Transform-based video coding method and apparatus

Abstract

The video decoding method according to the present document may include the steps of: deriving transform coefficients for a current block based on residual information; determining whether significant coefficients exist in a second region excluding a first region in the upper left corner of the current block; and if the significant coefficients do not exist in the second region, parsing an LFNST index from the bitstream; applying an LFNST matrix derived based on the LFNST index to the transform coefficients of the first region to derive modified transform coefficients; and deriving residual samples for the current block based on an inverse linear transform of the modified transform coefficients.

Description

[Technical Field]

[0001] This document relates to video coding technology, and more particularly to a transform-based video coding method and apparatus in a video coding system. [Background technology]

[0002] In recent years, the demand for high-resolution, high-quality images / videos, such as 4K or 8K or higher UHD (Ultra High Definition) images / videos, has been increasing in various fields. As the resolution and quality of image / video data increases, the amount of information or bits transmitted increases relatively compared to existing image / video data. Therefore, when transmitting image data using existing media such as wired or wireless broadband lines or storing image / video data using existing storage media, the transmission and storage costs increase.

[0003] In addition, interest and demand for immersive media such as VR (Virtual Reality), AR (Artificial Reality) content and holograms has been increasing in recent years, and the broadcast of images / videos with different image characteristics from real images, such as game images, is increasing.

[0004] Accordingly, there is a demand for highly efficient image / video compression technology to effectively compress and transmit, store, and play back high-resolution, high-quality image / video information having the above-mentioned various characteristics. Summary of the Invention [Problem to be solved by the invention]

[0005] The technical problem of this document is to provide a method and apparatus for improving video coding efficiency.

[0006] Another technical problem of this document is to provide a method and apparatus for improving the efficiency of transform index coding.

[0007] Another technical problem of this document is to provide a video coding method and apparatus using LFNST.

[0008] Another technical problem of this document is to provide a video coding method and apparatus for zero-out performed when LFNST is applied. [Means for solving the problem]

[0009] According to an embodiment of the present document, there is provided a video decoding method executed by a decoding device, the method including the steps of: deriving transform coefficients for a current block based on residual information; determining whether significant coefficients exist in a second region excluding a first region at an upper left corner of the current block; and if the significant coefficients do not exist in the second region, parsing an LFNST index from the bitstream; applying an LFNST matrix derived based on the LFNST index to the transform coefficients of the first region to derive modified transform coefficients; and deriving residual samples for the current block based on an inverse linear transform of the modified transform coefficients.

[0010] The first region is derived based on the size of the current block. If the size of the current block is 4x4 or 8x8, the first region is from the upper left side of the current block to the 8th sample position in the scanning direction. If the size of the current block is not 4x4 or 8x8, the first region may be a 4x4 region at the upper left side of the current block.

[0011] The scan direction may be a diagonal scan direction.

[0012] The modified transform coefficients are derived in a predetermined number based on the size of the current block. If the height and width of the current block are 8 or more, 48 modified transform coefficients are derived. If the width and height of the current block are 4 or more and the width or height of the current block is less than 8, 16 modified transform coefficients are derived.

[0013] The 48 modified transform coefficients may be arranged in the upper left, upper right, and lower left 4x4 regions of the upper left 8x8 region of the current block.

[0014] The 16 modified transform coefficients may be arranged in a 4x4 region at the upper left side of the current block.

[0015] According to an embodiment of the present document, there is provided a video encoding method performed by an encoding device, the method including the steps of: deriving residual samples for the current block based on predicted samples, deriving transform coefficients for the current block based on a linear transform of the residual samples, deriving modified transform coefficients for the current block based on transform coefficients of a first region in the upper left corner of the current block and a predetermined LFNST matrix, zeroing out a second region of the current block where the modified transform coefficients do not exist, and encoding residual information derived through quantization of the modified transform coefficients and an LFNST index indicating the LFNST matrix.

[0016] According to another embodiment of the present document, a digital storage medium may be provided that stores encoded video information generated according to a video encoding method performed by an encoding device and video data including a bitstream.

[0017] According to another embodiment of the present document, a digital storage medium may be provided that stores video data including encoded video information and a bitstream that causes a decoding device to perform the video decoding method. [Effects of the Invention]

[0018] This document can improve the overall image / video compression efficiency.

[0019] This document can improve the efficiency of transform index coding.

[0020] Another technical problem of this document is to provide a video coding method and apparatus using LFNST.

[0021] Another technical object of this document is to provide a video coding method and apparatus for zero-out performed when LFNST is applied.

[0022] The effects obtained through the specific examples of this specification are not limited to the effects listed above. For example, there may be various technical effects that a person having ordinary skill in the related art can understand or derive from this specification. Therefore, the specific effects of this specification are not limited to those explicitly described in this specification, but may include various effects that can be understood or derive from the technical features of this specification. [Brief explanation of the drawings]

[0023] [Figure 1] 1 illustrates, in simplified form, an example of a video / image coding system to which this document may be applied. [Figure 2] 1 is a diagram illustrating the configuration of a video / image encoding device to which this document can be applied. [Figure 3]1 is a diagram illustrating the configuration of a video / image decoding device to which this document can be applied. [Figure 4] 1 illustrates a schematic diagram of a multiple conversion technique according to an embodiment of the present document; [Figure 5] 65 intra-directional modes of prediction directions are shown exemplarily. [Figure 6] FIG. 1 is a diagram for explaining an RST according to one embodiment of this document. [Figure 7] FIG. 10 is a diagram illustrating an example of an order in which output data of a forward linear transform is arranged into a one-dimensional vector. [Figure 8] FIG. 10 is a diagram illustrating an example of an order in which output data of a forward quadratic transform is arranged into a two-dimensional vector. [Figure 9] FIG. 1 illustrates a wide-angle intra-prediction mode according to one embodiment of the present document. [Figure 10] FIG. 10 is a diagram showing the shape of a block to which LFNST is applied. [Figure 11] FIG. 10 is a diagram showing an example of an arrangement of output data from a forward LFNST. [Figure 12] 13 is a diagram illustrating an example in which the number of output data for a forward LFNST is limited to a maximum of 16. FIG. [Figure 13] FIG. 10 is a diagram illustrating zeroing out in a block to which a 4×4 LFNST is applied, according to an example. [Figure 14] FIG. 10 is a diagram illustrating zeroing out in a block to which an 8×8 LFNST is applied, according to an example. [Figure 15] FIG. 10 is a diagram illustrating zeroing out in a block to which 8×8 LFNST is applied according to another example. [Figure 16] 1 is a diagram illustrating an example of a method for decoding an image; [Figure 17] 1 is a diagram illustrating an example of a video encoding method; [Figure 18] 1 illustrates an exemplary structural diagram of a content streaming system to which this document applies. DETAILED DESCRIPTION OF THE INVENTION

[0024] Although this document may be modified in various ways and may have various embodiments, specific embodiments will be illustrated in the drawings and described in detail. However, this is not intended to limit this document to the specific embodiment. Common terms used in this specification are used merely to describe specific embodiments and are not intended to limit the technical ideas of this document. A singular expression includes a plural expression unless the context clearly indicates otherwise. In this specification, terms such as "comprise" or "have" are intended to specify the presence of features, numbers, steps, operations, components, parts, or combinations thereof described in the specification, and should be understood not to preclude the possibility of the presence or addition of one or more different features, numbers, steps, operations, components, parts, or combinations thereof.

