded video data to recover the video pictures and display video pictures according to the recovered video data. Unidirectional data transmission may be common in media serving applications and the like.

In another example, the communication system (200) includes a second pair of terminal devices (230) and (240) that performs bidirectional transmission of coded video data that may occur, for example, during videoconferencing. For bidirectional transmission of data, in an example, each terminal device of the terminal devices (230) and (240) may code video data (e.g., a stream of video pictures that are captured by the terminal device) for transmission to the other terminal device of the terminal devices (230) and (240) via the network (250). Each terminal device of the terminal devices (230) and (240) also may receive the coded video data transmitted by the other terminal device of the terminal devices (230) and (240), and may decode the coded video data to recover the video pictures and may display video pictures at an accessible display device according to the recovered video data.

In theFIG.2example, the terminal devices (210), (220), (230) and (240) may be illustrated as servers, personal computers and smart phones but the principles of the present disclosure may be not so limited. Embodiments of the present disclosure find application with laptop computers, tablet computers, media players and/or dedicated video conferencing equipment. The network (250) represents any number of networks that convey coded video data among the terminal devices (210), (220), (230) and (240), including for example wireline (wired) and/or wireless communication networks. The communication network (250) may exchange data in circuit-switched and/or packet-switched channels. Representative networks include telecommunications networks, local area networks, wide area networks and/or the Internet. For the purposes of the present discussion, the architecture and topology of the network (250) may be immaterial to the operation of the present disclosure unless explained herein below.

FIG.3illustrates, as an example for an application for the disclosed subject matter, the placement of a video encoder and a video decoder in a streaming environment. The disclosed subject matter can be equally applicable to other video enabled applications, including, for example, video conferencing, digital TV, storing of compressed video on digital media including CD, DVD, memory stick, and the like.

A streaming system may include a capture subsystem (313) that can include a video source (301), for example a digital camera, creating for example a stream of video pictures (302) that are uncompressed. In an example, the stream of video pictures (302) includes samples that are taken by the digital camera. The stream of video pictures (302), depicted as a bold line to emphasize a high data volume when compared to encoded video data (304) (or coded video bitstreams), can be processed by an electronic device (320) that includes a video encoder (303) coupled to the video source (301). The video encoder (303) can include hardware, software, or a combination thereof to enable or implement aspects of the disclosed subject matter as described in more detail below. The encoded video data (304) (or encoded video bitstream (304)), depicted as a thin line to emphasize the lower data volume when compared to the stream of video pictures (302), can be stored on a streaming server (305) for future use. One or more streaming client subsystems, such as client subsystems (306) and (308) inFIG.3can access the streaming server (305) to retrieve copies (307) and (309) of the encoded video data (304). A client subsystem (306) can include a video decoder (310), for example, in an electronic device (330). The video decoder (310) decodes the incoming copy (307) of the encoded video data and creates an outgoing stream of video pictures (311) that can be rendered on a display (312) (e.g., display screen) or other rendering device (not depicted). In some streaming systems, the encoded video data (304), (307), and (309) (e.g., video bitstreams) can be encoded according to certain video coding/compression standards. Examples of those standards include ITU-T Recommendation H.265. In an example, a video coding standard under development is informally known as Versatile Video Coding (VVC). The disclosed subject matter may be used in the context of VVC.

It is noted that the electronic devices (320) and (330) can include other components (not shown). For example, the electronic device (320) can include a video decoder (not shown) and the electronic device (330) can include a video encoder (not shown) as well.

FIG.4shows a block diagram of a video decoder (410) according to an embodiment of the present disclosure. The video decoder (410) can be included in an electronic device (430). The electronic device (430) can include a receiver (431) (e.g., receiving circuitry). The video decoder (410) can be used in the place of the video decoder (310) in theFIG.3example.

The receiver (431) may receive one or more coded video sequences to be decoded by the video decoder (410); in the same or another embodiment, one coded video sequence at a time, where the decoding of each coded video sequence is independent from other coded video sequences. The coded video sequence may be received from a channel (401), which may be a hardware/software link to a storage device which stores the encoded video data. The receiver (431) may receive the encoded video data with other data, for example, coded audio data and/or ancillary data streams, that may be forwarded to their respective using entities (not depicted). The receiver (431) may separate the coded video sequence from the other data. To combat network jitter, a buffer memory (415) may be coupled in between the receiver (431) and an entropy decoder/parser (420) (“parser (420)” henceforth). In certain applications, the buffer memory (415) is part of the video decoder (410). In others, it can be outside of the video decoder (410) (not depicted). In still others, there can be a buffer memory (not depicted) outside of the video decoder (410), for example to combat network jitter, and in addition another buffer memory (415) inside the video decoder (410), for example to handle playout timing. When the receiver (431) is receiving data from a store/forward device of sufficient bandwidth and controllability, or from an isosynchronous network, the buffer memory (415) may not be needed, or can be small. For use on best effort packet networks such as the Internet, the buffer memory (415) may be required, can be comparatively large and can be advantageously of adaptive size, and may at least partially be implemented in an operating system or similar elements (not depicted) outside of the video decoder (410).

The video decoder (410) may include the parser (420) to reconstruct symbols (421) from the coded video sequence. Categories of those symbols include information used to manage operation of the video decoder (410), and potentially information to control a rendering device such as a render device (412) (e.g., a display screen) that is not an integral part of the electronic device (430) but can be coupled to the electronic device (430), as was shown inFIG.4. The control information for the rendering device(s) may be in the form of Supplemental Enhancement Information (SEI messages) or Video Usability Information (VUI) parameter set fragments (not depicted). The parser (420) may parse/entropy-decode the coded video sequence that is received. The coding of the coded video sequence can be in accordance with a video coding technology or standard, and can follow various principles, including variable length coding, Huffman coding, arithmetic coding with or without context sensitivity, and so forth. The parser (420) may extract from the coded video sequence, a set of subgroup parameters for at least one of the subgroups of pixels in the video decoder, based upon at least one parameter corresponding to the group. Subgroups can include Groups of Pictures (GOPs), pictures, tiles, slices, macroblocks, Coding Units (CUs), blocks, Transform Units (TUs), Prediction Units (PUs) and so forth. The parser (420) may also extract from the coded video sequence information such as transform coefficients, quantizer parameter values, motion vectors, and so forth.

The parser (420) may perform an entropy decoding/parsing operation on the video sequence received from the buffer memory (415), so as to create symbols (421).

Reconstruction of the symbols (421) can involve multiple different units depending on the type of the coded video picture or parts thereof (such as: inter and intra picture, inter and intra block), and other factors. Which units are involved, and how, can be controlled by the subgroup control information that was parsed from the coded video sequence by the parser (420). The flow of such subgroup control information between the parser (420) and the multiple units below is not depicted for clarity.

Beyond the functional blocks already mentioned, the video decoder (410) can be conceptually subdivided into a number of functional units as described below. In a practical implementation operating under commercial constraints, many of these units interact closely with each other and can, at least partly, be integrated into each other. However, for the purpose of describing the disclosed subject matter, the conceptual subdivision into the functional units below is appropriate.

A first unit is the scaler/inverse transform unit (451). The scaler/inverse transform unit (451) receives a quantized transform coefficient as well as control information, including which transform to use, block size, quantization factor, quantization scaling matrices, etc. as symbol(s) (421) from the parser (420). The scaler/inverse transform unit (451) can output blocks comprising sample values that can be input into aggregator (455).

In some cases, the output samples of the scaler/inverse transform (451) can pertain to an intra coded block; that is: a block that is not using predictive information from previously reconstructed pictures, but can use predictive information from previously reconstructed parts of the current picture. Such predictive information can be provided by an intra picture prediction unit (452). In some cases, the intra picture prediction unit (452) generates a block of the same size and shape of the block under reconstruction, using surrounding already reconstructed information fetched from the current picture buffer (458). The current picture buffer (458) buffers, for example, partly reconstructed current picture and/or fully reconstructed current picture. The aggregator (455), in some cases, adds, on a per sample basis, the prediction information that the intra prediction unit (452) has generated to the output sample information as provided by the scaler/inverse transform unit (451).

In other cases, the output samples of the scaler/inverse transform unit (451) can pertain to an inter coded, and potentially motion compensated block. In such a case, a motion compensation prediction unit (453) can access reference picture memory (457) to fetch samples used for prediction. After motion compensating the fetched samples in accordance with the symbols (421) pertaining to the block, these samples can be added by the aggregator (455) to the output of the scaler/inverse transform unit (451) (in this case called the residual samples or residual signal) so as to generate output sample information. The addresses within the reference picture memory (457) from where the motion compensation prediction unit (453) fetches prediction samples can be controlled by motion vectors, available to the motion compensation prediction unit (453) in the form of symbols (421) that can have, for example X, Y, and reference picture components. Motion compensation also can include interpolation of sample values as fetched from the reference picture memory (457) when sub-sample exact motion vectors are in use, motion vector prediction mechanisms, and so forth.

The output samples of the aggregator (455) can be subject to various loop filtering techniques in the loop filter unit (456). Video compression technologies can include in-loop filter technologies that are controlled by parameters included in the coded video sequence (also referred to as coded video bitstream) and made available to the loop filter unit (456) as symbols (421) from the parser (420), but can also be responsive to meta-information obtained during the decoding of previous (in decoding order) parts of the coded picture or coded video sequence, as well as responsive to previously reconstructed and loop-filtered sample values.

The output of the loop filter unit (456) can be a sample stream that can be output to the render device (412) as well as stored in the reference picture memory (457) for use in future inter-picture prediction.

Certain coded pictures, once fully reconstructed, can be used as reference pictures for future prediction. For example, once a coded picture corresponding to a current picture is fully reconstructed and the coded picture has been identified as a reference picture (by, for example, the parser (420)), the current picture buffer (458) can become a part of the reference picture memory (457), and a fresh current picture buffer can be reallocated before commencing the reconstruction of the following coded picture.

The video decoder (410) may perform decoding operations according to a predetermined video compression technology in a standard, such as ITU-T Rec. H.265. The coded video sequence may conform to a syntax specified by the video compression technology or standard being used, in the sense that the coded video sequence adheres to both the syntax of the video compression technology or standard and the profiles as documented in the video compression technology or standard. Specifically, a profile can select certain tools as the only tools available for use under that profile from all the tools available in the video compression technology or standard. Also necessary for compliance can be that the complexity of the coded video sequence is within bounds as defined by the level of the video compression technology or standard. In some cases, levels restrict the maximum picture size, maximum frame rate, maximum reconstruction sample rate (measured in, for example megasamples per second), maximum reference picture size, and so on. Limits set by levels can, in some cases, be further restricted through Hypothetical Reference Decoder (HRD) specifications and metadata for HRD buffer management signaled in the coded video sequence.

In an embodiment, the receiver (431) may receive additional (redundant) data with the encoded video. The additional data may be included as part of the coded video sequence(s). The additional data may be used by the video decoder (410) to properly decode the data and/or to more accurately reconstruct the original video data. Additional data can be in the form of, for example, temporal, spatial, or signal noise ratio (SNR) enhancement layers, redundant slices, redundant pictures, forward error correction codes, and so on.

FIG.5shows a block diagram of a video encoder (503) according to an embodiment of the present disclosure. The video encoder (503) is included in an electronic device (520). The electronic device (520) includes a transmitter (540) (e.g., transmitting circuitry). The video encoder (503) can be used in the place of the video encoder (303) in theFIG.3example.

The video encoder (503) may receive video samples from a video source (501) (that is not part of the electronic device (520) in theFIG.5example) that may capture video image(s) to be coded by the video encoder (503). In another example, the video source (501) is a part of the electronic device (520).

The video source (501) may provide the source video sequence to be coded by the video encoder (503) in the form of a digital video sample stream that can be of any suitable bit depth (for example: 8 bit, 10 bit, 12 bit, . . . ), any colorspace (for example, BT.601 Y CrCB, RGB, . . . ), and any suitable sampling structure (for example Y CrCb 4:2:0, Y CrCb 4:4:4). In a media serving system, the video source (501) may be a storage device storing previously prepared video. In a videoconferencing system, the video source (501) may be a camera that captures local image information as a video sequence. Video data may be provided as a plurality of individual pictures that impart motion when viewed in sequence. The pictures themselves may be organized as a spatial array of pixels, wherein each pixel can comprise one or more samples depending on the sampling structure, color space, etc. in use. A person skilled in the art can readily understand the relationship between pixels and samples. The description below focuses on samples.

According to an embodiment, the video encoder (503) may code and compress the pictures of the source video sequence into a coded video sequence (543) in real time or under any other time constraints as required by the application. Enforcing appropriate coding speed is one function of a controller (550). In some embodiments, the controller (550) controls other functional units as described below and is functionally coupled to the other functional units. The coupling is not depicted for clarity. Parameters set by the controller (550) can include rate control related parameters (picture skip, quantizer, lambda value of rate-distortion optimization techniques, . . . ), picture size, group of pictures (GOP) layout, maximum motion vector allowed reference area, and so forth. The controller (550) can be configured to have other suitable functions that pertain to the video encoder (503) optimized for a certain system design.

In some embodiments, the video encoder (503) is configured to operate in a coding loop. As an oversimplified description, in an example, the coding loop can include a source coder (530) (e.g., responsible for creating symbols, such as a symbol stream, based on an input picture to be coded, and a reference picture(s)), and a (local) decoder (533) embedded in the video encoder (503). The decoder (533) reconstructs the symbols to create the sample data in a similar manner as a (remote) decoder also would create (as any compression between symbols and coded video bitstream is lossless in the video compression technologies considered in the disclosed subject matter). The reconstructed sample stream (sample data) is input to the reference picture memory (534). As the decoding of a symbol stream leads to bit-exact results independent of decoder location (local or remote), the content in the reference picture memory (534) is also bit exact between the local encoder and remote encoder. In other words, the prediction part of an encoder “sees” as reference picture samples exactly the same sample values as a decoder would “see” when using prediction during decoding. This fundamental principle of reference picture synchronicity (and resulting drift, if synchronicity cannot be maintained, for example because of channel errors) is used in some related arts as well.

The operation of the “local” decoder (533) can be the same as of a “remote” decoder, such as the video decoder (410), which has already been described in detail above in conjunction withFIG.4. Briefly referring also toFIG.4, however, as symbols are available and encoding/decoding of symbols to a coded video sequence by an entropy coder (545) and the parser (420) can be lossless, the entropy decoding parts of the video decoder (410), including the buffer memory (415) and the parser (420) may not be fully implemented in the local decoder (533).

An observation that can be made at this point is that any decoder technology except the parsing/entropy decoding that is present in a decoder also necessarily needs to be present, in substantially identical functional form, in a corresponding encoder. For this reason, the disclosed subject matter focuses on decoder operation. The description of encoder technologies can be abbreviated as they are the inverse of the comprehensively described decoder technologies. Only in certain areas a more detail description is required and provided below.

During operation, in some examples, the source coder (530) may perform motion compensated predictive coding, which codes an input picture predictively with reference to one or more previously coded picture from the video sequence that were designated as “reference pictures.” In this manner, the coding engine (532) codes differences between pixel blocks of an input picture and pixel blocks of reference picture(s) that may be selected as prediction reference(s) to the input picture.

The local video decoder (533) may decode coded video data of pictures that may be designated as reference pictures, based on symbols created by the source coder (530). Operations of the coding engine (532) may advantageously be lossy processes. When the coded video data may be decoded at a video decoder (not shown inFIG.5), the reconstructed video sequence typically may be a replica of the source video sequence with some errors. The local video decoder (533) replicates decoding processes that may be performed by the video decoder on reference pictures and may cause reconstructed reference pictures to be stored in the reference picture cache (534). In this manner, the video encoder (503) may store copies of reconstructed reference pictures locally that have common content as the reconstructed reference pictures that will be obtained by a far-end video decoder (absent transmission errors).

The predictor (535) may perform prediction searches for the coding engine (532). That is, for a new picture to be coded, the predictor (535) may search the reference picture memory (534) for sample data (as candidate reference pixel blocks) or certain metadata such as reference picture motion vectors, block shapes, and so on, that may serve as an appropriate prediction reference for the new pictures. The predictor (535) may operate on a sample block-by-pixel block basis to find appropriate prediction references. In some cases, as determined by search results obtained by the predictor (535), an input picture may have prediction references drawn from multiple reference pictures stored in the reference picture memory (534).

The controller (550) may manage coding operations of the source coder (530), including, for example, setting of parameters and subgroup parameters used for encoding the video data.

Output of all aforementioned functional units may be subjected to entropy coding in the entropy coder (545). The entropy coder (545) translates the symbols as generated by the various functional units into a coded video sequence, by lossless compressing the symbols according to technologies such as Huffman coding, variable length coding, arithmetic coding, and so forth.

The transmitter (540) may buffer the coded video sequence(s) as created by the entropy coder (545) to prepare for transmission via a communication channel (560), which may be a hardware/software link to a storage device which would store the encoded video data. The transmitter (540) may merge coded video data from the video coder (503) with other data to be transmitted, for example, coded audio data and/or ancillary data streams (sources not shown).

The controller (550) may manage operation of the video encoder (503). During coding, the controller (550) may assign to each coded picture a certain coded picture type, which may affect the coding techniques that may be applied to the respective picture. For example, pictures often may be assigned as one of the following picture types:

An Intra Picture (I picture) may be one that may be coded and decoded without using any other picture in the sequence as a source of prediction. Some video codecs allow for different types of intra pictures, including, for example Independent Decoder Refresh (“IDR”) Pictures. A person skilled in the art is aware of those variants of I pictures and their respective applications and features.