[0025] Meanwhile, each component in the drawings described in this document is shown independently for the convenience of explaining the different characteristic functions, and does not mean that each component is realized by separate hardware or software. For example, two or more components may be combined to form a single component, or a single component may be divided into multiple components. Embodiments in which each component is integrated and / or separated are also included within the scope of this document as long as they do not deviate from the essence of this document.

[0026] Hereinafter, preferred embodiments of the present invention will be described in more detail with reference to the accompanying drawings. Hereinafter, the same reference numerals will be used to refer to the same components in the drawings, and redundant description of the same components will be omitted.

[0027] This document relates to video / image coding. For example, methods / embodiments disclosed in this document may be related to the Versatile Video Coding (VVC) standard (ITU-T Rec. H.266), next-generation video / image coding standards beyond VVC, or other video coding-related standards (e.g., the High Efficiency Video Coding (HEVC) standard (ITU-T Rec. H.265), the essential video coding (EVC) standard, the AVS2 standard, etc.).

[0028] This document presents various embodiments relating to video / image coding, which may be implemented in combination with one another unless otherwise specified.

[0029] In this document, video can refer to a collection of a series of images over time. A picture generally refers to a unit that shows one image at a specific time, and a slice / tile is a unit that constitutes part of a picture in coding. A slice / tile can contain one or more coding tree units (CTUs). One picture can be composed of one or more slices / tiles. One picture can be composed of one or more tile groups. One tile group can contain one or more tiles.

[0030] A pixel or a pel can refer to the smallest unit constituting one picture (or image). A "sample" can also be used as a term corresponding to a pixel. A sample may generally refer to a pixel or a pixel value, or may refer to only a pixel / pixel value of a luma component, or may refer to only a pixel / pixel value of a chroma component. Alternatively, a sample may refer to a pixel value in the spatial domain, or, when such a pixel value is transformed into the frequency domain, may refer to a transform coefficient in the frequency domain.

[0031] A unit may refer to a basic unit of video processing. A unit may include at least one of a specific region of a picture and information about the region. One unit may include one luma block and two chroma (e.g., cb, cr) blocks. The term unit may be used interchangeably with terms such as block or area, depending on the situation. In a general case, an M×N block may include a set (or array) of samples or transform coefficients consisting of M columns and N rows.

[0032] In this document, the terms " / " and "," should be interpreted to mean "and / or." For example, "A / B" means "A and / or B," and "A, B" means "A and / or B." Furthermore, "A / B / C" means "at least one of A, B, and / or C." Also, "A, B, C" means "at least one of A, B, and / or C." (In this document, the terms " / " and "," should be interpreted to indicate "and / or." For instance, the expression "A / B" may mean "A and / or B." Further, "A, B" may mean "A and / or B." Further, "A / B / C" may mean "at least one of A, B, and / or C." Also, "A / B / C" may mean "at least one of A, B, and / or C.")

[0033] Furthermore, in this document, "or" should be interpreted as "and / or." For example, "A or B" may mean 1) only "A," 2) only "B," or 3) "A and B." In other words, "or" in this document may mean "additionally or alternatively." (Further, in the document, the term "or" should be interpreted to indicate "and / or." For instance, the expression "A or B" may comprise 1) only A, 2) only B, and / or 3) both A and B. In other words, the term "or" in this document should be interpreted to indicate "additionally or alternatively.")

[0034] As used herein, "at least one of A and B" can mean "only A," "only B," or "both A and B." Furthermore, as used herein, the expressions "at least one of A or B" and "at least one of A and / or B" can be interpreted in the same way as "at least one of A and B."

[0035] Furthermore, in this specification, "at least one of A, B, and C" can mean "only A," "only B," "only C," or "any combination of A, B, and C." Furthermore, "at least one of A, B, or C" or "at least one of A, B, and / or C" can mean "at least one of A, B, and C."

[0036] Furthermore, parentheses used herein may mean "for example." Specifically, when "prediction (intra prediction)" is displayed, "intra prediction" may be suggested as an example of "prediction." In other words, "prediction" in this specification is not limited to "intra prediction," and "intra prediction" may be suggested as an example of "prediction." Furthermore, when "prediction (i.e., intra prediction)" is displayed, "intra prediction" may be suggested as an example of "prediction."

[0037] Technical features individually described in one drawing in this specification may be embodied individually or simultaneously.

[0038] FIG. 1 illustrates schematically an example of a video / image coding system to which this document may be applied.

[0039] 1, a video / image coding system may include a source device and a receiving device. The source device may transmit encoded video / image information or data to the receiving device via a digital storage medium or a network in the form of a file or streaming.

[0040] The source device may include a video source, an encoding device, and a transmitting unit. The receiving device may include a receiving unit, a decoding device, and a renderer. The encoding device may be referred to as a video / video encoding device, and the decoding device may be referred to as a video / video decoding device. The transmitter may be included in the encoding device. The receiver may be included in the decoding device. The renderer may include a display unit, which may be a separate device or an external component.

[0041] A video source can acquire video / images through a video / image capture, synthesis, or generation process. A video source can include a video / image capture device and / or a video / image generation device. A video / image capture device can include, for example, one or more cameras, a video / image archive containing previously captured video / images, etc. A video / image generation device can include, for example, a computer, a tablet, a smartphone, etc., and can (electronically) generate video / images. For example, a virtual video / image can be generated via a computer, etc., in which case the video / image capture process can be replaced by a process in which related data is generated.

[0042] An encoding device can encode input video / images. The encoding device can perform a series of steps such as prediction, transformation, and quantization for compression and coding efficiency. The encoded data (encoded video / image information) can be output in the form of a bitstream.

[0043] The transmitter may transmit the encoded video / image information or data output in the form of a bitstream to a receiver of a receiving device via a digital storage medium or a network in the form of a file or streaming. The digital storage medium may include various storage media such as USB, SD, CD, DVD, Blu-ray, HDD, SSD, etc. The transmitter may include elements for generating a media file in a predetermined file format and elements for transmission via a broadcasting / communication network. The receiver may receive / extract the bitstream and transmit it to a decoding device.

[0044] The decoding device can decode the video / image by performing a series of steps such as inverse quantization, inverse transform, and prediction, which correspond to the operations of the encoding device.

[0045] The renderer can render the decoded video / image, and the rendered video / image can be displayed via a display unit.

[0046] 2 is a diagram illustrating the configuration of a video / image encoding device to which this document can be applied. Hereinafter, the term "video encoding device" may include a video encoding device.

[0047] Referring to FIG. 2, the encoding apparatus 200 may include an image partitioner 210, a predictor 220, a residual processor 230, an entropy encoder 240, an adder 250, a filter 260, and a memory 270. The predictor 220 may include an inter predictor 221 and an intra predictor 222. The residual processor 230 may include a transformer 232, a quantizer 233, a dequantizer 234, and an inverse transformer 235. The residual processor 230 may further include a subtractor 231. The adder 250 may be referred to as a reconstructor or a reconstructed block generator. The image dividing unit 210, the predicting unit 220, the residual processing unit 230, the entropy encoding unit 240, the adding unit 250, and the filtering unit 260 may be configured by one or more hardware components (e.g., an encoder chipset or a processor) depending on the embodiment. Also, the memory 270 may include a decoded picture buffer (DPB) and may be configured by a digital storage medium. The hardware components may further include the memory 270 as an internal / external component.

[0048] The image division unit 210 may divide an input image (or picture or frame) input to the encoding device 200 into one or more processing units. For example, the processing units may be called coding units (CUs). In this case, the coding units may be recursively divided from a coding tree unit (CTU) or a largest coding unit (LCU) according to a quad-tree, binary-tree, ternary-tree (QTBTTT) structure. For example, one coding unit may be divided into multiple coding units of deeper depths based on a quad-tree structure, a binary tree structure, and / or a ternary structure. In this case, for example, the quad-tree structure may be applied first, and then the binary tree structure and / or the ternary structure may be applied. Alternatively, the binary tree structure may be applied first. The coding procedure described herein may be performed based on the final coding unit that is not further divided. In this case, the largest coding unit may be immediately used as the final coding unit based on coding efficiency according to image characteristics, or the coding unit may be recursively divided into coding units of lower depths as needed, and the coding unit of the optimal size may be used as the final coding unit. Here, the coding procedure may include procedures such as prediction, transformation, and restoration, which will be described later. As another example, the processing unit may further include a prediction unit (PU) or a transform unit (TU). In this case, the prediction unit and the transform unit may each be divided or partitioned from the final coding unit.The prediction unit may be a unit of sample prediction, and the transform unit may be a unit for deriving transform coefficients and / or a unit for deriving a residual signal from the transform coefficients.

[0049] The term "unit" can be used interchangeably with terms such as "block" or "area" depending on the situation. In a general case, an MxN block can refer to a set of samples or transform coefficients consisting of M columns and N rows. A sample can generally refer to a pixel or pixel value, or can refer to only a pixel / pixel value of a luma component, or only a pixel / pixel value of a chroma component. A sample can be used as a term corresponding to one pixel or pel of a picture (or image).

[0050] The subtraction unit 231 may subtract a prediction signal (predicted block, prediction sample, or prediction sample array) output from the prediction unit 220 from an input video signal (original block, original sample, or original sample array) to generate a residual signal (residual block, residual sample, or residual sample array), and the generated residual signal is transmitted to the conversion unit 232. The prediction unit 220 may perform prediction on a block to be processed (hereinafter, referred to as a current block) and generate a predicted block including prediction samples for the current block. The prediction unit 220 may determine whether intra prediction or inter prediction is applied in units of the current block or CU. The prediction unit may generate various information related to prediction, such as prediction mode information, and transmit the information to the entropy encoding unit 240, as will be described later in the description of each prediction mode. The prediction information may be encoded by the entropy encoding unit 240 and output in the form of a bitstream.

[0051] The intra prediction unit 222 may predict the current block by referring to samples in the current picture. The referenced samples may be located in the neighborhood of the current block or may be located far away, depending on the prediction mode. Prediction modes in intra prediction may include a plurality of non-directional modes and a plurality of directional modes. The non-directional modes may include, for example, DC mode and planar mode. The directional modes may include, for example, 33 directional prediction modes or 65 directional prediction modes depending on the granularity of the prediction direction. However, this is merely an example, and more or less directional prediction modes may be used depending on the settings. The intra prediction unit 222 may also determine the prediction mode to be applied to the current block using the prediction modes applied to neighboring blocks.

[0052] The inter prediction unit 221 may derive a predicted block for a current block based on a reference block (reference sample array) identified by a motion vector on a reference picture. To reduce the amount of motion information transmitted in inter prediction mode, the motion information may be predicted in units of blocks, sub-blocks, or samples based on the correlation of motion information between neighboring blocks and the current block. The motion information may include a motion vector and a reference picture index. The motion information may further include information on the inter prediction direction (such as L0 prediction, L1 prediction, or Bi prediction). In the case of inter prediction, the neighboring blocks may include spatial neighboring blocks present in the current picture and temporal neighboring blocks present in the reference picture. The reference picture including the reference block and the reference picture including the temporal neighboring block may be the same or different. The temporal neighboring block may be called a collocated reference block, a collocated CU (col CU), or the like, and the reference picture including the temporal neighboring block may be called a collocated picture (colPic). For example, the inter predictor 221 may construct a motion information candidate list based on neighboring blocks and generate information indicating which candidate is used to derive a motion vector and / or a reference picture index for the current block. Inter prediction may be performed based on various prediction modes. For example, in the case of skip mode and merge mode, the inter predictor 221 may use motion information of neighboring blocks as motion information for the current block. In the case of skip mode, unlike in merge mode, a residual signal may not be transmitted.In the case of motion vector prediction (MVP) mode, the motion vector of the current block can be indicated by using the motion vector of a neighboring block as a motion vector predictor and signaling the motion vector difference.

[0053] The predictor 220 may generate a prediction signal based on various prediction methods, which will be described later. For example, the predictor may not only apply intra prediction or inter prediction for prediction of a block, but also apply intra prediction and inter prediction simultaneously. This may be referred to as combined inter and intra prediction (CIIP). The predictor may also perform intra block copy (IBC) for prediction of a block. The intra block copy may be used, for example, for coding content images / videos such as games, such as screen content coding (SCC). IBC basically performs prediction within a current picture, but may be performed similarly to inter prediction in deriving a reference block within the current picture. That is, IBC may use at least one of the inter prediction techniques described herein.

[0054] The prediction signal generated by the inter prediction unit 221 and / or the intra prediction unit 222 may be used to generate a reconstructed signal or a residual signal. The transform unit 232 may generate transform coefficients by applying a transform technique to the residual signal. For example, the transform technique may include a discrete cosine transform (DCT), a discrete sine transform (DST), a graph-based transform (GBT), or a conditionally non-linear transform (CNT). Here, GBT refers to a transform obtained from a graph representing relationship information between pixels. CNT refers to a transform obtained based on a prediction signal generated using all previously reconstructed pixels. In addition, the transform process may be applied to pixel blocks having the same square size or to non-square blocks of variable size.

[0055] The quantization unit 233 quantizes the transform coefficients and transmits the quantized signal to the entropy encoding unit 240. The entropy encoding unit 240 encodes the quantized signal (information about the quantized transform coefficients) and outputs the encoded signal as a bitstream. The information about the quantized transform coefficients may be referred to as residual information. The quantization unit 233 may rearrange the quantized transform coefficients in a block form into a one-dimensional vector form based on a coefficient scan order, and may generate information about the quantized transform coefficients based on the quantized transform coefficients in the one-dimensional vector form. The entropy encoding unit 240 may perform various encoding methods, such as exponential Golomb, context-adaptive variable length coding (CAVLC), context-adaptive binary arithmetic coding (CABAC), etc. The entropy encoding unit 240 may encode information required for video / image reconstruction (e.g., values ​​of syntax elements, etc.) together with or separately from the quantized transform coefficients. The encoded information (e.g., encoded video / image information) may be transmitted or stored in the form of a bitstream in network abstraction layer (NAL) units. The video / image information may further include information on various parameter sets, such as an adaptation parameter set (APS), a picture parameter set (PPS), a sequence parameter set (SPS), or a video parameter set (VPS). The video / image information may also include general constraint information. Signaled / transmitted information and / or syntax elements described later in this document may be encoded through the encoding procedures described above and included in the bitstream.The bitstream may be transmitted via a network or stored in a digital storage medium. Here, the network may include a broadcasting network and / or a communication network, and the digital storage medium may include various storage media such as a USB, SD, CD, DVD, Blu-ray, HDD, SSD, etc. A transmitter (not shown) for transmitting the signal output from the entropy encoding unit 240 and / or a storage unit (not shown) for storing the signal may be configured as an internal / external element of the encoding apparatus 200, or the transmitter may be included in the entropy encoding unit 240.