A predictive picture (P picture) may be one that may be coded and decoded using intra prediction or inter prediction using at most one motion vector and reference index to predict the sample values of each block.

A bi-directionally predictive picture (B Picture) may be one that may be coded and decoded using intra prediction or inter prediction using at most two motion vectors and reference indices to predict the sample values of each block. Similarly, multiple-predictive pictures can use more than two reference pictures and associated metadata for the reconstruction of a single block.

Source pictures commonly may be subdivided spatially into a plurality of sample blocks (for example, blocks of 4×4, 8×8, 4×8, or 16×16 samples each) and coded on a block-by-block basis. Blocks may be coded predictively with reference to other (already coded) blocks as determined by the coding assignment applied to the blocks' respective pictures. For example, blocks of I pictures may be coded non-predictively or they may be coded predictively with reference to already coded blocks of the same picture (spatial prediction or intra prediction). Pixel blocks of P pictures may be coded predictively, via spatial prediction or via temporal prediction with reference to one previously coded reference picture. Blocks of B pictures may be coded predictively, via spatial prediction or via temporal prediction with reference to one or two previously coded reference pictures.

The video encoder (503) may perform coding operations according to a predetermined video coding technology or standard, such as ITU-T Rec. H.265. In its operation, the video encoder (503) may perform various compression operations, including predictive coding operations that exploit temporal and spatial redundancies in the input video sequence. The coded video data, therefore, may conform to a syntax specified by the video coding technology or standard being used.

In an embodiment, the transmitter (540) may transmit additional data with the encoded video. The source coder (530) may include such data as part of the coded video sequence. Additional data may comprise temporal/spatial/SNR enhancement layers, other forms of redundant data such as redundant pictures and slices, SEI messages, VUI parameter set fragments, and so on.

A video may be captured as a plurality of source pictures (video pictures) in a temporal sequence. Intra-picture prediction (often abbreviated to intra prediction) makes use of spatial correlation in a given picture, and inter-picture prediction makes uses of the (temporal or other) correlation between the pictures. In an example, a specific picture under encoding/decoding, which is referred to as a current picture, is partitioned into blocks. When a block in the current picture is similar to a reference block in a previously coded and still buffered reference picture in the video, the block in the current picture can be coded by a vector that is referred to as a motion vector. The motion vector points to the reference block in the reference picture, and can have a third dimension identifying the reference picture, in case multiple reference pictures are in use.

In some embodiments, a bi-prediction technique can be used in the inter-picture prediction. According to the bi-prediction technique, two reference pictures, such as a first reference picture and a second reference picture that are both prior in decoding order to the current picture in the video (but may be in the past and future, respectively, in display order) are used. A block in the current picture can be coded by a first motion vector that points to a first reference block in the first reference picture, and a second motion vector that points to a second reference block in the second reference picture. The block can be predicted by a combination of the first reference block and the second reference block.

Further, a merge mode technique can be used in the inter-picture prediction to improve coding efficiency.

According to some embodiments of the disclosure, predictions, such as inter-picture predictions and intra-picture predictions are performed in the unit of blocks. For example, according to the HEVC standard, a picture in a sequence of video pictures is partitioned into coding tree units (CTU) for compression, the CTUs in a picture have the same size, such as 64×64 pixels, 32×32 pixels, or 16×16 pixels. In general, a CTU includes three coding tree blocks (CTBs), which are one luma CTB and two chroma CTBs. Each CTU can be recursively quad-tree split into one or multiple CUs. For example, a CTU of 64×64 pixels can be split into one CU of 64×64 pixels, or 4 CUs of 32×32 pixels, or 16 CUs of 16×16 pixels. In an example, each CU is analyzed to determine a prediction type for the CU, such as an inter prediction type or an intra prediction type. The CU is split into one or more prediction units (PUs) depending on the temporal and/or spatial predictability. Generally, each PU includes a luma prediction block (PB), and two chroma PBs. In an embodiment, a prediction operation in coding (encoding/decoding) is performed in the unit of a prediction block. Using a luma prediction block as an example of a prediction block, the prediction block includes a matrix of values (e.g., luma values) for pixels, such as 8×8 pixels, 16×16 pixels, 8×16 pixels, 16×8 pixels, and the like.

FIG.6shows a diagram of a video encoder (603) according to another embodiment of the disclosure. The video encoder (603) is configured to receive a processing block (e.g., a prediction block) of sample values within a current video picture in a sequence of video pictures, and encode the processing block into a coded picture that is part of a coded video sequence. In an example, the video encoder (603) is used in the place of the video encoder (303) in theFIG.3example.

In an HEVC example, the video encoder (603) receives a matrix of sample values for a processing block, such as a prediction block of 8×8 samples, and the like. The video encoder (603) determines whether the processing block is best coded using intra mode, inter mode, or bi-prediction mode using, for example, rate-distortion optimization. When the processing block is to be coded in intra mode, the video encoder (603) may use an intra prediction technique to encode the processing block into the coded picture; and when the processing block is to be coded in inter mode or bi-prediction mode, the video encoder (603) may use an inter prediction or bi-prediction technique, respectively, to encode the processing block into the coded picture. In certain video coding technologies, merge mode can be an inter picture prediction submode where the motion vector is derived from one or more motion vector predictors without the benefit of a coded motion vector component outside the predictors. In certain other video coding technologies, a motion vector component applicable to the subject block may be present. In an example, the video encoder (603) includes other components, such as a mode decision module (not shown) to determine the mode of the processing blocks.

In theFIG.6example, the video encoder (603) includes the inter encoder (630), an intra encoder (622), a residue calculator (623), a switch (626), a residue encoder (624), a general controller (621), and an entropy encoder (625) coupled together as shown inFIG.6.

The inter encoder (630) is configured to receive the samples of the current block (e.g., a processing block), compare the block to one or more reference blocks in reference pictures (e.g., blocks in previous pictures and later pictures), generate inter prediction information (e.g., description of redundant information according to inter encoding technique, motion vectors, merge mode information), and calculate inter prediction results (e.g., predicted block) based on the inter prediction information using any suitable technique. In some examples, the reference pictures are decoded reference pictures that are decoded based on the encoded video information.

The intra encoder (622) is configured to receive the samples of the current block (e.g., a processing block), in some cases compare the block to blocks already coded in the same picture, generate quantized coefficients after transform, and in some cases also intra prediction information (e.g., an intra prediction direction information according to one or more intra encoding techniques). In an example, the intra encoder (622) also calculates intra prediction results (e.g., predicted block) based on the intra prediction information and reference blocks in the same picture.

The general controller (621) is configured to determine general control data and control other components of the video encoder (603) based on the general control data. In an example, the general controller (621) determines the mode of the block, and provides a control signal to the switch (626) based on the mode. For example, when the mode is the intra mode, the general controller (621) controls the switch (626) to select the intra mode result for use by the residue calculator (623), and controls the entropy encoder (625) to select the intra prediction information and include the intra prediction information in the bitstream; and when the mode is the inter mode, the general controller (621) controls the switch (626) to select the inter prediction result for use by the residue calculator (623), and controls the entropy encoder (625) to select the inter prediction information and include the inter prediction information in the bitstream.

The residue calculator (623) is configured to calculate a difference (residue data) between the received block and prediction results selected from the intra encoder (622) or the inter encoder (630). The residue encoder (624) is configured to operate based on the residue data to encode the residue data to generate the transform coefficients. In an example, the residue encoder (624) is configured to convert the residue data from a spatial domain to a frequency domain, and generate the transform coefficients. The transform coefficients are then subject to quantization processing to obtain quantized transform coefficients. In various embodiments, the video encoder (603) also includes a residue decoder (628). The residue decoder (628) is configured to perform inverse-transform, and generate the decoded residue data. The decoded residue data can be suitably used by the intra encoder (622) and the inter encoder (630). For example, the inter encoder (630) can generate decoded blocks based on the decoded residue data and inter prediction information, and the intra encoder (622) can generate decoded blocks based on the decoded residue data and the intra prediction information. The decoded blocks are suitably processed to generate decoded pictures and the decoded pictures can be buffered in a memory circuit (not shown) and used as reference pictures in some examples.

The entropy encoder (625) is configured to format the bitstream to include the encoded block. The entropy encoder (625) is configured to include various information according to a suitable standard, such as the HEVC standard. In an example, the entropy encoder (625) is configured to include the general control data, the selected prediction information (e.g., intra prediction information or inter prediction information), the residue information, and other suitable information in the bitstream. Note that, according to the disclosed subject matter, when coding a block in the merge submode of either inter mode or bi-prediction mode, there is no residue information.

FIG.7shows a diagram of a video decoder (710) according to another embodiment of the disclosure. The video decoder (710) is configured to receive coded pictures that are part of a coded video sequence, and decode the coded pictures to generate reconstructed pictures. In an example, the video decoder (710) is used in the place of the video decoder (310) in theFIG.3example.

In theFIG.7example, the video decoder (710) includes an entropy decoder (771), an inter decoder (780), a residue decoder (773), a reconstruction module (774), and an intra decoder (772) coupled together as shown inFIG.7.

The entropy decoder (771) can be configured to reconstruct, from the coded picture, certain symbols that represent the syntax elements of which the coded picture is made up. Such symbols can include, for example, the mode in which a block is coded (such as, for example, intra mode, inter mode, bi-predicted mode, the latter two in merge submode or another submode), prediction information (such as, for example, intra prediction information or inter prediction information) that can identify certain sample or metadata that is used for prediction by the intra decoder (772) or the inter decoder (780), respectively, residual information in the form of, for example, quantized transform coefficients, and the like. In an example, when the prediction mode is inter or bi-predicted mode, the inter prediction information is provided to the inter decoder (780); and when the prediction type is the intra prediction type, the intra prediction information is provided to the intra decoder (772). The residual information can be subject to inverse quantization and is provided to the residue decoder (773).

The inter decoder (780) is configured to receive the inter prediction information, and generate inter prediction results based on the inter prediction information.

The intra decoder (772) is configured to receive the intra prediction information, and generate prediction results based on the intra prediction information.

The residue decoder (773) is configured to perform inverse quantization to extract de-quantized transform coefficients, and process the de-quantized transform coefficients to convert the residual from the frequency domain to the spatial domain. The residue decoder (773) may also require certain control information (to include the Quantizer Parameter (QP)), and that information may be provided by the entropy decoder (771) (data path not depicted as this may be low volume control information only).

The reconstruction module (774) is configured to combine, in the spatial domain, the residual as output by the residue decoder (773) and the prediction results (as output by the inter or intra prediction modules as the case may be) to form a reconstructed block, that may be part of the reconstructed picture, which in turn may be part of the reconstructed video. It is noted that other suitable operations, such as a deblocking operation and the like, can be performed to improve the visual quality.

It is noted that the video encoders (303), (503), and (603), and the video decoders (310), (410), and (710) can be implemented using any suitable technique. In an embodiment, the video encoders (303), (503), and (603), and the video decoders (310), (410), and (710) can be implemented using one or more integrated circuits. In another embodiment, the video encoders (303), (503), and (603), and the video decoders (310), (410), and (710) can be implemented using one or more processors that execute software instructions.

II. HEVC Primary Transform

Primary transforms can include 4-point, 8-point, 16-point, and 32-point DCT-2, such as in HEVC, and the transform core matrices can be represented using 8-bit integers, i.e., 8-bit transform core. The transform core matrices of smaller DCT-2 can be part of matrices of larger DCT-2 and include a 4×4 transform, an 8×8 transform, a 16×16 transform, and a 32×32 transform, as shown inFIGS.8A-8D, respectively.

The DCT-2 cores show symmetry/anti-symmetry characteristics, thus a so-called “partial butterfly” implementation is supported to reduce the number of operation counts (multiplications, adds/subs, shifts), and identical results of matrix multiplication can be obtained using partial butterfly.

III. VVC Primary Transform

Besides 4-point, 8-point, 16-point, and 32-point DCT-2 transforms, such as in HEVC, additional 2-point and 64-point DCT-2 can be also included, such as in VVC.