[0056] The quantized transform coefficients output from the quantization unit 233 may be used to generate a prediction signal. For example, a residual signal (residual block or residual sample) may be reconstructed by applying inverse quantization and inverse transform to the quantized transform coefficients via the inverse quantization unit 234 and the inverse transform unit 235. The adder 250 may generate a reconstructed signal (reconstructed picture, reconstructed block, reconstructed sample, or reconstructed sample array) by adding the reconstructed residual signal to the prediction signal output from the prediction unit 220. When there is no residual for the current block, such as when skip mode is applied, the predicted block may be used as the reconstructed block. The generated reconstructed signal may be used for intra prediction of the next block to be processed in the current picture, and may also be used for inter prediction of the next picture after filtering, as described below.

[0057] Meanwhile, luma mapping with chroma scaling (LMCS) can be applied during picture encoding and / or reconstruction.

[0058] The filtering unit 260 may apply filtering to the reconstructed signal to improve subjective / objective image quality. For example, the filtering unit 260 may apply various filtering methods to the reconstructed picture to generate a modified reconstructed picture and store the modified reconstructed picture in the memory 270, specifically, in the DPB of the memory 270. The various filtering methods may include, for example, deblocking filtering, sample adaptive offset (SAO), an adaptive loop filter, a bilateral filter, etc. The filtering unit 260 may generate various information related to filtering and transmit it to the entropy encoding unit 290, as will be described later in connection with each filtering method. The filtering information may be encoded by the entropy encoding unit 290 and output in the form of a bitstream.

[0059] The modified reconstructed picture transmitted to the memory 270 can be used as a reference picture in the inter prediction unit 280. When inter prediction is applied through this, the encoding apparatus can avoid a mismatch in prediction between the encoding apparatus 200 and the decoding apparatus, and can also improve coding efficiency.

[0060] The DPB of the memory 270 may store the modified reconstructed picture to be used as a reference picture in the inter predictor 221. The memory 270 may store motion information of a block from which motion information in the current picture is derived (or encoded) and / or motion information of a block in an already reconstructed picture. The stored motion information may be transmitted to the inter predictor 221 to be used as motion information of a spatially neighboring block or a temporally neighboring block. The memory 270 may store reconstructed samples of reconstructed blocks in the current picture and transmit them to the intra predictor 222.

[0061] FIG. 3 is a diagram illustrating the configuration of a video / image decoding device to which this document can be applied.

[0062] Referring to FIG. 3, the decoding device 300 may include an entropy decoder 310, a residual processor 320, a predictor 330, an adder 340, a filter 350, and a memory 360. The predictor 330 may include an inter predictor 331 and an intra predictor 332. The residual processor 320 may include a dequantizer 321 and an inverse transformer 321. Depending on the embodiment, the entropy decoding unit 310, the residual processor 320, the predictor 330, the adder 340, and the filter 350 may be configured as a single hardware component (e.g., a decoder chipset or processor). In addition, the memory 360 may include a decoded picture buffer (DPB) and may be configured as a digital storage medium. The hardware components may further include a memory 360 as an internal / external component.

[0063] When a bitstream including video / image information is input, the decoding apparatus 300 can reconstruct an image corresponding to the process by which the video / image information was processed by the encoding apparatus of FIG. 2. For example, the decoding apparatus 300 can derive units / blocks based on information about block division obtained from the bitstream. The decoding apparatus 300 can perform decoding using a processing unit applied by the encoding apparatus. Therefore, the processing unit for decoding may be, for example, a coding unit, and the coding unit may be divided from a coding tree unit or a maximal coding unit according to a quad tree structure, a binary tree structure, and / or a ternary tree structure. One or more transform units may be derived from the coding unit. The reconstructed image signal decoded and output by the decoding apparatus 300 can be played back via a playback device.

[0064] The decoding apparatus 300 may receive a signal output from the encoding apparatus of FIG. 2 in the form of a bitstream, and the received signal may be decoded via the entropy decoding unit 310. For example, the entropy decoding unit 310 may parse the bitstream to derive information (e.g., video / video information) necessary for video restoration (or picture restoration). The video / video information may further include information on various parameter sets, such as an adaptation parameter set (APS), a picture parameter set (PPS), a sequence parameter set (SPS), or a video parameter set (VPS). The video / video information may also include general constraint information. The decoding apparatus may further decode pictures based on the information on the parameter sets and / or the general constraint information. Signaling / received information and / or syntax elements, which will be described later in this document, may be decoded via the decoding procedure and obtained from the bitstream. For example, the entropy decoding unit 310 may decode information in a bitstream based on a coding method such as Exponential-Golomb coding, CAVLC, or CABAC, and output values ​​of syntax elements required for image restoration and quantized values ​​of transform coefficients related to residuals. More specifically, the CABAC entropy decoding method receives bins corresponding to each syntax element in the bitstream, determines a context model using information on the syntax element to be decoded, decoding information on neighboring and current blocks, or information on symbols / bins decoded in previous steps, predicts the occurrence probability of the bins based on the determined context model, and performs arithmetic decoding of the bins to generate symbols corresponding to the values ​​of each syntax element.In this case, after determining a context model, the CABAC entropy decoding method can update the context model using information about the decoded symbol / bin for the context model of the next symbol / bin. Prediction-related information from the information decoded by the entropy decoding unit 310 is provided to the prediction unit 330, and information about the residual on which entropy decoding is performed by the entropy decoding unit 310, i.e., quantized transform coefficients and related parameter information, can be input to the inverse quantization unit 321. In addition, filtering-related information from the information decoded by the entropy decoding unit 310 can be provided to the filtering unit 350. Meanwhile, a receiving unit (not shown) that receives a signal output from the encoding apparatus can be further configured as an internal / external element of the decoding apparatus 300, or the receiving unit can be a component of the entropy decoding unit 310. Meanwhile, the decoding device according to this document may be called a video / image / picture decoding device, and the decoding device may be divided into an information decoder (video / image / picture information decoder) and a sample decoder (video / image / picture sample decoder). The information decoder may include the entropy decoding unit 310, and the sample decoder may include at least one of the inverse quantization unit 321, the inverse transform unit 322, the prediction unit 330, the addition unit 340, the filtering unit 350, and the memory 360.

[0065] The inverse quantization unit 321 can inverse quantize the quantized transform coefficients and output transform coefficients. The inverse quantization unit 321 can rearrange the quantized transform coefficients in a two-dimensional block format. In this case, the rearrangement can be performed based on the coefficient scanning order performed in the encoding device. The inverse quantization unit 321 can perform inverse quantization on the quantized transform coefficients using a quantization parameter (e.g., quantization step size information) to obtain transform coefficients.

[0066] The inverse transform unit 322 performs an inverse transform on the transform coefficients to obtain a residual signal (residual block, residual sample array).

[0067] The prediction unit may perform prediction on a current block and generate a predicted block including prediction samples for the current block. The prediction unit may determine whether intra prediction or inter prediction is applied to the current block based on the prediction information output from the entropy decoding unit 310, and may determine a specific intra / inter prediction mode.

[0068] The predictor may generate a prediction signal based on various prediction methods, which will be described later. For example, the predictor may not only apply intra prediction or inter prediction for prediction of a block, but also apply intra prediction and inter prediction simultaneously. This may be referred to as combined inter and intra prediction (CIIP). The predictor may also perform intra block copy (IBC) for prediction of a block. The intra block copy may be used for content image / video coding, such as games, such as screen content coding (SCC). IBC basically performs prediction within a current picture, but may be performed similarly to inter prediction in deriving a reference block within the current picture. That is, IBC may utilize at least one of the inter prediction techniques described herein.

[0069] The intra prediction unit 332 can predict the current block by referring to samples in the current picture. The referenced samples may be located in the neighborhood of the current block or may be located far away from the current block depending on the prediction mode. Prediction modes in intra prediction can include a plurality of non-directional modes and a plurality of directional modes. The intra prediction unit 332 can also determine the prediction mode to be applied to the current block using the prediction modes applied to neighboring blocks.

[0070] The inter prediction unit 331 may derive a predicted block for a current block based on a reference block (reference sample array) identified by a motion vector on a reference picture. To reduce the amount of motion information transmitted in inter prediction mode, the motion information may be predicted in units of blocks, sub-blocks, or samples based on the correlation of motion information between neighboring blocks and the current block. The motion information may include a motion vector and a reference picture index. The motion information may further include information on the inter prediction direction (e.g., L0 prediction, L1 prediction, Bi prediction, etc.). In the case of inter prediction, the neighboring blocks may include spatial neighboring blocks present in the current picture and temporal neighboring blocks present in the reference picture. For example, the inter prediction unit 331 may construct a motion information candidate list based on the neighboring blocks and derive a motion vector and / or a reference picture index for the current block based on received candidate selection information. Inter prediction may be performed based on various prediction modes, and the prediction information may include information indicating the inter prediction mode for the current block.

[0071] The adder 340 may generate a reconstructed signal (reconstructed picture, reconstructed block, reconstructed sample array) by adding the obtained residual signal to the predicted signal (predicted block, predicted sample array) output from the prediction unit 330. When there is no residual for the current block, such as when skip mode is applied, the predicted block may be used as the reconstructed block.

[0072] The adder 340 may be referred to as a reconstruction unit or a reconstruction block generator. The generated reconstruction signal may be used for intra prediction of a next block to be processed in the current picture, may be output after filtering as described below, or may be used for inter prediction of a next picture.

[0073] Meanwhile, LMCS (luma mapping with chroma scaling) can be applied during picture decoding.

[0074] The filtering unit 350 may apply filtering to the reconstructed signal to improve subjective / objective image quality. For example, the filtering unit 350 may apply various filtering methods to the reconstructed picture to generate a modified reconstructed picture, and may transmit the modified reconstructed picture to the memory 360, specifically, to the DPB of the memory 360. The various filtering methods may include, for example, deblocking filtering, sample adaptive offset, an adaptive loop filter, a bilateral filter, etc.

[0075] The (modified) reconstructed picture stored in the DPB of the memory 360 can be used as a reference picture in the inter predictor 331. The memory 360 can store motion information of a block from which motion information in the current picture is derived (or decoded) and / or motion information of a block in an already reconstructed picture. The stored motion information can be transmitted to the inter predictor 331 to be used as motion information of a spatially neighboring block or a temporally neighboring block. The memory 360 can store reconstructed samples of reconstructed blocks in the current picture and transmit them to the intra predictor 332.

[0076] In this specification, the embodiments described for the prediction unit 330, inverse quantization unit 321, inverse transform unit 322, and filtering unit 350 of the decoding device 300 can also be applied identically or correspondingly to the prediction unit 220, inverse quantization unit 234, inverse transform unit 235, and filtering unit 260 of the decoding device 200, respectively.

[0077] As described above, prediction is performed to improve compression efficiency when performing video coding. Through this, a predicted block including predicted samples for a current block, which is a block to be coded, can be generated. Here, the predicted block includes predicted samples in the spatial domain (or pixel domain). The predicted block is derived in the same way by an encoding device and a decoding device. The encoding device can improve video coding efficiency by signaling to the decoding device information regarding the residual between the original block and the predicted block (residual information) rather than the original sample values ​​of the original block. The decoding device can derive a residual block including residual samples based on the residual information, combine the residual block with the predicted block to generate a reconstructed block including reconstructed samples, and generate a reconstructed picture including the reconstructed block.

[0078] The residual information may be generated through a transform and quantization procedure. For example, an encoding device may derive a residual block between the original block and the predicted block, perform a transform procedure on residual samples (residual sample array) included in the residual block to derive transform coefficients, perform a quantization procedure on the transform coefficients to derive quantized transform coefficients, and signal the related residual information (via a bitstream) to a decoding device. Here, the residual information may include information such as value information, position information, transform technique, transform kernel, and quantization parameter of the quantized transform coefficients. The decoding device may derive residual samples (or residual blocks) by performing an inverse quantization / inverse transform procedure based on the residual information. The decoding device may generate a reconstructed picture based on the predicted block and the residual block. The encoding device may also derive a residual block by inverse quantizing / inverse transforming quantized transform coefficients for reference for inter-prediction of a subsequent picture, and generate a reconstructed picture based on the residual block.

[0079] FIG. 4 shows a schematic diagram of the multiple transformation technique according to this document.

[0080] Referring to Figure 4, the transform unit may correspond to the transform unit in the encoding device of Figure 2 described above, and the inverse transform unit may correspond to the inverse transform unit in the encoding device of Figure 2 described above or the inverse transform unit in the decoding device of Figure 3.

[0081] The transform unit may perform a primary transform based on the residual samples (residual sample array) in the residual block to derive (primary) transform coefficients (S410). Such a primary transform may be referred to as a core transform. Here, the primary transform may be based on Multiple Transform Selection (MTS), and when multiple transforms are applied as the primary transform, it may be referred to as a multiple core transform.

[0082] The multi-kernel transform may refer to a transform method further using a Discrete Cosine Transform (DCT) type 2, a Discrete Sine Transform (DST) type 7, a DCT type 8, and / or a DST type 1. That is, the multi-kernel transform may refer to a transform method for transforming a spatial domain residual signal (or a residual block) into frequency domain transform coefficients (or first-order transform coefficients) based on a plurality of transform kernels selected from the DCT type 2, the DST type 7, the DCT type 8, and the DST type 1. Here, the first-order transform coefficients may be referred to as tentative transform coefficients from the perspective of a transform unit.