The 64-point DCT-2 core defined in VVC is shown below as a 64×64 matrix,{{aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa}{bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, by, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, ck, −ck, −cj, −ci, −ch, −cg, −cf, −ce, −cd, −cc, −cb, −ca, −bz, −by, −bx, −bw, −by, −bu, −bt, −bs, −br, −bq, −bp, −bo, −bn, −bm, −bl, −bk, −bj, −bi, −bh, −bg, −bf}{ap, aq, ar, as, at, au, av, aw, ax, ay, az, ba, bb, bC, bd, be, −be, −bd, −bC, −bb, −ba, −az, −ay, −ax, −aw, −av, −au, −at, −as, −ar, −aq, −ap, −ap, −aq, −ar, −as, −at, −au, −av, −aw, −ax, −ay, −az, −ba, −bb, −bC, −bd, −be, be, bd, bC, bb, ba, az, ay, ax, aw, av, au, at, as, ar, aq, ap}{bg, bj, bm, bp, bs, by, by, cb, ce, ch, ck, −ci, −cf, −cc, −bz, −bw, −bt, −bq, −bn, −bk, −bh, −bf, −bi, −bl, −bo, −br, −bu, −bx, −ca, −cd, −cg, −cj, cj, cg, cd, ca, bx, bu, br, bo, bl, bi, bf, bh, bk, bn, bq, bt, bw, bz, cc, cf, ci, −ck, −ch, −ce, −cb, −by, −by, −bs, −bp, −bm, −bj, −bg}{ah, ai, aj, ak, al, am, an, ao, −ao, −an, −am, −al, −ak, −aj, −ai, −ah, −ah, −ai, −aj, −ak, −al, −am, −an, −ao, ao, an, am, al, ak, aj, ai, ah, ah, ai, aj, ak, al, am, an, ao, −ao, −an, −am, −al, −ak, −aj, −ai, −ah, −ah, −ai, −aj, −ak, −al, −am, −an, −ao, ao, an, am, al, ak, aj, ai, ah}{bh, bm, br, bw, cb, cg, −ck, −cf, −ca, −by, −bq, −bl, −bg, −bi, −bn, −bs, −bx, −cc, −ch, cj, ce, bz, bu, bp, bk, bf, bj, bo, bt, by, cd, ci, −ci, −cd, −by, −bt, −bo, −bj, −bf, −bk, −bp, −bu, −bz, −ce, −cj, ch, cc, bx, bs, bn, bi, bg, bl, bq, by, ca, cf, ck, −cg, −cb, −bw, −br, −bm, −bh}{aq, at, aw, az, bC, −be, −bb, −ay, −av, −as, −ap, −ar, −au, −ax, −ba, −bd, bd, ba, ax, au, ar, ap, as, av, ay, bb, be, −bC, −az, −aw, −at, −aq, −aq, −at, −aw, −az, −bC, be, bb, ay, av, as, ap, ar, au, ax, ba, bd, −bd, −ba, −ax, −au, −ar, −ap, −as, −av, −ay, −bb, −be, bC, az, aw, at, aq}{bi, bp, bw, cd, ck, −ce, −bx, −bq, −bj, −bh, −bo, −by, −cc, −cj, cf, by, br, bk, bg, bn, bu, cb, ci, −cg, −bz, −bs, −bl, −bf, −bm, −bt, −ca, −ch, ch, ca, bt, bm, bf, bl, bs, bz, cg, −ci, −cb, −bu, −bn, −bg, −bk, −br, −by, −cf, cj, cc, by, bo, bh, bj, bq, bx, ce, −ck, −cd, −bw, −bp, −bi}{ad, ae, af, ag, −ag, −af, −ae, −ad, −ad, −ae, −af, −ag, ag, af, ae, ad, ad, ae, af, ag, −ag, −af, −ae, −ad, −ad, −ae, −af, −ag, ag, af, ae, ad, ad, ae, af, ag, −ag, −af, −ae, −ad, −ad, −ae, −af, −ag, ag, af, ae, ad, ad, ae, af, ag, −ag, −af, −ae, −ad, −ad, −ae, −af, −ag, ag, af, ae, ad}{bj, bs, cb, ck, −cc, −bt, −bk, −bi, −br, −ca, −cj, cd, bu, bl, bh, bq, bz, ci, −ce, −by, −bm, −bg, −bp, −by, −ch, cf, bw, bn, bf, bo, bx, cg, −cg, −bx, −bo, −bf, −bn, −bw, −cf, ch, by, bp, bg, bm, by, ce, −ci, −bz, −bq, −bh, −bl, −bu, −cd, cj, ca, br, bi, bk, bt, cc, −ck, −cb, −bs, −bj}{ar, aw, bb, −bd, −ay, −at, −ap, −au, −az, −be, ba, av, aq, as, ax, bC, −bC, −ax, −as, −aq, −av, −ba, be, az, au, ap, at, ay, bd, −bb, −aw, −ar, −ar, −aw, −bb, bd, ay, at, ap, au, az, be, −ba, −av, −aq, −as, −ax, −bC, bC, ax, as, aq, av, ba, −be, −az, −au, −ap, −at, −ay, −bd, bb, aw, ar}{bk, by, cg, −ce, −bt, −bi, −bm, −bx, −ci, cc, br, bg, bo, bz, ck, −ca, −bp, −bf, −bq, −cb, cj, by, bn, bh, bs, cd, −ch, −bw, −bl, −bj, −bu, −cf, cf, bu, bj, bl, bw, ch, −cd, −bs, −bh, −bn, −by, −cj, cb, bq, bf, bp, ca, −ck, −bz, −bo, −bg, −br, −cc, ci, bx, bm, bi, bt, ce, −cg, −by, −bk}{ai, al, ao, −am, −aj, −ah, −ak, −an, an, ak, ah, aj, am, −ao, −al, −ai, −ai, −al, −ao, am, aj, ah, ak, an, −an, −ak, −ah, −aj, −am, ao, al, ai, ai, al, ao, −am, −aj, −ah, −ak, −an, an, ak, ah, aj, am, −ao, −al, −ai, −ai, −al, −ao, am, aj, ah, ak, an, −an, −ak, −ah, −aj, −am, ao, al, ai}{bl, by, −ck, −bx, −bk, −bm, −bz, cj, bw, bj, bn, ca, −ci, −by, −bi, −bo, −cb, ch, bu, bh, bp, cc, −cg, −bt, −bg, −bq, −cd, cf, bs, bf, br, ce, −ce, −br, −bf, −bs, −cf, cd, bq, bg, bt, cg, −cc, −bp, −bh, −bu, −ch, cb, bo, bi, by, ci, −ca, −bn, −bj, −bw, −cj, bz, bm, bk, bx, ck, −by, −bl}{as, az, −bd, −aw, −ap, −av, −bC, ba, at, ar, ay, −be, −ax, −aq, −au, −bb, bb, au, aq, ax, be, −ay, −ar, −at, −ba, bC, av, ap, aw, bd, −az, −as, −as, −az, bd, aw, ap, av, bC, −ba, −at, −ar, −ay, be, ax, aq, au, bb, −bb, −au, −aq, −ax, −be, ay, ar, at, ba, −bC, −av, −ap, −aw, −bd, az, as}{bm, cb, −cf, −bq, −bi, −bx, cj, bu, bf, bt, ci, −by, −bj, −bp, −ce, cc, bn, bl, ca, −cg, −br, −bh, −bw, ck, by, bg, bs, ch, −bz, −bk, −bo, −cd, cd, bo, bk, bz, −ch, −bs, −bg, −by, −ck, bw, bh, br, cg, −ca, −bl, −bn, −cc, ce, bp, bj, by, −ci, −bt, −bf, −bu, −cj, bx, bi, bq, cf, −cb, −bm}{ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab}{bn, ce, −ca, −bj, −br, −ci, bw, bf, by, −cj, −bs, −bi, −bz, cf, bo, bm, cd, −cb, −bk, −bq, −ch, bx, bg, bu, −ck, −bt, −bh, −by, cg, bp, bl, cc, −cc, −bl, −bp, −cg, by, bh, bt, ck, −bu, −bg, −bx, ch, bq, bk, cb, −cd, −bm, −bo, −cf, bz, bi, bs, cj, −by, −bf, −bw, ci, br, bj, ca, −ce, −bn}{at, bC, −ay, −ap, −ax, bd, au, as, bb, −az, −aq, −aw, be, av, ar, ba, −ba, −ar, −av, −be, aw, aq, az, −bb, −as, −au, −bd, ax, ap, ay, −bC, −at, −at, −bC, ay, ap, ax, −bd, −au, −as, −bb, az, aq, aw, −be, −av, −ar, −ba, ba, ar, av, be, −aw, −aq, −az, bb, as, au, bd, −ax, −ap, −ay, bC, at}{bo, ch, −by, −bh, −ca, cc, bj, bt, −cj, −bq, −bm, −cf, bx, bf, by, −ce, −bl, −br, −ck, bs, bk, cd, −bz, −bg, −bw, cg, bn, bp, ci, −bu, −bi, −cb, cb, bi, bu, −ci, −bp, −bn, −cg, bw, bg, bz, −cd, −bk, −bs, ck, br, bl, ce, −by, −bf, −bx, cf, bm, bq, cj, −bt, −bj, −cc, ca, bh, by, −ch, −bo}{aj, ao, −ak, −ai, −an, al, ah, am, −am, −ah, −al, an, ai, ak, −ao, −aj, −aj, −ao, ak, ai, an, −al, −ah, −am, am, ah, al, −an, −ai, −ak, ao, aj, aj, ao, −ak, −ai, −an, al, ah, am, −am, −ah, −al, an, ai, ak, −ao, −aj, −aj, −ao, ak, ai, an, −al, −ah, −am, am, ah, al, −an, −ai, −ak, ao, aj}{bp, ck, −bq, −bo, −cj, br, bn, ci, −bs, −bm, −ch, bt, bl, cg, −bu, −bk, −cf, by, bj, ce, −bw, −bi, −cd, bx, bh, cc, −by, −bg, −cb, bz, bf, ca, −ca, −bf, −bz, cb, bg, by, −cc, −bh, −bx, cd, bi, bw, −ce, −bj, −by, cf, bk, bu, −cg, −bl, −bt, ch, bm, bs, −ci, −bn, −br, cj, bo, bq, −ck, −bp}{au, −be, −at, −av, bd, as, aw, −bC, −ar, −ax, bb, aq, ay, −ba, −ap, −az, az, ap, ba, −ay, −aq, −bb, ax, ar, bC, −aw, −as, −bd, av, at, be, −au, −au, be, at, av, −bd, −as, −aw, bC, ar, ax, −bb, −aq, −ay, ba, ap, az, −az, −ap, −ba, ay, aq, bb, −ax, −ar, −bC, aw, as, bd, −av, −at, −be, au}{bq, −ci, −bl, −by, cd, bg, ca, −by, −bi, −cf, bt, bn, ck, −bo, −bs, cg, bj, bx, −cb, −bf, −cc, bw, bk, ch, −br, −bp, cj, bm, bu, −ce, −bh, −bz, bz, bh, ce, −bu, −bm, −cj, bp, br, −ch, −bk, −bw, cc, bf, cb, −bx, −bj, −cg, bs, bo, −ck, −bn, −bt, cf, bi, by, −ca, −bg, −cd, by, bl, ci, −bq}{ae, −ag, −ad, −af, af, ad, ag, −ae, −ae, ag, ad, af, −af, −ad, −ag, ae, ae, −ag, −ad, −af, af, ad, ag, −ae, −ae, ag, ad, af, −af, −ad, −ag, ae, ae, −ag, −ad, −af, af, ad, ag, −ae, −ae, ag, ad, af, −af, −ad, −ag, ae, ae, −ag, −ad, −af, af, ad, ag, −ae, −ae, ag, ad, af, −af, −ad, −ag, ae}{br, −cf, −bg, −cc, bu, bo, −ci, −bj, −bz, bx, bl, ck, −bm, −bw, ca, bi, ch, −bp, −bt, cd, bf, ce, −bs, −bq, cg, bh, cb, −by, −bn, cj, bk, by, −by, −bk, −cj, bn, by, −cb, −bh, −cg, bq, bs, −ce, −bf, −cd, bt, bp, −ch, −bi, −ca, bw, bm, −ck, −bl, −bx, bz, bj, ci, −bo, −bu, cc, bg, cf, −br}{av, −bb, −ap, −bC, au, aw, −ba, −aq, −bd, at, ax, −az, −ar, −be, as, ay, −ay, −as, be, ar, az, −ax, −at, bd, aq, ba, −aw, −au, bC, ap, bb, −av, −av, bb, ap, bC, −au, −aw, ba, aq, bd, −at, −ax, az, ar, be, −as, −ay, ay, as, −be, −ar, −az, ax, at, −bd, −aq, −ba, aw, au, −bC, −ap, −bb, av}{bs, −cc, −bi, −cj, bl, bz, −by, −bp, cf, bf, cg, −bo, −bw, by, bm, −ci, −bh, −cd, br, bt, −cb, −bj, −ck, bk, ca, −bu, −bq, ce, bg, ch, −bn, −bx, bx, bn, −ch, −bg, −ce, bq, bu, −ca, −bk, ck, bj, cb, −bt, −br, cd, bh, ci, −bm, −by, bw, bo, −cg, −bf, −cf, bp, by, −bz, −bl, cj, bi, cc, −bs}{ak, −am, −ai, ao, ah, an, −aj, −al, al, aj, −an, −ah, −ao, ai, am, −ak, −ak, am, ai, −ao, −ah, −an, aj, al, −al, −aj, an, ah, ao, −ai, −am, ak, ak, −am, −ai, ao, ah, an, −aj, −al, al, aj, −an, −ah, −ao, ai, am, −ak, −ak, am, ai, −ao, −ah, −an, aj, al, −al, −aj, an, ah, ao, −ai, −am, ak}{bt, −bz, −bn, cf, bh, ck, −bi, −ce, bo, by, −bu, −bs, ca, bm, −cg, −bg, −cj, bj, cd, −bp, −bx, by, br, −cb, −bl, ch, bf, ci, −bk, −cc, bq, bw, −bw, −bq, cc, bk, −ci, −bf, −ch, bl, cb, −br, −by, bx, bp, −cd, −bj, cj, bg, cg, −bm, −ca, bs, bu, −by, −bo, ce, bi, −ck, −bh, −cf, bn, bz, −bt}{aw, −ay, −au, ba, as, −bc, −aq, be, ap, bd, −ar, −bb, at, az, −av, −ax, ax, av, −az, −at, bb, ar, −bd, −ap, −be, aq, bc, −as, −ba, au, ay, −aw, −aw, ay, au, −ba, −as, bc, aq, −be, −ap, −bd, ar, bb, −at, −az, av, ax, −ax, −av, az, at, −bb, −ar, bd, ap, be, −aq, −bc, as, ba, −au, −ay, aw}{bu, −bw, −bs, by, bq, −ca, −bo, cc, bm, −ce, −bk, cg, bi, −ci, −bg, ck, bf, cj, −bh, −ch, bj, cf, −bl, −cd, bn, cb, −bp, −bz, br, bx, −bt, −by, by, bt, −bx, −br, bz, bp, −cb, −bn, cd, bl, −cf, −bj, ch, bh, −cj, −bf, −ck, bg, ci, −bi, −cg, bk, ce, −bm, −cc, bo, ca, −bq, −by, bs, bw, −bu}{aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa}{by, −bt, −bx, br, bz, −bp, −cb, bn, cd, −bl, −cf, bj, ch, −bh, −cj, bf, −ck, −bg, ci, bi, −cg, −bk, ce, bm, −cc, −bo, ca, bq, −by, −bs, bw, bu, −bu, −bw, bs, by, −bq, −ca, bo, cc, −bm, −ce, bk, cg, −bi, −ci, bg, ck, −bf, cj, bh, −ch, −bj, cf, bl, −cd, −bn, cb, bp, −bz, −br, bx, bt, −by}{ax, −av, −az, at, bb, −ar, −bd, ap, −be, −aq, bC, as, −ba, −au, ay, aw, −aw, −ay, au, ba, −as, −bC, aq, be, −ap, bd, ar, −bb, −at, az, av, −ax, −ax, av, az, −at, −bb, ar, bd, −ap, be, aq, −bC, −as, ba, au, −ay, −aw, aw, ay, −au, −ba, as, bC, −aq, −be, ap, −bd, −ar, bb, at, −az, −av, ax}{bw, −bq, −cc, bk, ci, −bf, ch, bl, −cb, −br, by, bx, −bp, −cd, bj, cj, −bg, cg, bm, −ca, −bs, bu, by, −bo, −ce, bi, ck, −bh, cf, bn, −bz, −bt, bt, bz, −bn, −cf, bh, −ck, −bi, ce, bo, −by, −bu, bs, ca, −bm, −cg, bg, −cj, −bj, cd, bp, −bx, −by, br, cb, −bl, −ch, bf, −ci, −bk, cc, bq, −bw}{al, −aj, −an, ah, −ao, −ai, am, ak, −ak, −am, ai, ao, −ah, an, aj, −al, −al, aj, an, −ah, ao, ai, −am, −ak, ak, am, −ai, −ao, ah, −an, −aj, al, al, −aj, −an, ah, −ao, −ai, am, ak, −ak, −am, ai, ao, −ah, an, aj, −al, −al, aj, an, −ah, ao, ai, −am, −ak, ak, am, −ai, −ao, ah, −an, −aj, al}{bx, −bn, −ch, bg, −ce, −bq, bu, ca, −bk, −ck, bj, −cb, −bt, br, cd, −bh, ci, bm, −by, −bw, bo, cg, −bf, cf, bp, −by, −bz, bl, cj, −bi, cc, bs, −bs, −cc, bi, −cj, −bl, bz, by, −bp, −cf, bf, −cg, −bo, bw, by, −bm, −ci, bh, −cd, −br, bt, cb, −bj, ck, bk, −ca, −bu, bq, ce, −bg, ch, bn, −bx}{ay, −as, −be, ar, −az, −ax, at, bd, −aq, ba, aw, −au, −bC, ap, −bb, −av, av, bb, −ap, bC, au, −aw, −ba, aq, −bd, −at, ax, az, −ar, be, as, −ay, −ay, as, be, −ar, az, ax, −at, −bd, aq, −ba, −aw, au, bC, −ap, bb, av, −av, −bb, ap, −bC, −au, aw, ba, −aq, bd, at, −ax, −az, ar, −be, −as, ay}{by, −bk, cj, bn, −by, −cb, bh, −cg, −bq, bs, ce, −bf, cd, bt, −bp, −ch, bi, −ca, −bw, bm, ck, −bl, bx, bz, −bj, ci, bo, −bu, −cc, bg, −cf, −br, br, cf, −bg, cc, bu, −bo, −ci, bj, −bz, −bx, bl, −ck, −bm, bw, ca, −bi, ch, bp, −bt, −cd, bf, −ce, −bs, bq, cg, −bh, cb, by, −bn, −cj, bk, −by}{af, −ad, ag, ae, −ae, −ag, ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af, af, −ad, ag, ae, −ae, −ag, ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af, af, −ad, ag, ae, −ae, −ag, ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af, af, −ad, ag, ae, −ae, −ag, ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af}{bz, −bh, ce, bu, −bm, cj, bp, −br, −ch, bk, −bw, −cc, bf, −cb, −bx, bj, −cg, −bs, bo, ck, −bn, bt, cf, −bi, by, ca, −bg, cd, by, −bl, ci, bq, −bq, −ci, bl, −by, −cd, bg, −ca, −by, bi, −cf, −bt, bn, −ck, −bo, bs, cg, −bj, bx, cb, −bf, cc, bw, −bk, ch, br, −bp, −cj, bm, −bu, −ce, bh, −bz}{az, −ap, ba, ay, −aq, bb, ax, −ar, bC, aw, −as, bd, av, −at, be, au, −au, −be, at, −av, −bd, as, −aw, −bC, ar, −ax, −bb, aq, −ay, −ba, ap, −az, −az, ap, −ba, −ay, aq, −bb, −ax, ar, −bC, −aw, as, −bd, −av, at, −be, −au, au, be, −at, av, bd, −as, aw, bC, −ar, ax, bb, −aq, ay, ba, −ap, az}{ca, −bf, bz, cb, −bg, by, cc, −bh, bx, cd, −bi, bw, ce, −bj, by, cf, −bk, bu, cg, −bl, bt, ch, −bm, bs, ci, −bn, br, cj, −bo, bq, ck, −bp, bp, −ck, −bq, bo, −cj, −br, bn, −ci, −bs, bm, −ch, −bt, bl, −cg, −bu, bk, −cf, −by, bj, −ce, −bw, bi, −cd, −bx, bh, −cc, −by, bg, −cb, −bz, bf, −ca}{am, −ah, al, an, −ai, ak, ao, −aj, aj, −ao, −ak, ai, −an, −al, ah, −am, −am, ah, −al, −an, ai, −ak, −ao, aj, −aj, ao, ak, −ai, an, al, −ah, am, am, −ah, al, an, −ai, ak, ao, −aj, aj, −ao, −ak, ai, −an, −al, ah, −am, −am, ah, −al, −an, ai, −ak, −ao, aj, −aj, ao, ak, −ai, an, al, −ah, am}{cb, −bi, bu, ci, −bp, bn, −cg, −bw, bg, −bz, −cd, bk, −bs, −ck, br, −bl, ce, by, −bf, bx, cf, −bm, bq, −cj, −bt, bj, −cc, −ca, bh, −by, −ch, bo, −bo, ch, by, −bh, ca, cc, −bj, bt, cj, −bq, bm, −cf, −bx, bf, −by, −ce, bl, −br, ck, bs, −bk, cd, bz, −bg, bw, cg, −bn, bp, −ci, −bu, bi, −cb}{ba, −ar, av, −be, −aw, aq, −az, −bb, as, −au, bd, ax, −ap, ay, bC, −at, at, −bC, −ay, ap, −ax, −bd, au, −as, bb, az, −aq, aw, be, −av, ar, −ba, −ba, ar, −av, be, aw, −aq, az, bb, −as, au, −bd, −ax, ap, −ay, −bC, at, −at, bC, ay, −ap, ax, bd, −au, as, −bb, −az, aq, −aw, −be, av, −ar, ba}{cc, −bl, bp, −cg, −by, bh, −bt, ck, bu, −bg, bx, ch, −bq, bk, −cb, −cd, bm, −bo, cf, bz, −bi, bs, −cj, −by, bf, −bw, −ci, br, −bj, ca, ce, −bn, bn, −ce, −ca, bj, −br, ci, bw, −bf, by, cj, −bs, bi, −bz, −cf, bo, −bm, cd, cb, −bk, bq, −ch, −bx, bg, −bu, −ck, bt, −bh, by, cg, −bp, bl, −cc}{ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac}{cd, −bo, bk, −bz, −ch, bs, −bg, by, −ck, −bw, bh, −br, cg, ca, −bl, bn, −cc, −ce, bp, −bj, by, ci, −bt, bf, −bu, cj, bx, −bi, bq, −cf, −cb, bm, −bm, cb, cf, −bq, bi, −bx, −cj, bu, −bf, bt, −ci, −by, bj, −bp, ce, cc, −bn, bl, −ca, −cg, br, −bh, bw, ck, −by, bg, −bs, ch, bz, −bk, bo, −cd}{bb, −au, aq, −ax, be, ay, −ar, at, −ba, −bC, av, −ap, aw, −bd, −az, as, −as, az, bd, −aw, ap, −av, bC, ba, −at, ar, −ay, −be, ax, −aq, au, −bb, −bb, au, −aq, ax, −be, −ay, ar, −at, ba, bC, −av, ap, −aw, bd, az, −as, as, −az, −bd, aw, −ap, av, −bC, −ba, at, −ar, ay, be, −ax, aq, −au, bb}{ce, −br, bf, −bs, cf, cd, −bq, bg, −bt, cg, cc, −bp, bh, −bu, ch, cb, −bo, bi, −by, ci, ca, −bn, bj, −bw, cj, bz, −bm, bk, −bx, ck, by, −bl, bl, −by, −ck, bx, −bk, bm, −bz, −cj, bw, −bj, bn, −ca, −ci, by, −bi, bo, −cb, −ch, bu, −bh, bp, −cc, −cg, bt, −bg, bq, −cd, −cf, bs, −bf, br, −ce}{an, −ak, ah, −aj, am, ao, −al, ai, −ai, al, −ao, −am, aj, −ah, ak, −an, −an, ak, −ah, aj, −am, −ao, al, −ai, ai, −al, ao, am, −aj, ah, −ak, an, an, −ak, ah, −aj, am, ao, −al, ai, −ai, al, −ao, −am, aj, −ah, ak, −an, −an, ak, −ah, aj, −am, −ao, al, −ai, ai, −al, ao, am, −aj, ah, −ak, an}{cf, −bu, bj, −bl, bw, −ch, −cd, bs, −bh, bn, −by, cj, cb, −bq, bf, −bp, ca, ck, −bz, bo, −bg, br, −cc, −ci, bx, −bm, bi, −bt, ce, cg, −by, bk, −bk, by, −cg, −ce, bt, −bi, bm, −bx, ci, cc, −br, bg, −bo, bz, −ck, −ca, bp, −bf, bq, −cb, −cj, by, −bn, bh, −bs, cd, ch, −bw, bl, −bj, bu, −cf}{bC, −ax, as, −aq, av, −ba, −be, az, −au, ap, −at, ay, −bd, −bb, aw, −ar, ar, −aw, bb, bd, −ay, at, −ap, au, −az, be, ba, −av, aq, −as, ax, −bC, −bC, ax, −as, aq, −av, ba, be, −az, au, −ap, at, −ay, bd, bb, −aw, ar, −ar, aw, −bb, −bd, ay, −at, ap, −au, az, −be, −ba, av, −aq, as, −ax, bC}{cg, −bx, bo, −bf, bn, −bw, cf, ch, −by, bp, −bg, bm, −by, ce, ci, −bz, bq, −bh, bl, −bu, cd, cj, −ca, br, −bi, bk, −bt, cc, ck, −cb, bs, −bj, bj, −bs, cb, −ck, −cc, bt, −bk, bi, −br, ca, −cj, −cd, bu, −bl, bh, −bq, bz, −ci, −ce, by, −bm, bg, −bp, by, −ch, −cf, bw, −bn, bf, −bo, bx, −cg}{ag, −af, ae, −ad, ad, −ae, af, −ag, −ag, af, −ae, ad, −ad, ae, −af, ag, ag, −af, ae, −ad, ad, −ae, af, −ag, −ag, af, −ae, ad, −ad, ae, −af, ag, ag, −af, ae, −ad, ad, −ae, af, −ag, −ag, af, −ae, ad, −ad, ae, −af, ag, ag, −af, ae, −ad, ad, −ae, af, −ag, −ag, af, −ae, ad, −ad, ae, −af, ag}{ch, −ca, bt, −bm, bf, −bl, bs, −bz, cg, ci, −cb, bu, −bn, bg, −bk, br, −by, cf, cj, −cc, by, −bo, bh, −bj, bq, −bx, ce, ck, −cd, bw, −bp, bi, −bi, bp, −bw, cd, −ck, −ce, bx, −bq, bj, −bh, bo, −by, cc, −cj, −cf, by, −br, bk, −bg, bn, −bu, cb, −ci, −cg, bz, −bs, bl, −bf, bm, −bt, ca, −ch}{bd, −ba, ax, −au, ar, −ap, as, −av, ay, −bb, be, bC, −az, aw, −at, aq, −aq, at, −aw, az, −bC, −be, bb, −ay, av, −as, ap, −ar, au, −ax, ba, −bd, −bd, ba, −ax, au, −ar, ap, −as, av, −ay, bb, −be, −bC, az, −aw, at, −aq, aq, −at, aw, −az, bC, be, −bb, ay, −av, as, −ap, ar, −au, ax, −ba, bd}{ci, −cd, by, −bt, bo, −bj, bf, −bk, bp, −bu, bz, −ce, cj, ch, −cc, bx, −bs, bn, −bi, bg, −bl, bq, −by, ca, −cf, ck, cg, −cb, bw, −br, bm, −bh, bh, −bm, br, −bw, cb, −cg, −ck, cf, −ca, by, −bq, bl, −bg, bi, −bn, bs, −bx, cc, −ch, −cj, ce, −bz, bu, −bp, bk, −bf, bj, −bo, bt, −by, cd, −ci}{ao, −an, am, −al, ak, −aj, ai, −ah, ah, −ai, aj, −ak, al, −am, an, −ao, −ao, an, −am, al, −ak, aj, −ai, ah, −ah, ai, −aj, ak, −al, am, −an, ao, ao, −an, am, −al, ak, −aj, ai, −ah, ah, −ai, aj, −ak, al, −am, an, −ao, −ao, an, −am, al, −ak, aj, −ai, ah, −ah, ai, −aj, ak, −al, am, −an, ao}{cj, −cg, cd, −ca, bx, −bu, br, −bo, bl, −bi, bf, −bh, bk, −bn, bq, −bt, bw, −bz, cc, −cf, ci, ck, −ch, ce, −cb, by, −by, bs, −bp, bm, −bj, bg, −bg, bj, −bm, bp, −bs, by, −by, cb, −ce, ch, −ck, −ci, cf, −cc, bz, −bw, bt, −bq, bn, −bk, bh, −bf, bi, −bl, bo, −br, bu, −bx, ca, −cd, cg, −cj}{be, −bd, bC, −bb, ba, −az, ay, −ax, aw, −av, au, −at, as, −ar, aq, −ap, ap, −aq, ar, −as, at, −au, av, −aw, ax, −ay, az, −ba, bb, −bC, bd, −be, −be, bd, −bC, bb, −ba, az, −ay, ax, −aw, av, −au, at, −as, ar, −aq, ap, −ap, aq, −ar, as, −at, au, −av, aw, −ax, ay, −az, ba, −bb, bC, −bd, be}{ck, −cj, ci, −ch, cg, −cf, ce, −cd, cc, −cb, ca, −bz, by, −bx, bw, −by, bu, −bt, bs, −br, bq, −bp, bo, −bn, bm, −bl, bk, −bj, bi, −bh, bg, −bf, bf, −bg, bh, −bi, bj, −bk, bl, −bm, bn, −bo, bp, −bq, br, −bs, bt, −bu, by, −bw, bx, −by, bz, −ca, cb, −cc, cd, −ce, cf, −cg, ch, −ci, cj, −ck}}where{aa, ab, ac, ad, ae, af, ag, ah, ai, aj, ak, al, am, an, ao, ap, aq, ar, as, at, au, av, aw, ax, ay, az, ba, bb, bC, bd, be, bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, by, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, ck}={64, 83, 36, 89, 75, 50, 18, 90, 87, 80, 70, 57, 43, 25, 9, 90, 90, 88, 85, 82, 78, 73, 67, 61, 54, 46, 38, 31, 22, 13, 4, 91, 90, 90, 90, 88, 87, 86, 84, 83, 81, 79, 77, 73, 71, 69, 65, 62, 59, 56, 52, 48, 44, 41, 37, 33, 28, 24, 20, 15, 11, 7, 2}