[0083] In other words, when an existing transform method is applied, a spatial-domain to frequency-domain transform is applied to a residual signal (or residual block) based on DCT type 2 to generate transform coefficients. In contrast, when the multi-kernel transform is applied, a spatial-domain to frequency-domain transform is applied to a residual signal (or residual block) based on DCT type 2, DST type 7, DCT type 8, and / or DST type 1, etc. to generate transform coefficients (or primary transform coefficients). Here, DCT type 2, DST type 7, DCT type 8, DST type 1, etc. may be referred to as transform types, transform kernels, or transform cores. Such DCT / DST transform types may be defined based on basis functions.

[0084] When the multi-kernel transform is performed, a vertical transform kernel and a horizontal transform kernel for a current block may be selected from the transform kernels, and a vertical transform for the current block may be performed based on the vertical transform kernel, and a horizontal transform for the current block may be performed based on the horizontal transform kernel. Here, the horizontal transform may indicate a transform for a horizontal component of the current block, and the vertical transform may indicate a transform for a vertical component of the current block. The vertical transform kernel / horizontal transform kernel may be adaptively determined based on a prediction mode and / or a transform index of a current block (CU or sub-block) including a residual block.

[0085] Also, according to one example, when a linear transform is performed by applying MTS, a specific basis function is set to a predetermined value, and when it is a vertical transform or a horizontal transform, a mapping relationship for the transform kernel can be set by combining which basis function is applied or not. For example, if the horizontal transform kernel is represented by trTypeHor and the vertical transform kernel is represented by trTypeVer, a value of 0 for trTypeHor or trTypeVer can be set to DCT2, a value of 1 for trTypeHor or trTypeVer can be set to DCT7, and a value of 2 for trTypeHor or trTypeVer can be set to DCT8.

[0086] In this case, MTS index information can be encoded and signaled to a decoding device to indicate one of a number of transform kernel sets. For example, an MTS index of 0 indicates that the values ​​of trTypeHor and trTypeVer are all 0, an MTS index of 1 indicates that the values ​​of trTypeHor and trTypeVer are all 1, an MTS index of 2 indicates that the value of trTypeHor is 2 and the value of trTypeVer is 1, an MTS index of 3 indicates that the value of trTypeHor is 1 and the value of trTypeVer is 2, and an MTS index of 4 indicates that the values ​​of trTypeHor and trTypeVer are all 2.

[0087] As an example, a conversion kernel set according to index information of MTS is shown in the table below.

[0088] [Table 1]

[0089] The transform unit may perform a secondary transform based on the (primary) transform coefficients to derive modified (secondary) transform coefficients (S420). The primary transform is a transform from the spatial domain to the frequency domain, and the secondary transform refers to a transform using correlations existing between the (primary) transform coefficients to a more compressed representation. The secondary transform may include a non-separable transform. In this case, the secondary transform may be referred to as a non-separable secondary transform (NSST) or a mode-dependent non-separable secondary transform (MDNSST). The non-separable secondary transform may refer to a transform that performs a secondary transform on the (primary) transform coefficients derived through the primary transform based on a non-separable transform matrix to generate modified transform coefficients (or secondary transform numbers) for the residual signal. Here, based on the non-separable transform matrix, the (first-order) transform coefficients may be simultaneously subjected to a vertical transform and a horizontal transform without being separately applied (or the horizontal-vertical transform independently). In other words, the non-separable second-order transform may refer to a transform method in which, for example, a two-dimensional signal (transform coefficient) is rearranged into a one-dimensional signal in a specific direction (e.g., row-first direction or column-first direction) without separating the vertical and horizontal components of the (first-order) transform coefficients, and then a modified transform coefficient (or second-order transform coefficient) is generated based on the non-separable transform matrix. For example, the row-major order is an arrangement of a first row, a second row, ..., an Nth row for an MxN block, and the column-major order is an arrangement of a first column, a second column, ..., an Mth column for an MxN block. The non-separable quadratic transform may be applied to the top-left region of a block composed of (first-order) transform coefficients (hereinafter, referred to as a transform coefficient block).For example, if the width (W) and height (H) of the transform coefficient block are both equal to or greater than 8, an 8x8 non-separable quadratic transform may be applied to the 8x8 region at the upper left of the transform coefficient block. Also, if the width (W) and height (H) of the transform coefficient block are both equal to or greater than 4 and the width (W) or height (H) of the transform coefficient block is less than 8, a 4x4 non-separable quadratic transform may be applied to the min(8,W) x min(8,H) region at the upper left of the transform coefficient block. However, the embodiment is not limited thereto. For example, even if the width (W) or height (H) of the transform coefficient block is both equal to or greater than 4, a 4x4 non-separable quadratic transform may also be applied to the min(8,W) x min(8,H) region at the upper left of the transform coefficient block.

[0090] Specifically, for example, if a 4x4 input block is used, the non-separable quadratic transform can be performed as follows:

[0091] The 4x4 input block X can be expressed as follows:

[0092]

number

[0093] When X is expressed in the form of a vector, the vector TIFF0007736573000003.tif84 can be displayed as follows:

[0094]

number

[0095] As shown in Equation 2, the vector TIFF0007736573000005.tif84 rearranges the two-dimensional block of X in Equation 1 into a one-dimensional vector in row-first order.

[0096] In this case, the second-order non-separable transform can be calculated as follows:

[0097]

number

[0098] where: TIFF0007736573000007.tif75 denotes the transform coefficient vector, and T denotes the 16x16 (non-separable) transform matrix.

[0099] Through Equation 3, a 16×1 transform coefficient vector TIFF0007736573000008.tif75 can be derived, TIFF0007736573000009.tif75 can be re-organized into 4x4 blocks via the scan order (horizontal, vertical, diagonal, etc.). However, the above calculation is an example, and in order to reduce the computational complexity of the non-separable quadratic transform, HyGT (Hypercube-Givens Transform) or the like can also be used to calculate the non-separable quadratic transform.

[0100] Meanwhile, the non-separable quadratic transform may be mode-dependent, with the transform kernel (or transform core, transform type) being selectable, where the mode may include an intra-prediction mode and / or an inter-prediction mode.

[0101] As described above, the non-separable quadratic transform may be performed based on an 8x8 transform or a 4x4 transform determined based on the width (W) and height (H) of the transform coefficient block. The 8x8 transform refers to a transform that can be applied to an 8x8 region contained within the transform coefficient block when W and H are both equal to or greater than 8, and the 8x8 region may be the upper-left 8x8 region within the transform coefficient block. Similarly, the 4x4 transform refers to a transform that can be applied to a 4x4 region contained within the transform coefficient block when W and H are both equal to or greater than 4, and the 4x4 region may be the upper-left 4x4 region within the transform coefficient block. For example, an 8x8 transform kernel matrix may be a 64x64 / 16x64 matrix, and a 4x4 transform kernel matrix may be a 16x16 / 8x16 matrix.

[0102] Then, for mode-based transform kernel selection, two non-separable quadratic transform kernels may be configured per transform set for the non-separable quadratic transform for both the 8×8 transform and the 4×4 transform, and the number of transform sets may be four. That is, four transform sets may be configured for the 8×8 transform and four transform sets may be configured for the 4×4 transform. In this case, each of the four transform sets for the 8×8 transform may include two 8×8 transform kernels, and each of the four transform sets for the 4×4 transform may include two 4×4 transform kernels.

[0103] However, the size of the transform, i.e., the size of the region to which the transform is applied, may be other than, for example, 8x8 or 4x4, the number of sets may be n, and the number of transform kernels in each set may be k.

[0104] The transform set may be referred to as an NSST set or an LFNST set. The selection of a particular one of the transform sets may be performed based on, for example, the intra prediction mode of the current block (CU or sub-block). LFNST (Low-Frequency Non-Separable Transform) may be an example of a reduced non-separable transform, which will be described later, and refers to a non-separable transform for low-frequency components.

[0105] For reference, for example, the intra prediction modes may include two non-directional (or non-angular) intra prediction modes and 65 directional (or angular) intra prediction modes. The non-directional intra prediction modes may include a planar intra prediction mode numbered 0 and a DC intra prediction mode numbered 1, and the directional intra prediction modes may include 65 intra prediction modes numbered 2 to 66. However, this is merely an example, and this document may also be applied to cases where the number of intra prediction modes is different. Meanwhile, an intra prediction mode numbered 67 may also be used depending on the case, and the 67th intra prediction mode may indicate a linear model (LM) mode.

[0106] FIG. 5 exemplarily shows the intra-directional modes of 65 prediction directions.

[0107] Referring to FIG. 5, intra prediction modes may be classified into those with horizontal directionality and those with vertical directionality, centered on the 34th intra prediction mode, which has a prediction direction on the lower right diagonal. In FIG. 5, H and V represent horizontal and vertical directionality, respectively, and the numbers -32 to 32 indicate displacements in 1 / 32 units on the sample grid position. This may indicate an offset to the mode index value. The 2nd to 33rd intra prediction modes have horizontal directionality, while the 34th to 66th intra prediction modes have vertical directionality. Meanwhile, the 34th intra prediction mode can be considered neither horizontal nor vertical, strictly speaking, but can be classified as horizontally oriented from the perspective of determining a transform set for a secondary transform. This is because input data is transposed for vertical modes symmetrical with respect to the 34th intra prediction mode, and the 34th intra prediction mode uses the same input data alignment method as the horizontal mode. Transposing the input data means that for an MxN two-dimensional block of data, rows become columns and columns become rows, creating NxM data. The 18th and 50th intra prediction modes indicate a horizontal intra prediction mode and a vertical intra prediction mode, respectively. The 2nd intra prediction mode predicts in the upper right direction using a reference pixel on the left, so it can be called an upper right diagonal intra prediction mode. In the same context, the 34th intra prediction mode can be called a lower right diagonal intra prediction mode, and the 66th intra prediction mode can be called a lower left diagonal intra prediction mode.

[0108] For example, depending on the intra prediction mode, the mapping of the four transform sets may be shown as in the following table.

[0109] [Table 2]

[0110] As shown in Table 2, one of four transform sets, i.e., lfnstTrSetIdx, can be mapped to any of 0 to 3, i.e., 4, depending on the intra prediction mode.

[0111] Meanwhile, if it is determined that a specific set is to be used for a non-separable transform, one of k transform kernels in the specific set can be selected through a non-separable quadratic transform index. The encoding device can derive a non-separable quadratic transform index that points to a specific transform kernel based on a rate-distortion (RD) check and signal the non-separable quadratic transform index to a decoding device. The decoding device can select one of k transform kernels in the specific set based on the non-separable quadratic transform index. For example, an lfnst index value of 0 can point to the first non-separable quadratic transform kernel, an lfnst index value of 1 can point to the second non-separable quadratic transform kernel, and an lfnst index value of 2 can point to the third non-separable quadratic transform kernel. Alternatively, an lfnst index value of 0 can indicate that the first non-separable quadratic transform is not applied to the current block, and lfnst index values ​​1 to 3 can point to the three transform kernels.

[0112] The transform unit may perform the non-separable quadratic transform based on the selected transform kernel to obtain modified (quadratic) transform coefficients. The modified transform coefficients may be derived as quantized transform coefficients via the quantizer unit as described above, encoded, and signaled to a decoding device and transmitted to an inverse quantization / inverse transform unit in the encoding device.

[0113] On the other hand, when the secondary transform is omitted as described above, the (primary) transform coefficients, which are the output of the primary (separate) transform, can be derived as quantized transform coefficients through the quantization unit as described above, encoded, signaled to the decoding device, and transmitted to the inverse quantization / inverse transform unit within the encoding device.

[0114] The inverse transform unit may perform a series of steps in the reverse order of the steps performed by the transform unit described above. The inverse transform unit may receive (dequantized) transform coefficients, perform a secondary (inverse) transform to derive (primary) transform coefficients (S450), and perform a primary (inverse) transform on the (primary) transform coefficients to obtain residual blocks (residual samples) (S460). Here, the primary transform coefficients may be referred to as modified transform coefficients from the perspective of the inverse transform unit. As described above, the encoding device and the decoding device may generate reconstructed blocks based on the residual blocks and predicted blocks, and generate reconstructed pictures based on the reconstructed blocks.

[0115] Meanwhile, the decoding apparatus may further include a secondary inverse transform application determining unit (or an element determining whether to apply the secondary inverse transform) and a secondary inverse transform determining unit (or an element determining the secondary inverse transform). The secondary inverse transform application determining unit may determine whether to apply the secondary inverse transform. For example, the secondary inverse transform may be NSST, RST, or LFNST, and the secondary inverse transform application determining unit may determine whether to apply the secondary inverse transform based on a secondary transform flag parsed from the bitstream. As another example, the secondary inverse transform application determining unit may determine whether to apply the secondary inverse transform based on transform coefficients of a residual block.

[0116] The secondary inverse transform decision unit may determine a secondary inverse transform. In this case, the secondary inverse transform decision unit may determine a secondary inverse transform to be applied to a current block based on an LFNST (NSST or RST) transform set specified by an intra prediction mode. In addition, in one embodiment, the secondary transform decision method may be determined depending on the primary transform decision method. Various combinations of primary transform and secondary transform may be determined depending on the intra prediction mode. In addition, as one example, the secondary inverse transform decision unit may determine an area to which the secondary inverse transform is applied based on the size of the current block.

[0117] On the other hand, as described above, if the second-order (inverse) transform is omitted, the (dequantized) transform coefficients can be received and the first-order (separate) inverse transform can be performed to obtain a residual block (residual sample). As described above, the encoding device and the decoding device can generate a reconstructed block based on the residual block and the predicted block, and generate a reconstructed picture based on the reconstructed block.

[0118] On the other hand, in this paper, in order to reduce the computational complexity and memory requirements associated with non-separable secondary transforms, the RST (reduced secondary transform) can be applied, in which the size of the transformation matrix (kernel) is reduced using the concept of NSST.

[0119] Meanwhile, the coefficients constituting the transform kernels, transform matrices, and transform kernel matrices described herein, i.e., kernel coefficients or matrix coefficients, can be expressed in 8 bits. This may be one condition for implementation in a decoding device and an encoding device, and compared to the existing 9-bit or 10-bit implementation, it may reduce the memory requirements for storing the transform kernels with a reasonably acceptable performance degradation. In addition, by expressing the kernel matrix in 8 bits, a small multiplier may be used, which may be more suitable for SIMD (Single Instruction Multiple Data) instructions used for optimal software implementation.