In addition to DCT-2 and 4×4 DST-7 which have been employed in HEVC, an adaptive multiple transform (AMT) scheme has been used in VVC for residual coding of both inter and intra coded blocks. The AMT is also referred to as enhanced multiple transform (EMT) or multiple transform selection (MTS), and uses multiple selected transforms from the DCT/DST families other than the current transforms in HEVC. The newly introduced transform matrices are DST-7 and DCT-8. Table 1 shows exemplary basis functions of the selected DST/DCT.

TABLE 1Transform TypeBasis function Ti(j), i, j = 0, 1, . . . , N − 1DCT-2Ti(j)=ω0·2N·cos⁡(π·i·(2⁢j+1)2⁢N)where⁢⁢ω0={2Ni=01i≠0DCT-8Ti(j)=42⁢N+1·cos⁡(π·(2⁢i+1)·(2⁢j+1)4⁢N+2)DST-7Ti(j)=42⁢N+1·sin⁡(π·(2⁢i+1)·(j+1)2⁢N+1)

The primary transform matrices in VVC are used with 8-bit representation. The AMT applies to the CUs with both width and height smaller than or equal to 32, and whether AMT applies or not is controlled by a flag called mts_flag. When the mts_flag is equal to 0, only DCT-2 is applied for coding the residue. When the mts_flag is equal to 1, an index mts_idx is further signalled using 2 bins to identify the horizontal and vertical transform to be used according to Table 2, where value 1 means using DST-7 and value 2 means using DCT-8.

TABLE 2mts_idx[ xTbY ][ yTbY ][ cIdx ]trTypeHortrTypeVer−100011121212322

An implicit MTS can also be applied (e.g., in VVC) in case the signaling based MTS (i.e., explicit MTS) is not used. With the implicit MTS, the transform selection is made according to a block width and a block height of a coding block instead of signaling. For example, with the implicit MTS, DST-7 is selected for a shorter side of the coding block and DCT-2 is selected for a longer side of the coding block.

The transform core, which is a matrix composed by the basis vectors, of DST-7 can be also represented below:

4-Point DST-7:

{a, b, c, d}{c, c, 0, −c}{d, −a, −c, b}{b, −d, c, −a}
where {a, b, c, d}={29, 55, 74, 84}
8-point DST-7:{a, b, c, d, e, f, g, h,}{c, f, h, e, b, −a, −d, −g,}{e, g, b, −c, −h, −d, a, f,}{g, c, −d, −f, a, h, b, −e,}{h, −a, −g, b, f, −c, −e, d,}{f, −e, −a, g, −d, −b, h, −c,}{d, −h, e, −a, −c, g, −f, b,}{b, −d, f, −h, g, −e, c, −a,}
where {a, b, c, d, e, f, g, h}={17, 32, 46, 60, 71, 78, 85, 86}
16-Point DST-7:{a, b, c, d, e, f, g, h, i, j, k, 1, m, n, o, p,}{c, f, i, 1, o, o, 1, i, f, c, 0, −c, −f, −i, −1, −o,}{e, j, o, m, h, c, −b, −g, −1, −p, −k, −f, −a, d, i, n,}{g, n, 1, e, −b, −i, −p, −j, −c, d, k, o, h, a, −f, −m,}{i, o, f, −c, −1, −1, −c, f, o, i, 0, −i, −o, −f, c, 1,}{k, k, 0, −k, −k, 0, k, k, 0, −k, −k, 0, k, k, 0, −k,}{m, g, −f, −n, −a, 1, h, −e, −o, −b, k, i, −d, −p, −c, j,}{o, c, −1, −f, i, i, −f, −1, c, o, 0, −o, −c, 1, f, −i,}{p, −a, −o, b, n, −c, −m, d, 1, −e, −k, f, j, −g, −i, h,}{n, −e, −i, j, d, −o, a, m, −f, −h, k, c, −p, b, 1, −g,}{1, −i, −c, o, −f, −f, o, −c, −i, 1, 0, −1, i, c, −o, f,}{j, −m, c, g, −p, f, d, −n, i, a, −k, 1, −b, −h, o, −e,}{h, −p, i, −a, −g, o, −j, b, f, −n, k, −c, −e, m, −1, d,}{f, −1, o, −i, c, c, −i, o, −1, f, 0, −f, 1, −o, i, −c,}{d, −h, 1, −p, m, −i, e, −a, −c, g, −k, o, −n, j, −f, b,}{b, −d, f, −h, j, −1, n, −p, o, −m, k, −i, g, −e, c, −a,}
where {a, b, c, d, e, f, g, h, i, j, k, 1, m, n, o, p}={9, 17, 25, 33, 41, 49, 56, 62, 66, 72, 77, 81, 83, 87, 89, 90}
32-Point DST-7:{a, b, c, d, e, f, g, h, i, j, k, 1, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, F,}{c, f, i, 1, o, r, u, x, A, D, F, C, z, w, t, q, n, k, h, e, b, −a, −d, −g, −j, −m, −p, −s, −v, −y, −B, −E,}{e, j, o, t, y, D, D, y, t, o, j, e, 0, −e, −j, −o, −t, −y, −D, −D, −y, −t, −o, −j, −e, 0, e, j, o, t, y, D,}{g, n, u, B, D, w, p, i, b, −e, −1, −s, −z, −F, −y, −r, −k, −d, c, j, q, x, E, A, t, m, f, −a, −h, −o, −v, −C,}{i, r, A, C, t, k, b, −g, −p, −y, −E, −v, −m, −d, e, n, w, F, x, o, f, −c, −1, −u, −D, −z, −q, −h, a, j, s, B,}{k, v, F, u, j, −a, −1, −w, −E, −t, −i, b, m, x, D, s, h, −c, −n, −y, −C, −r, −g, d, o, z, B, q, f, −e, −p, −A,}{m, z, z, m, 0, −m, −z, −z, −m, 0, m, z, z, m, 0, −m, −z, −z, −m, 0, m, z, z, m, 0, −m, −z, −z, −m, 0, m, z,}{o, D, t, e, −j, −y, −y, −j, e, t, D, o, 0, −o, −D, −t, −e, j, y, y, j, −e, −t, −D, −o, 0, o, D, t, e, −j, −y,}{q, E, n, −c, −t, −B, −k, f, w, y, h, −i, −z, −v, −e, 1, C, s, b, −o, −F, −p, a, r, D, m, −d, −u, −A, −j, g, x,}{s, A, h, −k, −D, −p, c, v, x, e, −n, −F, −m, f, y, u, b, −q, −C, −j, i, B, r, −a, −t, −z, −g, 1, E, o, −d, −w,}{u, w, b, −s, −y, −d, q, A, f, −o, −C, −h, m, E, j, −k, −F, −1, i, D, n, −g, −B, −p, e, z, r, −c, −x, −t, a, v,}{w, s, −d, −A, −o, h, E, k, −1, −D, −g, p, z, c, −t, −v, a, x, r, −e, −B, −n, i, F, j, −m, −C, −f, q, y, b, −u,}{y, o, −j, −D, −e, t, t, −e, −D, −j, o, y, 0, −y, −o, j, D, e, −t, −t, e, D, j, −o, −y, 0, y, o, −j, −D, −e, t,}{A, k, −p, −v, e, F, f, −u, −q, j, B, a, −z, −1, o, w, −d, −E, −g, t, r, −i, −C, −b, y, m, −n, −x, c, D, h, −s,}{C, g, −v, −n, o, u, −h, −B, a, D, f, −w, −m, p, t, −i, −A, b, E, e, −x, −1, q, s, −j, −z, c, F, d, −y, −k, r,}{E, c, −B, −f, y, i, −v, −1, s, o, −p, −r, m, u, −j, −x, g, A, −d, −D, a, F, b, −C, −e, z, h, −w, −k, t, n, −q,}{F, −a, −E, b, D, −c, −C, d, B, −e, −A, f, z, −g, −y, h, x, −i, −w, j, v, −k, −u, 1, t, −m, −s, n, r, −o, −q, p,}{D, −e, −y, j, t, −o, −o, t, j, −y, −e, D, 0, −D, e, y, −j, −t, o, o, −t, −j, y, e, −D, 0, D, −e, −y, j, t, −o,}{B, −i, −s, r, j, −A, −a, C, −h, −t, q, k, −z, −b, D, −g, −u, p, 1, −y, −c, E, −f, −v, o, m, −x, −d, F, −e, −w, n,}{z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m,}{x, −q, −g, E, −j, −n, A, −c, −u, t, d, −B, in, k, −D, f, r, −w, −a, y, −p, −h, F, −i, −o, z, −b, −v, s, e, −C, 1,}{v, −u, −a, w, −t, −b, x, −s, −c, y, −r, −d, z, −q, −e, A, −p, −f, B, −o, −g, C, −n, −h, D, −m, −i, E, −1, −j, F, −k,}{t, −y, e, o, −D, j, j, −D, o, e, −y, t, 0, −t, y, −e, −o, D, −j, −j, D, −o, −e, y, −t, 0, t, −y, e, o, −D, j,}{r, −C, k, g, −y, v, −d, −n, F, −o, −c, u, −z, h, j, −B, s, −a, −q, D, −1, −f, x, −w, e, m, −E, p, b, −t, A, −i,}{p, −F, q, −a, −o, E, −r, b, n, −D, s, −c, −m, C, −t, d, 1, −B, u, −e, −k, A, −v, f, j, −z, w, −g, −i, y, −x, h,}{n, −B, w, −i, −e, s, −F, r, −d, −j, x, −A, m, a, −o, C, −v, h, f, −t, E, −q, c, k, −y, z, −1, −b, p, −D, u, −g,}{1, −x, C, −q, e, g, −s, E, −v, j, b, −n, z, −A, o, −c, −i, u, −F, t, −h, −d, p, −B, y, −m, a, k, −w, D, −r, f,}{j, −t, D, −y, o, −e, −e, o, −y, D, −t, j, 0, −j, t, −D, y, −o, e, e, −o, y, −D, t, −j, 0, j, −t, D, −y, o, −e,}{h, −p, x, −F, y, −q, i, −a, −g, o, −w, E, −z, r, −j, b, f, −n, v, −D, A, −s, k, −c, −e, m, −u, C, −B, t, −1, d,}{f, −1, r, −x, D, −C, w, −q, k, −e, −a, g, −m, s, −y, E, −B, v, −p, j, −d, −b, h, −n, t, −z, F, −A, u, −o, i, −c,}{d, −h, 1, −p, t, −x, B, −F, C, −y, u, −q, m, −i, e, −a, −c, g, −k, o, −s, w, −A, E, −D, z, −v, r, −n, j, −f, b,}{b, −d, f, −h, j, −1, n, −p, r, −t, v, −x, z, −B, D, −F, E, −C, A, −y, w, −u, s, −q, o, −m, k, −i, g, −e, c, −a,}
where {a, b, c, d, e, f, g, h, i, k, 1, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, F}={4, 9, 13, 17, 21, 26, 30, 34, 38, 42, 45, 50, 53, 56, 60, 63, 66, 68, 72, 74, 77, 78, 80, 82, 84, 85, 86, 88, 88, 89, 90, 90}
4-Point DCT-8:{a, b, c, d,}{b, 0, −b, −b,}{c, −b, −d, a,}{d, −b, a, −c,}
where {a, b, c, d}={84, 74, 55, 29}
8-Point DCT-8:{a, b, c, d, e, f, g, h,}{b, e, h, −g, −d, −a, −c, −f,}{c, h, −e, −a, −f, g, b, d,}{d, −g, −a, −h, c, e, −f, −b,}{e, −d, −f, c, g, −b, −h, a,}{f, −a, g, e, −b, h, d, −c,}{g, −c, b, −f, −h, d, −a, e,}{h, −f, d, −b, a, −c, e, −g,}
where {a, b, c, d, e, f, g, h}={86, 85, 78, 71, 60, 46, 32, 17}
16-Point DCT-8:{a, b, c, d, e, f, g, h, i, j, k, 1, m, n, o, p,}{b, e, h, k, n, 0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n,}{c, h, m, −p, −k, −f, −a, −e, −j, −o, n, i, d, b, g, 1,}{d, k, −p, −i, −b, −f, −m, n, g, a, h, o, −1, −e, −c, −j,}{e, n, −k, −b, −h, 0, h, b, k, −n, −e, −e, −n, k, b, h,}{f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0, −f, −f,}{g, −n, −a, −m, h, f, −o, −b, −1, i, e, −p, −c, −k, j, d,}{h, −k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b,}{i, −h, −j, g, k, −f, −1, e, m, −d, −n, c, o, −b, −p, a,}{j, −e, −o, a, −n, −f, i, k, −d, −p, b, −m, −g, h, 1, −c,}{k, −b, n, h, −e, 0, e, −h, −n, b, −k, −k, b, −n, −h, e,}{1, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j, −n, d, −g,}{m, −e, d, −1, −n, f, −c, k, o, −g, b, −j, −p, h, −a, i,}{n, −h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k,}{o, −k, g, −c, b, −f, j, −n, −p, 1, −h, d, −a, e, −i, m,}{p, −n, 1, −j, h, −f, d, −b, a, −c, e, −g, i, −k, m, −o,}
where {a, b, c, d, e, f, g, h, i, j, k, 1, m, n, o, p}={90, 89, 87, 83, 81, 77, 72, 66, 62, 56, 49, 41, 33, 25, 17, 9}
32-Point DCT-8:{a, b, c, d, e, f, g, h, i, j, k, 1, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, F,}{b, e, h, k, n, q, t, w, z, C, F, −E, −B, −y, −v, −s, −p, −m, −j, −g, −d, −a, −c, −f, −i, −1, −o, −r, −u, −x, −A, −D,}{c, h, m, r, w, B, 0, −B, −w, −r, −m, −h, −c, −c, −h, −m, −r, −w, −B, 0, B, w, r, m, h, c, c, h, m, r, w, B,}{d, k, r, y, F, −A, −t, −m, −f, −b, −i, −p, −w, −D, C, v, o, h, a, g, n, u, B, −E, −x, −q, −j, −c, −e, −1, −s, −z,}{e, n, w, F, −y, −p, −g, −c, −1, −u, −D, A, r, i, a, j, s, B, −C, −t, −k, −b, −h, −q, −z, E, v, m, d, f, o, x,}{f, q, B, −A, −p, −e, −g, −r, −C, z, o, d, h, s, D, −y, −n, −c, −i, −t, −E, x, m, b, j, u, F, −w, −1, −a, −k, −v,}{g, t, 0, −t, −g, −g, −t, 0, t, g, g, t, 0, −t, −g, −g, −t, 0, t, g, g, t, 0, −t, −g, −g, −t, 0, t, g, g, t,}{h, w, −B, −m, −c, −r, 0, r, c, m, B, −w, −h, −h, −w, B, m, c, r, 0, −r, −c, −m, −B, w, h, h, w, −B, −m, −c, −r,}{i, z, −w, −f, −1, −C, t, c, o, F, −q, −a, −r, E, n, d, u, −B, −k, −g, −x, y, h, j, A, −v, −e, −m, −D, s, b, p,}{j, C, −r, −b, −u, z, g, m, F, −o, −e, −x, w, d, p, −E, −1, −h, −A, t, a, s, −B, −i, −k, −D, q, c, v, −y, −f, −n,}{k, F, −m, −i, −D, o, g, B, −q, −e, −z, s, c, x, −u, −a, −v, w, b, t, −y, −d, −r, A, f, p, −C, −h, −n, E, j, 1,}{1, −E, −h, −p, A, d, t, −w, −a, −x, s, e, B, −o, −i, −F, k, m, −D, −g, −q, z, c, u, −v, −b, −y, r, f, C, −n, −j,}{m, −B, −c, −w, r, h, 0, −h, −r, w, c, B, −m, −m, B, c, w, −r, −h, 0, h, r, −w, −c, −B, m, m, −B, −c, −w, r, h,}{n, −y, −c, −D, i, s, −t, −h, E, d, x, −o, −m, z, b, C, −j, −r, u, g, −F, −e, −w, p, 1, −A, −a, −B, k, q, −v, −f,}{o, −v, −h, C, a, D, −g, −w, n, p, −u, −i, B, b, E, −f, −x, m, q, −t, −j, A, c, F, −e, −y, 1, r, −s, −k, z, d,}{p, −s, −m, v, j, −y, −g, B, d, −E, −a, −F, c, C, −f, −z, i, w, −1, −t, o, q, −r, −n, u, k, −x, −h, A, e, −D, −b,}{q, −p, −r, o, s, −n, −t, m, u, −1, −v, k, w, −j, −x, i, y, −h, −z, g, A, −f, −B, e, C, −d, −D, c, E, −b, −F, a,}{r, −m, −w, h, B, −c, 0, c, −B, −h, w, m, −r, −r, m, w, −h, −B, c, 0, −c, B, h, −w, −m, r, r, −m, −w, h, B, −c,}{s, −j, −B, a, −C, −i, t, r, −k, −A, b, −D, −h, u, q, −1, −z, c, −E, −g, v, p, −m, −y, d, −F, −f, w, o, −n, −x, e,}{t, −g, 0, g, −t, −t, g, 0, −g, t, t, −g, 0, g, −t, −t, g, 0, −g, t, t, −g, 0, g, −t, −t, g, 0, −g, t, t, −g,}{u, −d, B, n, −k, −E, g, −r, −x, a, −y, −q, h, −F, −j, o, A, −c, v, t, −e, C, m, −1, −D, f, −s, −w, b, −z, −p, i,}{v, −a, w, u, −b, x, t, −c, y, s, −d, z, r, −e, A, q, −f, B, p, −g, C, o, −h, D, n, −i, E, m, −j, F, 1, −k,}{w, −c, r, B, −h, m, 0, −m, h, −B, −r, c, −w, −w, c, −r, −B, h, −m, 0, m, −h, B, r, −c, w, w, −c, r, B, −h, m,}{x, −f, m, −E, −q, b, −t, −B, j, −i, A, u, −c, p, F, −n, e, −w, −y, g, −1, D, r, −a, s, C, −k, h, −z, −v, d, −o,}{y, −i, h, −x, −z, j, −g, w, A, −k, f, −v, −B, 1, −e, u, C, −m, d, −t, −D, n, −c, s, E, −o, b, −r, −F, p, −a, q,}{z, −1, c, −q, E, u, −g, h, −v, −D, p, −b, m, −A, −y, k, −d, r, −F, −t, f, −i, w, C, −o, a, −n, B, x, −j, e, −s,}{A, −o, c, −j, v, F, −t, h, −e, q, −C, −y, m, −a, 1, −x, −D, r, −f, g, −s, E, w, −k, b, −n, z, B, −p, d, −i, u,}{B, −r, h, −c, m, −w, 0, w, −m, c, −h, r, −B, −B, r, −h, c, −m, w, 0, −w, m, −c, h, −r, B, B, −r, h, −c, m, −w,}{C, −u, m, −e, d, −1, t, −B, −D, v, −n, f, −c, k, −s, A, E, −w, o, −g, b, −j, r, −z, −F, x, −p, h, −a, i, −q, y,}{D, −x, r, −1, f, −a, g, −m, s, −y, E, C, −w, q, −k, e, −b, h, −n, t, −z, F, B, −v, p, −j, d, −c, i, −o, u, −A,}{E, −A, w, −s, o, −k, g, −c, b, −f, j, −n, r, −v, z, −D, −F, B, −x, t, −p, 1, −h, d, −a, e, −i, m, −q, u, −y, C,}{F, −D, B, −z, x, −v, t, −r, p, −n, 1, −j, h, −f, d, −b, a, −c, e, −g, i, −k, m, −o, q, −s, u, −w, y, −A, C, −E,}
where {a, b, c, d, e, f, g, h, i, j, k, 1, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, F}={90, 90, 89, 88, 88, 86, 85, 84, 82, 80, 78, 77, 74, 72, 68, 66, 63, 60, 56, 53, 50, 45, 42, 38, 34, 30, 26, 21, 17, 13, 9, 4}

When both the height and width of the coding block are smaller than or equal to 64, the transform size is the same as the coding block size, such as in VVC. When either the height or width of the coding block is larger than 64, for performing the transform or intra prediction, the coding block is further split into multiple sub-blocks, where the width and height of each sub-block are smaller than or equal to 64, and one transform is performed on each sub-block.

IV. Non-Separable Secondary Transform (NSST)

A mode-dependent non-separable secondary transform (NSST) can be applied between the forward core transform (i.e., primary transform) and quantization (at the encoder) and between the de-quantization and inverse core transform (at the decoder). To keep low complexity, NSST is only applied to low frequency coefficients after the primary transform. If both width (W) and height (H) of a transform coefficient block are larger than or equal to 8, then 8×8 non-separable secondary transform is applied to the top-left 8×8 region of the transform coefficients block. Otherwise, if either W or H of the transform coefficient block is equal to 4, a 4×4 non-separable secondary transform is applied and the 4×4 non-separable transform is performed on the top-left min(8,W)×min(8,H) region of the transform coefficient block. The above transform selection rule is applied for both luma and chroma components.

Matrix multiplication implementation of a non-separable transform is described as follows using a 4×4 input block as an example. To apply the non-separable transform, the 4×4 input block X in Eq.1 can be represented as a vector {right arrow over (X)} in Eq.2.

X=[X00X01X02X03X10X11X12X13X20X21X22X23X30X31X32X33]Eq.1
{right arrow over (X)}=[X00X01X02X03X10X11X12X13X20X21X22X23X30X31X32X33]TEq. 2

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 {right arrow over (F)} is subsequently re-organized as a 4×4 block using the scanning order for the block (horizontal, vertical or diagonal). A coefficient with a smaller index can be placed with a smaller scanning index in the 4×4 coefficient block. In an example, a hypercube-givens transform (HyGT) with butterfly implementation is used instead of matrix multiplication to reduce the complexity of non-separable transform.

In one embodiment, there can be totally 35×3 non-separable secondary transforms for both 4×4 and 8×8 block sizes in NSST, where 35 is the total number of transform sets and 3 is the number of NSST candidates included in each transform set. Each transform set is specified by an intra prediction mode. The mapping from the intra prediction mode to the corresponding transform set is defined in Table 3. The transform set applied to luma/chroma transform coefficients is specified by the corresponding luma/chroma intra prediction modes, according to Table 3. For intra prediction modes larger than 34 (diagonal prediction direction), the transform coefficient block is transposed before/after the secondary transform at the encoder/decoder.

TABLE 3Intra Mode012345678910111213141516Transform Set012345678910111213141516Intra Mode1718192021222324252627282930313233Transform Set1718192021222324252627282930313233Intra Mode3435363738394041424344454647484950Transform Set3433323130292827262524232221201918Intra Mode5152535455565758596061626364656667Transform Set171615141312111098765432NULL

For each transform set, the selected non-separable secondary transform candidate is further specified by an explicitly signalled CU-level NSST index. The NSST index is signalled in a bitstream once per intra CU after transform coefficients and truncated unary binarization are used. The truncated value is 2 in case of planar or DC mode, and 3 for an angular intra prediction mode. The NSST index is signalled only when there is more than one non-zero coefficient in a CU. The default value is zero when the NSST index is not signalled. Zero value of this syntax element indicates the secondary transform is not applied to the current CU, values 1-3 indicates which secondary transform from the transform set can be applied.

In an embodiment, NSST may be not applied for a block coded with transform skip mode. When the NSST index is signalled for a CU and not equal to zero, NSST is not used for a block of a component that is coded with transform skip mode in the CU. When a CU with blocks of all components are coded in transform skip mode or the number of non-zero coefficients of non-transform-skip mode CBs is less than 2, the NSST index is not signalled for the CU.

V. Reduced Size Transform (RST)

In an embodiment, NSST can use a transform zero-out scheme, namely reduced size transform (RST), which is also referred to as low-frequency non-separable secondary transform (LFNST) in some related cases such as VVC Draft 5. The RST checks whether the intra prediction mode is planar or DC for entropy coding the transform index of NSST.

In RST, a total of 4 transform sets are applied, and each transform set includes three RST transform cores. A size of a RST transform core can be either 16×48 (or 16×64) (applied for transform coefficient block with height and width both being greater than or equal to 8) or 16×16 (applied for transform coefficient block with either height or width being equal to 4). For notational convenience, the 16×48 (or 16×64) transform is denoted as RST8×8 and the 16×16 transform is denoted as RST4×4.

For RST8×8, two exemplary alternatives using 16×64 transform cores and 16×48 transform cores are shown inFIG.9andFIG.10, respectively. In an example, the one using 16×48 transform cores is employed.

VI. Computation of RST

RST is to map an N dimensional vector to an R dimensional vector in a different space, where R/N (R<N) is a reduction factor. The RST matrix is an R×N matrix as shown inFIG.11, where the R rows of the transform are R bases of the N dimensional space. The inverse transform matrix for RT is the transpose of its forward transform.FIGS.12A and12Bshow a simplified reduced transform and a simplified reduced inverse transform, respectively.

In an embodiment, the RST8×8 with a reduction factor of 4 (¼ size) is applied. Hence, instead of 64×64, which is a typical 8×8 non-separable transform matrix size, a 16×64 direct matrix is used in the RST8×8. In other words, the 64×16 inverse RST matrix is used at the decoder side to generate core (primary) transform coefficients in an 8×8 top-left region, as shown inFIG.13A. The forward RST8×8 uses 16×64 (or 8×64 for an 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 a 4×4 block) direct matrix multiplication is applied.

In addition, for RST8×8, to further reduce the transform matrix size, instead of the using the whole top-left 8×8 coefficients as input for calculating secondary transform, the top-left three 4×4 coefficients are used as the input for calculating secondary transform, as shown inFIG.13B.

An inverse RST is conditionally applied when the following two conditions are satisfied: (1) block size is greater than or equal to a given threshold (e.g., W>=4 && H>=4); and (2) transform skip mode flag is equal to zero.

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 and an RST kernel is chosen with the RST index.

Furthermore, RST can be applied for intra CUs 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 an inter slice in which the dual tree is disabled, a single RST index is signaled and used for both luma and chroma. When intra sub-partition (ISP) mode is selected, RST is disabled, and the RST index is not signaled.

An RST matrix is chosen from four transform sets, each of which includes two transforms. Which transform set is applied is determined by the intra prediction mode as the following: if one of three cross-component linear model (CCLM) modes is indicated, transform set 0 is selected; otherwise, transform set selection is performed according to Table 4. The index IntraPredMode has a range of [−14, 83], which is a transformed mode index used for wide angle intra prediction.

TABLE 4IntraPredModeTr. set indexIntraPredMode < 010 <= IntraPredMode <= 102 <= IntraPredMode <= 12113 <= IntraPredMode <= 23224 <= IntraPredMode <= 44345 <= IntraPredMode <= 55256 <= IntraPredMode1
VII. Memory Cost of RST

According to aspects of the disclosure, eight (4×2) 16×16 transform matrices (RST4×4) and eight (4×2) 16×48 transform matrices (RST8×8) are utilized in RST (or LFNST, or NSST), and each element in one transform matrix is represented using 8-bit integers. Accordingly, a total of 4×2×(256+768)=8K bytes memory is required in RST, which is relatively expensive for hardware design. This is because two transform processes are used in RST, i.e., RST4×4 and RST8×8. In addition, using different sizes of transform cores may not be a unified solution since a switching of transform cores is needed in RST.

In addition, in some related examples, the secondary transform index in RST is signaled after residual coding. That is, the RST index is not available until all residual coefficients are parsed. This may cause latency since the secondary transform cannot be started until the RST index is available.

VIII. Alternative of LFNST

The current LFNST method incurs relative high encoder search burden since the encoder has to try three options (e.g., no LFNST, LFNST index 1, and LFNST index 2) and then picks up the most efficient candidate per block.

Instead of two candidates, only one candidate of LFNST can be used and signaled for each block (e.g., in JVET-00292 and JVET-00350), as shown in Table 5. In Table 5, the LFSNT index signaled in the bitstream is denoted as lfnstIdx, the selected LFNST core index in the given transform set is denoted as coreIdx, and intra prediction mode is denoted as intraMode.

TABLE 5VTM-6JVET-O0292JVET-O0349lfnstIdx 0No LFNSTNo LFNSTNo LFNSTlfnstIdx 1lfnstIdx = 1If intraMode < 35coreIdx =coreIdx = intraMode % 2 == 0 ? 1 : 2( intramode % 2 ) + 1Otherwise,coreIdx = intraMode % 2 == 0 ? 2 : 1lfnstIdx 2lfnstIdx = 2——

With the method proposed in JVET-00292 and JVET-00350, only one LFNST candidate remains but the scheme still supports selecting all the LFNST candidates, for example, as defined in the current VVC Draft 6. Since only one LFNST candidate is kept, the burden of selecting LFNST at the encoder is reduced.

However, the proposed method in JVET-00292 and JVET-00350 requires normatively dropping the second LFNST candidate, and thus is risky since the coding performance relies on how the encoder search is designed. For example, if the encoder drops lfnstIdx 2 to achieve a similar encoder speedup as reported by JVET-00292 and JVET-00350, there can be a significant coding loss since the second LFNST candidate can never be chosen.

IX. Unified Secondary Transform

The following application includes various unified secondary transform methods for reducing memory cost of the secondary transform and improving performance of the secondary transform.

It is noted that LFNST will be discussed as an example in the methods, but the methods can also be applied to other transforms such as NSST or RST. In addition, a TU refers to a unit on which a transform process is performed. A TU may include multiple color components, and each color component is represented as a TB. Therefore, a TU can include multiple TBs.

According to aspects of the disclosure, the LFNST transform core applied on blocks with sizes being greater than or equal to M×N (RSTM×N) can also be applied on smaller blocks with either block width being smaller than M or block height being smaller than N. Exemplary values of M include but are not limited to 8, 16 and 32, and exemplary values of N include but are not limited to 8, 16 and 32.

In one embodiment, taking M=N=8 as an example, in order to apply the forward LFNST on a W×H primary transform coefficient block with either height (H) or width (W) being smaller than 8, an 8×8 block is first initialized as all 0. Then for each coordinate position, a value of this 8×8 block is set as a value located at a same coordinate of the W×H primary transform coefficient block. Finally, this 8×8 block is input to the RST8×8 transform process using RST8×8 transform cores, and the output is used as the output of the secondary transform applied on the W×H primary transform coefficient block.

FIG.14shows an exemplary unified secondary transform according to an embodiment of the disclosure. InFIG.14, an 8×4 TU is first processed by the forward primary transform1401, and then an 8×4 primary transform coefficient block1402is output from the forward primary transform1401. An 8×8 block1403is generated based on the 8×4 primary transform coefficient block1402. A top 8×4 region of the 8×8 block1403is directly copied from the 8×4 primary transform coefficient block1402and a bottom 8×4 region of the 8×8 block1403is set as 0. Then the 8×8 block1403is input to a secondary transform1404(e.g., RST8×8). The output of the secondary transform1404is an 8×4 secondary transform coefficient block1405, which is further input to a quantization process1406.

In another embodiment, taking both M and N being 8 as an example, in order to apply the inverse LFNST on a W×H primary transform coefficient block with height (H) or width (W) being smaller than 8, given the input which is a vector of secondary transform coefficients, an 8×8 primary transform coefficient block can be generated. However, only an overlapping part between the W×H block and the 8×8 block is calculated and a non-overlapping part is not calculated because of being located out of a coordinate range of the W×H block.

FIG.15shows an exemplary unified secondary transform according to an embodiment of the disclosure. InFIG.15, an 8×4 secondary transform coefficient block1502is first output from a de-quantization block1501and then input to an inverse secondary transform1503(e.g., inverse RST8×8). Only a top 8×4 region of the inverse secondary transform1503is applied on the 8×4 secondary transform coefficient block1502and a bottom 8×4 region of the inverse secondary transform1503is not calculated. Therefore, an 8×8 block1504is output from the inverse secondary transform1503, and a top 8×4 region of the 8×8 block1504is used as an 8×4 primary transform coefficient block1505and input to a forward primary transform1506.

According to aspects of the disclosure, the present LFNST schemes above can be applied on any block sizes with a height and/or a width being smaller than a threshold (e.g., 8). For example, the present LFNST schemes above can be applied on 2×H blocks, W×2 blocks, 6×H blocks, and W×6 blocks.

In one embodiment, the disclosed unified LFNST scheme can be applied to chroma TUs, such as 2×H and W×2 chroma TUs. If H (or W) is less than or equal to 8, only a first number of coefficients (e.g., the first 8 coefficients) such as along a forward scanning order (e.g., scanning from low-frequency to high frequency) are kept and remaining coefficients are set or considered as 0, regardless of the secondary transform having any impact or not. If H (or W) is greater than 8, only a second number of coefficients (e.g., the first 16 coefficients) such as along the forward scanning order are kept and remaining coefficients are set or considered as 0, regardless of the secondary transform having any impact or not.

In one embodiment, for certain block sizes (e.g., 8×4 and 4×8 blocks), when performing LFNST, only up to a predetermined number of transform coefficients (e.g., only up to 8 transform coefficients) are calculated and remaining coefficients are set as 0. For example, the predetermined number of transform coefficients can be the last predetermined number of coefficient positions in a coefficient parsing order.

In one embodiment, for certain block sizes (e.g., 8×4 and 4×8 blocks), in case a non-zero coefficient is identified from a certain position, for example an 8th position (inclusive) along the forward coefficient scanning order, a secondary transform index is not signaled and a secondary transform is not applied.

In one embodiment, for certain block sizes (e.g., N×4 and 4×N blocks), where N is greater than 8, instead of performing two RST4×4, only one RST8×8 is performed, and the disclosed unified LFNST scheme can generate up to 16 nonzero coefficients instead of up to 32 nonzero coefficients.

In one embodiment, if the secondary transform index is signaled before transform coefficients, a modified coefficient coding scheme is employed. For an M×N TU, when M and N are both less than or equal to 8 but greater than 2, only the first 8 coefficients along the scanning order are coded, syntax elements of the remaining coefficients (e.g., significance flag) are not coded. When both M and N are greater than 4, only the first 16 coefficients along the scanning order are coded, syntax elements of the remaining coefficients (e.g., CG flag, significance flag) are not coded.

According to aspects of the disclosure, an LFNST index is signaled at a TB-level. That is, each TB or each color component of one TU corresponds to an individual LFNST index.

In one embodiment, the LFNST index is signaled after a last position (e.g., a last non-zero transform coefficient in the transform coefficient block) and before one or more coefficient coding related syntax, such as CG flags (coded_sub_block_flag), significance flags (sig_coeff_flag), gtX flags (abs_level_gtx_flag), parity flags (par_level_flag), sign flags (coeff_sign_flag), and/or absolute remainder levels (abs_remainder).

In one embodiment, depending on the signaled LFNST index value and a position of a coefficient to be coded, one or more coefficient coding related syntax may be skipped and not signaled and derived as a default value.

In one embodiment, the one or more coefficient coding related syntax which may be skipped and not signaled include CG flags (coded_sub_block_flag), significance flags (sig_coeff_flag), gtX flags (abs_level_gtx_flag), parity flags (par_level_flag), sign flags (coeff_sign_flag), and/or absolute remainder levels (abs_remainder).

In one embodiment, the coding related syntax which is skipped and not signaled can be derived as 0 which indicates the associated coefficient is 0.

In one embodiment, when the signaled LFNST index indicates that LFNST is applied, one or more coefficient coding related syntax may be not signaled and derived as a default value. The one or more coefficient coding related syntax which may be skipped and not signaled include CG flags (coded_sub_block_flag), significance flags (sig_coeff_flag), gtX flags (abs_level_gtx_flag), parity flags (par_level_flag), sign flags (coeff_sign_flag), and/or absolute remainder levels (abs_remainder).

In one embodiment, for a current TB with a size of W×H, where both W and H are smaller than or equal to a threshold (e.g., 8), if the LFNST index is applied on the current TB, the CG flag for the first CG is still signaled, but other syntax elements (e.g., sig_coeff_flag, abs_level_gtx_flag, par_level_flag, coeff_sign_flag, and/or abs_remainder) for a coefficient located after the Nth (for example 8th) position along the scanning order are not signaled and derived as a default value. The default value may be a value indicating that the coefficient is 0.

In one embodiment, for a current TB with a size of W×H, where either W or H is greater than a threshold like 8, if the LFNST index is applied on the current TB, the coefficient coding related syntax elements for a coefficient located after the first CG along the scanning order are not signaled and derived as a default value. The default value may be a value indicating that the coefficients within the associated CG are all 0.

In one embodiment, if the LFNST index is applied on the current TB, the coefficient coding related syntax elements for a coefficient located after the first CG along the scanning order are not signaled and derived as a default value. The default value may be a value indicating that the coefficients within the associated CG are all 0.

According to aspects of the disclosure, a syntax element tu_mts_idx is signalled after a last position (e.g., a last non-zero transform coefficient in the transform coefficient block) and before one or more coefficient coding related syntax, such as CG flags (coded_sub_block_flag), significance flags (sig_coeff_flag), gtX flags (abs_level_gtx_flag), parity flags (par_level_flag), sign flags (coeff_sign_flag), and/or absolute remainder levels (abs_remainder). The syntax element tu_mts_idx indicates one of multiple transform selections, such as DCT-2, DST-7, and DCT-8. It is noted that a skip transform is included in the multiple transform selections.

In one embodiment, the syntax element tu_mts_idx is signalled after the last position and before the LFNST index and also before some coefficient coding related syntax, such as CG flags (coded_sub_block_flag), significance flags (sig_coeff_flag), gtX flags (abs_level_gtx_flag), parity flags (par_level_flag), sign flags (coeff_sign_flag), and/or absolute remainder levels (abs_remainder).

According to aspects of the disclosure, context used for entropy coding of the LFNST index depends on a shape of the LFNST kernel. The context used can depend on a comparison of a block width or height to a value (e.g., 4).

In one embodiment, depending on whether the block width or height is the value (e.g., 4), different contexts may be applied for entropy coding of the LFNST index.

In one embodiment, depending on whether either the block width or height is greater than the value (e.g., 4), different contexts may be applied for entropy coding of the LFNST index.

According to aspects of the disclosure, for one-dimensional cross-component linear model (CCLM) mode CCLM_TOP, which uses only top reference samples for deriving CCLM model parameters, and CCLM_LEFT, which uses only left reference samples for deriving CCLM model parameters, a decision on whether an output of the inverse LFNST (or an input of the forward LFNST) is transposed is different.

In one embodiment, for CCLM_TOP mode, the output of the inverse LFNST (or the input of the forward LFNST) is transposed, but for CCLM_LEFT mode, the output of the inverse LFNST (or the input of the forward LFNST) is not transposed.

In one embodiment, for CCLM_TOP mode, the output of the inverse LFNST (or the input of the forward LFNST) is not transposed, but for CCLM_LEFT mode, the output of the inverse LFNST (or the input of the forward LFNST) is transposed.

According to aspects of the disclosure, for one block, a transform set is first identified. The transform set includes N LFNST candidates. Then an LFNST index value is signaled in the bitstream, i.e., lfnstIdx, which ranges from 1˜N. When lfnstIdx is equal to 0, LFNST is not applied. lfnstIdx is mapped to one of the N candidates in the given transform set, specifying which LFNST core is selected for the signaled lfnstIdx value. For adjacent intra prediction modes, the same transform set is applied, but lfnstIdx is mapped to a different LFNST candidate in the given transform set.

In one embodiment, the transform set includes two LFNST candidates, i.e., N is equal to 2, and lfnstIdx is mapped according to Table 6. For example, intraMode 2 and intraMode 3 may share a same transform set. For intraMode 2, the lfnstIdx 1 and lfnstIdx 2 refer to a first candidate and a second candidate in the given transform set, respectively; while for intraMode 3, the lfnstIdx 1 and lfnstIdx 2 refer to the second candidate and first candidate in the given transform set, respectively.

TABLE 6VTM-6Proposed in This DisclsourelfnstIdx 0LFNST offLFNST offlfnstIdx 111 + ( intraMode % 2 )lfnstIdx 222 − ( intraMode % 2 )

In one embodiment, the transform set includes two LFNST candidates, i.e., N equal to 2, and lfnstIdx is mapped according to Table 7. For example, intraMode 2 and intraMode 3 may share a same transform set. Since both intraMode 2 and intraMode 3 are less than a threshold (e.g., 35), for intraMode 2, the lfnstIdx 1 and lfnstIdx 2 refer to a first and a second candidate in the given transform set, respectively; while for intraMode 3, the lfnstIdx 1 and lfnstIdx 2 refer to the second candidate and first candidate in the given transform set, respectively.

TABLE 7VTM-6Proposed in This DisclosurelfnstIdx 0No LFNSTNo LFNSTlfnstIdx 11If intraMode <35coreIdx = intraMode % 2 == 0 ? 1 : 2Otherwise,coreIdx = intraMode % 2 == 0 ? 2 : 1lfnstIdx 22If intraMode <35coreIdx = intraMode % 2 == 0 ? 2 : 1Otherwise,coreIdx = intraMode % 2 == 0 ? 1 : 2

According to aspects of the disclosure, a same transform set and a same transform selection scheme for LFNST can be applied. However, a context for entropy coding bins of the LFNST index depends on whether the intra prediction mode is an even or odd number, and/or whether the intra prediction mode is greater than a threshold (e.g., a diagonal intra prediction mode index 34 in VVC Draft 6).

According to aspects of the disclosure, the coreIdx derivation methods described above may be used as a prediction (or error prediction) of the current block. As there are only two options for such a prediction, lfnstIdx may be indicated in bitstreams by signaling whether the prediction is correct or not.

In an embodiment, two bins of a binarization for lfnstIdx 1 and lfnstIdx 2 are 10 and 11, respectively. Since a first bin is always 1, a second bin of the two bins can be used for indicating whether the prediction is correct or not. For example, if lfnstIdx 1 is chosen and the second bin is 0, the prediction is right; if lfnstIdx 1 is chosen and the second bin is 1, the prediction is wrong.

X. Modified Residual Coding Syntax

Table 8 shows an exemplary modified residual coding syntax according to an embodiment of the disclosure.

TABLE 8Descriptorresidual_coding( x0, y0, log2TbWidth, log2TbHeight, cIdx ) {if( ( tu_mts_idx[ x0 ][ y0 ] > 0 | |( cu_sbt_flag && log2TbWidth < 6 && log2TbHeight < 6 ) )&& cIdx == 0 && log2TbWidth > 4 )log2ZoTbWidth = 4elselog2ZoTbWidth = Min( log2TbWidth, 5 )if( tu_mts_idx[ x0 ][ y0 ] > 0 | |( cu_sbt_flag && log2TbWidth < 6 && log2TbHeight < 6 ) )&& cIdx == 0 && log2TbHeight > 4 )log2ZoTbHeight = 4elselog2ZoTbHeight = Min( log2TbHeight, 5 )if( log2TbWidth > 0 )last_sig_coeff_x_prefixae(v)if( log2TbHeight > 0 )last_sig_coeff_y_prefixae(v)if( last_sig_coeff_x_prefix > 3 )last_sig_coeff_x_suffixae(v)if( last_sig_coeff_y_prefix > 3 )last_sig_coeff_y_suffixae(v)log2Tb Width = log2ZoTbWidthlog2TbHeight = log2ZoTbHeightlog2SbW = ( Min( log2TbWidth, log2TbHeight ) < 2 ? 1 : 2 )log2SbH = log2SbWif( log2TbWidth + log2TbHeight > 3 ) {if( log2Tb Width < 2 ) {log2SbW = log2TbWidthlog2SbH = 4 − log2SbW} else if( log2TbHeight < 2 ) {log2SbH = log2TbHeightlog2SbW = 4 − log2SbH}}numSbCoeff = 1 << ( log2SbW + log2SbH )lastScanPos = numSbCoefflastSubBlock = ( 1 << ( log2TbWidth + log2TbHeight − ( log2SbW + log2SbH ) ) ) − 1do {if( lastScanPos == 0 ) {lastScanPos = numSbCoefflastSubBlock− −}lastScanPos− −xS = DiagScanOrder[ log2Tb Width − log2SbW ][ log2TbHeight − log2SbH ][ lastSubBlock ][ 0 ]yS = DiagScanOrder[ log2TbWidth − log2SbW ][ log2TbHeight − log2SbH ][ lastSubBlock ][ 1 ]xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ lastScanPos ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ lastScanPos ][ 1 ]} while( ( xC != LastSignificantCoeffX ) | | ( yC != LastSignificantCoeffY ) )QState = 0for( i = lastSubBlock; i >= 0; i− − ) {startQStateSb = QStatexS = DiagScanOrder[ log2Tb Width − log2SbW ][ log2TbHeight − log2SbH ][ i ][ 0 ]yS = DiagScanOrder[ log2TbWidth − log2SbW ][ log2TbHeight − log2SbH ][ i ][ 1 ]inferSbDcSigCoeffFlag = 0if( ( i < lastSubBlock ) && ( i > 0 ) ) {coded_sub_block_flag[ xS ][ yS ]ae(v)inferSbDcSigCoeffFlag = 1}firstSigScanPosSb = numSbCoefflastSigScanPosSb = −1remBinsPass1 = ( ( log2SbW + log2SbH ) < 4 ? 8 : 32 )firstPosMode0 = ( i == lastSubBlock ? lastScanPos : numSbCoeff − 1 )firstPosMode1 = −1for( n = firstPosMode0; n >= 0 && remBinsPass1 >= 4; n− − ) {xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]if( coded_sub_block_flag[ xS ][ yS ] && ( n > 0 | | !inferSbDcSigCoeffFlag ) &&( xC != LastSignificantCoeffX | | yC != Last SignificantCoeffY ) ) {sig_coeff_flag[ xC ][ yC ]ae(v)remBinsPass1− −if( sig_coeff_flag[ xC ][ yC ] )inferSbDcSigCoeffFlag = 0}if( sig_coeff_flag[ xC ][ yC ] ) {if( !transform_skip_flag[ x0 ][ y0 ] ) {numSigCoeff++if( ( n >= 8 && i == 0 && ( log2TbWidth <= 3 )&& ( log2TbWidth == log2TbHeight ) ) | | ( ( i == 1 | | i == 2 )&& log2TbWidth >= 3 && log2TbHeight >= 3 ) )numZeroOutSigCoeff++}abs_level_gtx_flag[ n ][ 0 ]ae(v)remBinsPass1− −if( abs_level_gtx_flag[ n ][ 0 ] ) {par_level_flag[ n ]ae(v)remBinsPass1− −abs_level_gtx_flag[ n ][ 1 ]ae(v)remBinsPass1− −}if( lastSigScanPosSb == −1 )lastSigScanPosSb = nfirstSigScanPosSb = n}AbsLevelPass1[ xC ][ yC ] = sig_coeff_flag[ xC ][ yC ] + par_level_flag[ n ] +abs_level_gtx_flag[ n ][ 0 ] + 2 * abs_level_gtx_flag[ n ][ 1 ]if( dep_quant_enabled_flag )QState = QStateTransTable[ QState ][ AbsLevelPass ][ xC ][ yC ] & 1 ]if( remBinsPass1 < 4 )firstPosMode1 = n − 1}for( n = numSbCoeff − 1; n >= firstPosMode1; n− − ) {xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]if( abs_level_gtx_flag[ n ][ 1 ] )abs_remainder[ n ]ae(v)AbsLevel[ xC ][ yC ] = AbsLevelPass1 [ xC ][ yC ] + 2 * abs_remainder[ n ]}for( n = firstPosMode1; n >= 0; n− − ) {xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]dec_abs_level[ n ]ae(v)if(AbsLevel[ xC ][ yC ] > 0 )firstSigScanPosSb = nif( dep_quant_enabled_flag )QState = QStateTransTable[ QState ][ AbsLevel[ xC ][ yC ] & 1 ]}if( dep_quant_enabled_flag | | !sign_data_hiding_enabled_flag )signHidden = 0elsesignHidden = ( lastSigScanPosSb − firstSigScanPosSb > 3 ? 1 : 0 )for( n = numSbCoeff − 1; n >= 0; n− − ) {xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]if( ( AbsLevel[ xC ][ yC ] > 0 ) &&( !signHidden | | ( n != firstSigScanPosSb ) ) )coeff_sign_flag[ n ]ae(v)}if( dep_quant_enabled_flag ) {QState = startQStateSbfor( n = numSbCoeff − 1; n >= 0; n− − ) {xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]if( AbsLevel[ xC ][ yC ] > 0 )TransCoeffLevel[ x0 ][ y0 ][ cIdx ][ xC ][ yC ] =( 2 * AbsLevel[ xC ][ yC ] − ( QState > 1 ? 1 : 0 ) ) *( 1 − 2 * coeff_sign_flag[ n])QState = QStateTransTable[ QState ][ par_level_flag[ n ] ]} else {sumAbsLevel = 0for( n = numSbCoeff - 1; n >= 0; n− − ) {xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]if( AbsLevel[ xC ][ yC ] > 0 ) {TransCoeffLevel[ x0 ][ y0 ][ cIdx ][ xC ][ yC ] =AbsLevel[ xC ][ yC ] * ( 1 − 2 * coeff_sign_flag[ n ] )if( signHidden ) {sumAbsLevel += AbsLevel[ xC ][ yC ]if( (n == firstSigScanPosSb ) && ( sumAbsLevel % 2 ) == 1 ) )TransCoeffLevel[ x0 ][ y0 ][ cIdx ][ xC ][ yC ] =...TransCoeffLevel[ x0 ][ y0 ][ cIdx ][ xC ][ yC ]}}}}}}

Table 9 shows another exemplary modified residual coding syntax according to an embodiment of the disclosure.

TABLE 9Descriptorresidual_coding( x0, y0, log2TbWidth, log2TbHeight, cIdx ) {if( ( tu_mts_idx[ x0 ][ y0 ] > 0 | |( cu_sbt_flag && log2TbWidth < 6 && log2TbHeight < 6 ) )&& cIdx == 0 && log2Tb Width > 4 )log2ZoTbWidth = 4elselog2ZoTbWidth = Min( log2Tb Width, 5 )MaxCcbs = 2 * ( 1 << log2TbWidth ) * ( 1 << log2TbHeight )if( tu_mts_idx[ x0 ][ y0 ] > 0 | |( cu_sbt_flag && log2TbWidth < 6 && log2TbHeight < 6 ) )&& cIdx == 0 && log2TbHeight > 4 )log2ZoTbHeight = 4elselog2ZoTbHeight = Min( log2TbHeight, 5 )if( log2TbWidth > 0 )last_sig_coeff_x_prefixae(v)if( log2TbHeight > 0 )last_sig_coeff_y_prefixae(v)if( last_sig_coeff_x_prefix > 3 )last_sig_coeff_x_suffixae(v)if( last_sig_coeff_y_prefix > 3 )last_sig_coeff_y_suffixae(v)log2TbWidth = log2ZoTbWidthlog2TbHeight = log2ZoTbHeightremBinsPass1 = ( ( 1 << ( log2TbWidth + log2TbHeight ) ) * 7 ) >> 2log2SbW = ( Min( log2TbWidth, log2TbHeight ) < 2 ? 1 : 2 )log2SbH = log2SbWif( log2Tb Width + log2TbHeight > 3 ) {if( log2Tb Width < 2 ) {log2SbW = log2TbWidthlog2SbH = 4 − log2SbW} else if( log2TbHeight < 2 ) {log2SbH = log2TbHeightlog2SbW = 4 − log2SbH}}numSbCoeff = 1 << ( log2SbW + log2SbH )lastScanPos = numSbCoefflastSubBlock = ( 1 << ( log2TbWidth + log2TbHeight − ( log2SbW + log2SbH ) ) ) − 1do {if( lastScanPos == 0 ) {lastScanPos = numSbCoefflastSubBlock− −}lastScanPos− −xS = DiagScanOrder[ log2TbWidth − log2SbW ][ log2TbHeight − log2SbH ][ lastSubBlock ][ 0 ]yS = DiagScanOrder[ log2TbWidth − log2SbW ][ log2TbHeight − log2SbH ][ lastSubBlock ][ 1 ]xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ lastScanPos ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ lastScanPos ][ 1 ]} while( ( xC != LastSignificantCoeffX ) || ( yC != LastSignificantCoeffY ) )if( lastSubBlock == 0 && log2TbWidth >= 2 && log2TbHeight >= 2 &&!transform_skip_flag[ x0 ][ y0 ] && lastScanPos > 0 )LfnstDcOnly = 0if( Min( lfnstWidth, lfnstHeight ) >= 4 && sps_lfnst_enabled flag == 1 &&CuPredMode[ x0 ][ y0 ] == MODE INTRA &&IntraSubPartitionsSplitType == ISP_NO_SPLIT &&( !intra_mip_flag[ x0 ][ y0 ] || Min( lfnstWidth, lfnstHeight ) >= 16 ) &&tu_mts_idx[ x0 ][ y0 ] == 0 && Max( cbWidth, cbHeight ) <= MaxTbSizeY &&LfnstDcOnly == 0 ) {lfnst_idx[ x0 ][ y0 ]ae(v)}QState = 0for( i = lastSubBlock; i >= 0; i− − ) {startQStateSb = QStatexS = DiagScanOrder[ log2TbWidth − log2SbW ][ log2TbHeight − log2SbH ][ i ][ 0 ]yS = DiagScanOrder[ log2TbWidth − log2SbW ][ log2TbHeight − log2SbH ][ i ][ 1 ]inferSbDcSigCoeffFlag = 0if( ( i < lastSubBlock ) && ( i > 0 ) && !lfnst_idx[ x0 ][ y0 ] ) {coded_sub_block_flag[ xS ][ yS ]ae(v)inferSbDcSigCoeffFlag = 1}firstSigScanPosSb = numSbCoefflastSigScanPosSb = −1firstPosMode0 = ( i == lastSubBlock ? lastScanPos : numSbCoeff − 1 )firstPosMode1 = −1for( n = firstPosMode0; n >= 0 && remBinsPass1 >= 4; n− − ) {xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]if( coded_sub_block_flag[ xS ][ yS ] && ( n > 0 | | !inferSbDcSigCoeffFlag ) &&( xC != LastSignificantCoeffX | | yC != Last SignificantCoeffY ) ) {sig_coeff_flag[ xC ][ yC ]ae(v)remBinsPass1− −if( sig_coeff_flag[ xC ][ yC ] )inferSbDcSigCoeffFlag = 0}if( sig_coeff_flag[ xC ][ yC ] ) {abs_level_gtx_flag[ n ][ 0 ]ae(v)remBinsPass1− −if( abs_level_gtx_flag[ n ][ 0 ] ) {par_level_flag[ n ]ae(v)remBinsPass1− −abs_level_gtx_flag[ n ][ 1 ]ae(v)remBinsPass1− −}if( lastSigScanPosSb == −1 )lastSigScanPosSb = nfirstSigScanPosSb = n}AbsLevelPass1[ xC ][ yC ] = sig_coeff_flag[ xC ][ yC ] + par_level_flag[ n ] +abs_level_gtx_flag[ n ][ 0 ] + 2 * abs_level_gtx_flag[ n ][ 1 ]if( dep_quant_enabled_flag )QState = QState TransTable[ QState ][ AbsLevelPass1[ xC ][ yC ] & 1 ]if( remBinsPass1 < 4 )firstPosMode1 = n − 1}for( n = numSbCoeff − 1; n >= firstPosMode1; n− − ) {xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]if( abs_level_gtx_flag[ n ][ 1] )abs_remainder[ n ]ae(v)AbsLevel[ xC ][ yC ] = AbsLevelPass1 [ xC ][ yC ] + 2 * abs_remainder[ n ]}for( n = firstPosMode1; n >= 0; n− − ) {xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]dec_abs_level[ n ]ae(v)if(AbsLevel[ xC ][ yC ] > 0 )firstSigScanPosSb = nif( dep_quant_enabled_flag )QState = QStateTransTable[ QState ][ AbsLevel[ xC ][ yC ] & 1 ]}if( dep_quant_enabled_flag | | !sign_data_hiding_enabled_flag )signHidden = 0elsesignHidden = ( lastSigScanPosSb − firstSigScanPosSb > 3 ? 1 : 0 )for( n = numSbCoeff − 1; n >= 0; n− − ) {xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]if( ( AbsLevel[ xC ][ yC ] > 0 ) &&( !signHidden | | ( n != firstSigScanPosSb ) ) )coeff_sign_flag[ n ]ae(v)}if( dep_quant_enabled_flag ) {QState = startQStateSbfor( n = numSbCoeff − 1; n >= 0; n− − ) {xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]if( AbsLevel[ xC ][ yC ] > 0 )TransCoeffLevel[ x0 ][ y0 ][ cIdx ][ xC ][ yC ] =( 2 * AbsLevel[ xC ][ yC ] − ( QState > 1 ? 1 : 0 ) ) *( 1 − 2 * coeff_sign_flag[ n ])QState = QStateTransTable[ QState ][ par_level_flag[ n ] ]} else {sumAbsLevel = 0for( n = numSbCoeff − 1; n >= 0; n− − ) {xC = (xS << log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 0 ]yC = ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][ n ][ 1 ]if( AbsLevel[ xC ][ yC ] > 0 ) {TransCoeffLevel[ x0 ][ y0 ][ cIdx ][ xC ][ yC ] =AbsLevel[ xC ][ yC ] * ( 1 − 2 * coeff_sign_flag[ n ] )if( signHidden ) {sumAbsLevel += AbsLevel[ xC ][ yC ]if( (n == firstSigScanPosSb ) && ( sumAbsLevel % 2) == 1 ) )TransCoeffLevel[ x0 ][ y0 ][ cIdx ][ xC ][ yC ] =...TransCoeffLevel[ x0 ][ y0 ][ cIdx ][ xC ][ yC ]}}}}}}

The CG flag coded_sub_block_flag[xS][yS] specifies the following for the subblock at location (xS, yS) within the current transform block, where a subblock is a (4×4) array of 16 transform coefficient levels:If coded_sub_block_flag[xS][yS] is equal to 0, the 16 transform coefficient levels of the subblock at location (xS, yS) are inferred to be equal to 0.Otherwise (coded_sub_block_flag[xS][yS] is equal to 1), the following applies:If (xS, yS) is equal to (0, 0) and (LastSignificantCoeffX, LastSignificantCoeffY) is not equal to (0, 0), at least one of the 16 sig_coeff_flag syntax elements is present for the subblock at location (xS, yS).Otherwise, at least one of the 16 transform coefficient levels of the subblock at location (xS, yS) has a non-zero value.

When coded_sub_block_flag[xS][yS] is not present, it is inferred as follows:If lfnst_idx[xS][yS] is equal to 0 or (xS, yS) is equal to (0, 0) or (xS, yS) is equal to (LastSignificantCoeffX, LastSignificantCoeffY), coded_sub_block_flag[xS][yS] is inferred as 1.Otherwise, coded_sub_block_flag[xS][yS] is inferred as 0.
XI. Modified General Transform Process

The following process shows an exemplary modified transform process on a current luma TB according to an embodiment of the disclosure.

Inputs to this process include: (1) a luma location (xTbY, yTbY) specifying the top-left sample of the current luma TB relative to the top left luma sample of the current picture; (2) a variable nTbW specifying the width of the current TB; (3) a variable nTbH specifying the height of the current TB; (3) a variable cIdx specifying the colour component of the CB; and (4) an (nTbW)×(nTbH) array d[x][y] of scaled transform coefficients with x=0 . . . nTbW−1, y=0 . . . nTbH−1.

An output of this process is the (nTbW)×(nTbH) array r[x][y] of residual samples with x=0 . . . nTbW−1, y=0 . . . nTbH−1.

When lfnst_idx[xTbY][yTbY] is not equal to 0 and both nTbW and nTbH are greater than or equal to 4, the variables nLfnstSize, log2LfnstSize, numLfnstX, numLfnstY, and nonZeroSize are derived as follows: (1) log2LfnstSize is set equal to 3 and nLfnstOutSize is set equal to 48; (2) nLfnstSize is set to (1<<log2LfnstSize); (3) numLfnstX set equal to 1; (4) numLfnstY set equal to 1; (5) if both nTbW and nTbH are less than or equal to 8, nonZeroSize is set equal to 8; (6) otherwise, nonZeroSize set equal to 16.

For xSbIdx=0 . . . numLfnstX−1 and ySbIdx=0 . . . numLfnstY−1, the variable array u[x] with x=0 . . . nonZeroSize−1 are derived as follows:
xC=(xSbIdx<<log2LfnstSize)+DiagScanOrder[log2LfnstSize][log2LfnstSize][x][0]   (Eq.3)
yC=(ySbIdx<<log2LfnstSize)+DiagScanOrder[log2LfnstSize][log2LfnstSize][x][1]   (Eq.4)
u[x]=d[xC][yC](Eq.5)

u[x] with x=0 . . . nonZeroSize−1 is transformed to the variable array v[x] with x=0 . . . nLfnstOutSize−1 by invoking the one-dimensional transformation process with the transform input length of the scaled transform coefficients nonZeroSize, the transform output length nLfnstOutSize, the list u[x] with x=0 . . . nonZeroSize−1, the index for transform set selection lfnstPredModeIntra, and the index for transform selection in a transform set lfnst_idx[xTbY][yTbY] as inputs, and the output is the list v[x] with x=0 . . . nLfnstOutSize−1. The variable lfnstPredModeIntra is set equal to IntraPredModeY[xTbY][yTbY].

The array d[(xSbIdx<<log2LfnstSize)+x][(ySbIdx<<log2LfnstSize)+y] with x=0 . . . min(nTbW, nLfnstSize)−1, y=0 . . . min(nTbH, nLfnstSize)−1 are derived as follows.

If lfnstPredModeIntra is less than or equal to 34, or equal to INTRA_LT_CCLM, INTRA_T_CCLM, or INTRA_L_CCLM, the following applies:
d[(xSbIdx<<log2LfnstSize)+x][(ySbIdx<<log2LfnstSize)+y]=(y<4)?v[x+(y<<log2LfnstSize)]:((x<4)?v[32+x+((y−4)<<2)]:d[x][y])  (Eq.7)

Otherwise, the following applies:
d[(xSbIdx<<log2LfnstSize)+x][(ySbIdx<<log2LfnstSize)+y]=(x<4)?v[y+(x<<log2LfnstSize)]:((y<4)?v[32+y+((x−4)<<2)]:d[x][y])  (Eq.8)
XII. Modified LFNST Process

The following process shows an exemplary modified LFNST process according to an embodiment of the disclosure.

Inputs to this process include: (1) a variable nonZeroSize specifying the transform input length; (2) a variable nTrS specifying the transform output length; (3) a list of transform input x[j] with j=0 . . . nonZeroSize−1; (4) a variable lfnstPredModeIntra specifying the index for transform set selection; and (5) a variable lfnstIdx specifying the index for transform selection in a transform set.

An output of this process is the list of transformed samples y[i] with i=0 . . . nTrS−1.

The transformation matrix derivation process is involved with the transform output length nTrS, the index for transform set selection lfnstPredModeIntra, and the index for transform selection in a transform set lfnstIdx as inputs, and the transformation matrix lowFreqTransMatrix as output.

The list of transformed samples y[i] with i=0 . . . nTrS−1 is derived as follows:
y[i]=Clip3(CoeffMin,CoeffMax,((Σj=0nonzerosize−1lowFreqTransMatrix[i][j]*x[j])+64)>>7)  (Eq.9)

The following process shows another exemplary modified LFNST process according to an embodiment of the disclosure.

Inputs to this process include: (1) a variable nonZeroSize specifying the transform input length; (2) a variable nTrS specifying the transform output length; (3) a list of scaled non-zero transform coefficients x[j] with j=0 . . . nonZeroSize−1; (4) a variable predModeIntra specifying the intra prediction mode for LFNST set selection; and (5) a variable lfnstIdx specifying the LFNST index for transform selection in the selected LFNST set.

An output of this process is the list of transformed samples y[i] with i=0 . . . nTrS−1.

The variable lfnstIdx is set equal to (predModeIntra%2)==0?lfnstIdx:(3−lfnstIdx).

The transformation matrix derivation process as specified is invoked with the transform output length nTrS, the intra prediction mode for LFNST set selection predModeIntra, and the LFNST index for transform selection in the selected LFNST set lfnstIdx as inputs, and the (nTrS)×(nonZeroSize) LFNST matrix lowFreqTransMatrix as output.

The list of transformed samples y[i] with i=0 . . . nTrS−1 is derived as follows:
y[i]=Clip3(CoeffMin,CoeffMax,((Σj=0nonzerosize−1lowFreqTransMatrix[i][j]*x[j])+64)>>7)   (Eq.10)
XIII. Modified LFNST Matrix Derivation Process

The following process shows an exemplary modified LFNST matrix derivation process.

Inputs to this process include a variable lfnstPredModeIntra specifying the index for transform set selection and a variable lfnstIdx specifying the index for transform selection in the selected transform set.

An output of this process is the transformation matrix lowFreqTransMatrix.

The variable lfnstTrSetIdx is specified in Table 10 depending on lfnstPredModeIntra.

TABLE 10lfnstPredModeIntralfnstTrSetIdxlfnstPredModeIntra < 010 <= lfnstPredModeIntra <= 102 <= lfnstPredModeIntra <= 12113 <= lfnstPredModeIntra <= 23224 <= lfnstPredModeIntra <= 44345 <= lfnstPredModeIntra <= 55256 <= lfnstPredModeIntra <= 80181 <= lfnstPredModeIntra <= 830

The transformation matrix lowFreqTransMatrix is derived based on lfnstTrSetIdx and lfnstIdx, in regardless of the transform output length nTrS.

XIV. Flowchart

FIG.16shows a flow chart outlining an exemplary process (1600) according to an embodiment of the disclosure. In various embodiments, the process (1600) is executed by processing circuitry, such as the processing circuitry in the terminal devices (210), (220), (230) and (240), the processing circuitry that performs functions of the video encoder (303), the processing circuitry that performs functions of the video decoder (310), the processing circuitry that performs functions of the video decoder (410), the processing circuitry that performs functions of the intra prediction module (452), the processing circuitry that performs functions of the video encoder (503), the processing circuitry that performs functions of the predictor (535), the processing circuitry that performs functions of the intra encoder (622), the processing circuitry that performs functions of the intra decoder (772), and the like. In some embodiments, the process (1600) is implemented in software instructions, thus when the processing circuitry executes the software instructions, the processing circuitry performs the process (1600).

The process (1600) may generally start at step (51610), where the process (1600) decodes prediction information for a current block in a current picture that is a part of a coded video sequence. The prediction information indicates a first intra prediction mode and a secondary transform index for the current block. Then the process (1600) proceeds to step (S1620).

At step (S1620), the process (1600) determines a secondary transform core based on the first intra prediction mode and the secondary transform index. Then the process (1600) proceeds to step (S1630).

At step (S1630), the process (1600) generates a primary transform coefficient block based on the secondary transform core and a first transform coefficient block of the current block. The first transform coefficient block is de-quantized from the prediction information, and a size of the first transform coefficient block is less than a size of the secondary transform core. Then the process (1600) proceeds to step (S1640).

At step (S1640), the process (1600) reconstructs the current block based on the primary transform coefficient block.

After reconstructing the current block, the process (1600) terminates.

In an embodiment, the process (1600) generates a second transform coefficient block with a value at each coordinate position being 0. Then the process (1600) determines a value at a coordinate position of the second transform coefficient block based on a value at a same coordinate position of the first transform coefficient block. The process (1600) generates the primary transform coefficient block based on the secondary transform core and the second transform coefficient block.

In an embodiment, the process (1600) applies a part of the secondary transform core to the first transform coefficient block.

In an embodiment, the process (1600) determines whether to transpose the primary transform coefficient block based on a type of one-dimensional cross-component linear model. Then the process (1600) transposes the primary transform coefficient block based on a determination that the primary transform coefficient block is to be transposed.

According to aspects of the disclosure, syntax elements of the first transform coefficient block include a syntax element that indicates the secondary transform index.

In an embodiment, the secondary transform index is signaled after a last non-zero transform coefficient of the first transform coefficient block and before one or more of the syntax elements related to coefficient coding of the first transform coefficient block.

In an embodiment, whether one of the syntax elements is signaled is dependent on the secondary transform index and a transform coefficient associated with the one of the syntax elements.

In an embodiment, a syntax element (e.g., tu_mts_idx) indicating one or more primary transform cores for the current block is signaled after a last non-zero transform coefficient of the first transform coefficient block and before one or more syntax elements related to coefficient coding of the first transform coefficient block.

In an embodiment, the process (1600) determines a context used for entropy coding of the secondary transform index based on a shape of the secondary transform core.

In an embodiment, the process (1600) determines the secondary transform core based on the secondary transform index, a mode number of the first intra prediction mode, and a second intra prediction mode adjacent to the first intra prediction mode.

In an embodiment, the process (1600) determines a context used for entropy coding of the secondary transform index based on a mode number of the first intra prediction mode.

XV. Computer System

The presented methods may be used separately or combined in any order. Further, each of the embodiments, encoder, and decoder may be implemented by processing circuitry (e.g., one or more processors or one or more integrated circuits). In one example, the one or more processors execute a program that is stored in a non-transitory computer-readable medium.

The techniques described above, can be implemented as computer software using computer-readable instructions and physically stored in one or more computer-readable media. For example,FIG.17shows a computer system (1700) suitable for implementing certain embodiments of the disclosed subject matter.

The computer software can be coded using any suitable machine code or computer language, that may be subject to assembly, compilation, linking, or like mechanisms to create code comprising instructions that can be executed directly, or through interpretation, micro-code execution, and the like, by one or more computer central processing units (CPUs), Graphics Processing Units (GPUs), and the like.

The instructions can be executed on various types of computers or components thereof, including, for example, personal computers, tablet computers, servers, smartphones, gaming devices, internet of things devices, and the like.

The components shown inFIG.17for computer system (1700) are exemplary in nature and are not intended to suggest any limitation as to the scope of use or functionality of the computer software implementing embodiments of the present disclosure. Neither should the configuration of components be interpreted as having any dependency or requirement relating to any one or combination of components illustrated in the exemplary embodiment of a computer system (1700).

Computer system (1700) may include certain human interface input devices. Such a human interface input device may be responsive to input by one or more human users through, for example, tactile input (such as: keystrokes, swipes, data glove movements), audio input (such as: voice, clapping), visual input (such as: gestures), olfactory input (not depicted). The human interface devices can also be used to capture certain media not necessarily directly related to conscious input by a human, such as audio (such as: speech, music, ambient sound), images (such as: scanned images, photographic images obtain from a still image camera), video (such as two-dimensional video, three-dimensional video including stereoscopic video).

Input human interface devices may include one or more of (only one of each depicted): keyboard (1701), mouse (1702), trackpad (1703), touch screen (1710), data-glove (not shown), joystick (1705), microphone (1706), scanner (1707), camera (1708).

Computer system (1700) may also include certain human interface output devices. Such human interface output devices may be stimulating the senses of one or more human users through, for example, tactile output, sound, light, and smell/taste. Such human interface output devices may include tactile output devices (for example tactile feedback by the touch-screen (1710), data-glove (not shown), or joystick (1705), but there can also be tactile feedback devices that do not serve as input devices), audio output devices (such as: speakers (1709), headphones (not depicted)), visual output devices (such as screens (1710) to include CRT screens, LCD screens, plasma screens, OLED screens, each with or without touch-screen input capability, each with or without tactile feedback capability-some of which may be capable to output two dimensional visual output or more than three dimensional output through means such as stereographic output; virtual-reality glasses (not depicted), holographic displays and smoke tanks (not depicted)), and printers (not depicted). These visual output devices (such as screens (1710)) can be connected to a system bus (1748) through a graphics adapter (1750).

Computer system (1700) can also include human accessible storage devices and their associated media such as optical media including CD/DVD ROM/RW (1720) with CD/DVD or the like media (1721), thumb-drive (1722), removable hard drive or solid state drive (1723), legacy magnetic media such as tape and floppy disc (not depicted), specialized ROM/ASIC/PLD based devices such as security dongles (not depicted), and the like.

Those skilled in the art should also understand that term “computer readable media” as used in connection with the presently disclosed subject matter does not encompass transmission media, carrier waves, or other transitory signals.

Computer system (1700) can also include a network interface (1754) to one or more communication networks (1755). The one or more communication networks (1755) can for example be wireless, wireline, optical. The one or more communication networks (1755) can further be local, wide-area, metropolitan, vehicular and industrial, real-time, delay-tolerant, and so on. Examples of the one or more communication networks (1755) include local area networks such as Ethernet, wireless LANs, cellular networks to include GSM, 3G, 4G, 5G, LTE and the like, TV wireline or wireless wide area digital networks to include cable TV, satellite TV, and terrestrial broadcast TV, vehicular and industrial to include CANBus, and so forth. Certain networks commonly require external network interface adapters that attached to certain general purpose data ports or peripheral buses (1749) (such as, for example USB ports of the computer system (1700)); others are commonly integrated into the core of the computer system (1700) by attachment to a system bus as described below (for example Ethernet interface into a PC computer system or cellular network interface into a smartphone computer system). Using any of these networks, computer system (1700) can communicate with other entities. Such communication can be uni-directional, receive only (for example, broadcast TV), uni-directional send-only (for example CANbus to certain CANbus devices), or bi-directional, for example to other computer systems using local or wide area digital networks. Certain protocols and protocol stacks can be used on each of those networks and network interfaces as described above.

Aforementioned human interface devices, human-accessible storage devices, and network interfaces can be attached to a core (1740) of the computer system (1700).

The core (1740) can include one or more Central Processing Units (CPU) (1741), Graphics Processing Units (GPU) (1742), specialized programmable processing units in the form of Field Programmable Gate Areas (FPGA) (1743), hardware accelerators for certain tasks (1744), and so forth. These devices, along with Read-only memory (ROM) (1745), Random-access memory (1746), internal mass storage such as internal non-user accessible hard drives, SSDs, and the like (1747), may be connected through the system bus (1748). In some computer systems, the system bus (1748) can be accessible in the form of one or more physical plugs to enable extensions by additional CPUs, GPU, and the like. The peripheral devices can be attached either directly to the core's system bus (1748), or through a peripheral bus (1749). Architectures for a peripheral bus include PCI, USB, and the like.

CPUs (1741), GPUs (1742), FPGAs (1743), and accelerators (1744) can execute certain instructions that, in combination, can make up the aforementioned computer code. That computer code can be stored in ROM (1745) or RAM (1746). Transitional data can be also be stored in RAM (1746), whereas permanent data can be stored for example, in the internal mass storage (1747). Fast storage and retrieve to any of the memory devices can be enabled through the use of cache memory, that can be closely associated with one or more CPU (1741), GPU (1742), mass storage (1747), ROM (1745), RAM (1746), and the like.

The computer readable media can have computer code thereon for performing various computer-implemented operations. The media and computer code can be those specially designed and constructed for the purposes of the present disclosure, or they can be of the kind well known and available to those having skill in the computer software arts.

As an example and not by way of limitation, the computer system having architecture (1700), and specifically the core (1740) can provide functionality as a result of processor(s) (including CPUs, GPUs, FPGA, accelerators, and the like) executing software embodied in one or more tangible, computer-readable media. Such computer-readable media can be media associated with user-accessible mass storage as introduced above, as well as certain storage of the core (1740) that are of non-transitory nature, such as core-internal mass storage (1747) or ROM (1745). The software implementing various embodiments of the present disclosure can be stored in such devices and executed by core (1740). A computer-readable medium can include one or more memory devices or chips, according to particular needs. The software can cause the core (1740) and specifically the processors therein (including CPU, GPU, FPGA, and the like) to execute particular processes or particular parts of particular processes described herein, including defining data structures stored in RAM (1746) and modifying such data structures according to the processes defined by the software. In addition or as an alternative, the computer system can provide functionality as a result of logic hardwired or otherwise embodied in a circuit (for example: accelerator (1744)), which can operate in place of or together with software to execute particular processes or particular parts of particular processes described herein. Reference to software can encompass logic, and vice versa, where appropriate. Reference to a computer-readable media can encompass a circuit (such as an integrated circuit (IC)) storing software for execution, a circuit embodying logic for execution, or both, where appropriate. The present disclosure encompasses any suitable combination of hardware and software.

While this disclosure has described several exemplary embodiments, there are alterations, permutations, and various substitute equivalents, which fall within the scope of the disclosure. It will thus be appreciated that those skilled in the art will be able to devise numerous systems and methods which, although not explicitly shown or described herein, embody the principles of the disclosure and are thus within the spirit and scope thereof.

APPENDIX A: ACRONYMS

AMT: Adaptive Multiple TransformAMVP: Advanced Motion Vector PredictionASIC: Application-Specific Integrated CircuitATMVP: Alternative/Advanced Temporal Motion Vector PredictionBDOF: Bi-directional Optical FlowBDPCM (or RDPCM): Residual Difference Pulse Coded ModulationBIO: Bi-directional Optical FlowBMS: Benchmark SetBT: Binary TreeBV: Block VectorCANBus: Controller Area Network BusCB: Coding BlockCBF: Coded Block FlagCCLM: Cross-Component Linear Mode/ModelCD: Compact DiscCPR: Current Picture ReferencingCPU: Central Processing UnitCRT: Cathode Ray TubeCTB: Coding Tree BlockCTU: Coding Tree UnitCU: Coding UnitDM: Derived ModeDPB: Decoder Picture BufferDVD: Digital Video DiscEMT: Enhanced Multiple TransformFPGA: Field Programmable Gate AreasGOP: Group of PictureGPU: Graphics Processing UnitGSM: Global System for Mobile communicationsHDR: High Dynamic RangeHEVC: High Efficiency Video CodingHRD: Hypothetical Reference DecoderIBC: Intra Block CopyIC: Integrated CircuitIDT: Identify TransformISP: Intra Sub-PartitionsJEM: Joint Exploration ModelJVET: Joint Video Exploration TeamLAN: Local Area NetworkLCD: Liquid-Crystal DisplayLFNST: Low Frequency Non-Separable Transform, or Low Frequency Non-SeparableSecondary TransformLTE: Long-Term EvolutionL_CCLM: Left-Cross-Component Linear Mode/ModelLT_CCLM: Left and Top Cross-Component Linear Mode/ModelMIP: Matrix based Intra PredictionMPM: Most Probable ModeMRLP (or MRL): Multiple Reference Line PredictionMTS: Multiple Transform SelectionMV: Motion VectorNSST: Non-Separable Secondary TransformOLED: Organic Light-Emitting DiodePBs: Prediction BlocksPCI: Peripheral Component InterconnectPDPC: Position Dependent Prediction CombinationPLD: Programmable Logic DevicePPR: Parallel-Processable RegionPPS: Picture Parameter SetPU: Prediction UnitQT: Quad-TreeRAM: Random Access MemoryROM: Read-Only MemoryRST: Reduced-Size TransformSBT: Sub-block TransformSCC: Screen Content CodingSCIPU: Small Chroma Intra Prediction UnitSDR: Standard Dynamic RangeSEI: Supplementary Enhancement InformationSNR: Signal Noise RatioSPS: Sequence Parameter SetSSD: Solid-state DriveSVT: Spatially Varying TransformTSM: Transform Skip ModeTT: Ternary TreeTU: Transform UnitT_CCLM: Top Cross-Component Linear Mode/ModelUSB: Universal Serial BusVPDU: Visual Process Data UnitVPS: Video Parameter SetVUI: Video Usability InformationVVC: Versatile Video CodingWAIP: Wide-Angle Intra Prediction