[0120] In this specification, RST may refer to a transformation performed on residual samples of a target block based on a transform matrix whose size is reduced by a simplification factor. When a simplified transformation is performed, the amount of calculation required during the transformation may be reduced due to the reduction in the size of the transform matrix. In other words, RST can be used to resolve issues of computational complexity that arise during the transformation of large blocks or non-separable transformations.

[0121] The RST may be referred to by various terms such as a reduced transform, a reduced transform, a reduced secondary transform, a reduction transform, a simplified transform, a simple transform, etc., and the names by which the RST may be referred to are not limited to the examples given. Alternatively, the RST may be referred to as an LFNST (Low-Frequency Non-Separable Transform) because it is mainly performed in the low-frequency domain including non-zero coefficients in the transform block. The transform index may be called an LFNST index.

[0122] On the other hand, when the second-order inverse transform is performed based on an RST, the inverse transform unit 235 of the encoding apparatus 200 and the inverse transform unit 322 of the decoding apparatus 300 may include an inverse RST unit that derives modified transform coefficients based on the inverse RST for the transform coefficients, and an inverse linear transform unit that derives residual samples for the current block based on an inverse linear transform for the modified transform coefficients. The inverse linear transform refers to the inverse transform of the linear transform applied to the residual. In this document, deriving transform coefficients based on a transform may refer to deriving transform coefficients by applying the transform.

[0123] FIG. 6 is a diagram illustrating an RST according to an embodiment of the present document.

[0124] In this specification, the term "target block" may refer to a current block, a residual block, or a transform block on which coding is performed.

[0125] In an RST according to one embodiment, an N-dimensional vector is mapped to an R-dimensional vector located in a different space, and a reduced transformation matrix can be determined, where R is smaller than N. N may represent the square of the length of one side of a block to which a transformation is applied, or the total number of transformation coefficients corresponding to the block to which a transformation is applied, and the simplification factor may represent an R / N value. The simplification factor may be referred to by various terms such as a reduced factor, reduction factor, simplified factor, simple factor, etc. Meanwhile, R may be referred to as a simplification coefficient, but depending on the situation, the simplification factor may also represent R. Depending on the situation, the simplification factor may also represent an N / R value.

[0126] In one embodiment, the simplification factors or simplification coefficients may be signaled via the bitstream, but the embodiment is not limited thereto. For example, predefined values ​​for the simplification factors or simplification coefficients may be stored in each encoding device 200 and decoding device 300, in which case the simplification factors or simplification coefficients may not be separately signaled.

[0127] The size of the simplified transformation matrix according to one embodiment is RxN, which is smaller than the size NxN of the normal transformation matrix, and can be defined as Equation 4 below.

[0128]

number

[0129] The matrix T in the Reduced Transform block shown in (a) of FIG. 6 is the matrix T in Equation 4. RxN As shown in FIG. 6(a), the simplified transformation matrix T RxN When multiplied by , the transform coefficients for the current block can be derived.

[0130] In one embodiment, if the size of the block to which the transform is applied is 8x8 and R=16 (i.e., R / N=16 / 64=1 / 4), the RST according to (a) of Figure 6 can be expressed by the matrix operation shown in Equation 5 below. In this case, the memory and multiplication operations can be reduced by approximately 1 / 4 due to the simplification factor.

[0131] In this document, a matrix operation can be understood as an operation in which a matrix is ​​placed to the left of a column vector and multiplied by the column vector to obtain the column vector.

[0132]

number

[0133] In Equation 5, r1 to r 64 may represent a residual sample for the current block, and more specifically, may be a transform coefficient generated by applying a linear transform. As a result of the calculation of Equation 5, the transform coefficient c for the current block is i can be derived, and c i The derivation process is as shown in Equation 6.

[0134]

number

[0135] The calculation result of Equation 6 is the transform coefficients c1 to c2 for the target block. R That is, when R=16, the transform coefficients c1 to c2 for the target block can be derived. 16can be derived. If a regular transform, rather than RST, were applied and a transform matrix of size 64x64 (NxN) were multiplied by residual samples of size 64x1 (Nx1), 64 (N) transform coefficients for the current block would be derived. However, because RST is applied, only 16 (R) transform coefficients for the current block are derived. Since the total number of transform coefficients for the current block is reduced from N to R, the amount of data transmitted from encoding apparatus 200 to decoding apparatus 300 is reduced, and therefore, transmission efficiency between encoding apparatus 200 and decoding apparatus 300 can be improved.

[0136] Considering the size of the transformation matrix, the size of a normal transformation matrix is ​​64x64 (NxN), but the size of the simplified transformation matrix is ​​reduced to 16x64 (RxN), so compared to performing normal transformation, memory usage when performing RST can be reduced by a ratio of R / N. Also, compared to the number of multiplication operations when using a normal transformation matrix (NxN), the number of multiplication operations can be reduced by a ratio of R / N (RxN) when using a simplified transformation matrix.

[0137] In one embodiment, the transform unit 232 of the encoding apparatus 200 may derive transform coefficients for the current block by performing a primary transform and an RST-based secondary transform on residual samples for the current block. These transform coefficients may be transmitted to an inverse transform unit 322 of the decoding apparatus 300, and the inverse transform unit 322 of the decoding apparatus 300 may derive modified transform coefficients based on an inverse reduced secondary transform (RST) on the transform coefficients and derive residual samples for the current block based on an inverse primary transform on the modified transform coefficients.

[0138] Inverse RST matrix T according to one embodiment NxRThe size of the simplified transformation matrix T shown in Equation 4 is NxR, which is smaller than the size of the normal inverse transformation matrix NxN. RxN and are in a transpose relationship.

[0139] The matrix T in the Reduced Inverse Transform block shown in Figure 6(b) t is the inverse RST matrix T RxN T (The superscript T means transpose.) As shown in FIG. 6(b), the inverse RST matrix T RxN T When the inverse RST matrix T is multiplied by the inverse RST matrix T, the modified transform coefficients for the current block or the residual samples for the current block can be derived. RxN T is (T RxN ) T NxR It is also sometimes expressed as:

[0140] More specifically, when the inverse RST is applied to the secondary inverse transform, the inverse RST matrix T RxN T On the other hand, an inverse RST can be applied to the inverse linear transform, in which case the inverse RST matrix T RxN T When multiplied by , the residual sample for the target block can be derived.

[0141] In one embodiment, when the size of the block to which the inverse transform is applied is 8x8 and R=16 (i.e., R / N=16 / 64=1 / 4), the RST according to (b) of FIG. 6 can be expressed by a matrix operation as shown in Equation 7 below.

[0142]

number

[0143] In Equation 7, c1 to c 16 The result of the calculation of Equation 7 is r, which indicates the modified transform coefficients for the current block or the residual samples for the current block. j can be derived, and r j The derivation process is as shown in Equation 8.

[0144]

number

[0145] The calculation result of Equation 8 is r1 to r2, which indicate the modified transform coefficients for the target block or the residual samples for the target block. N can be derived. Considering the size of the inverse transformation matrix, the size of a normal inverse transformation matrix is ​​64x64 (NxN), but the size of the simplified inverse transformation matrix is ​​reduced to 64x16 (NxR). Therefore, compared to performing a normal inverse transformation, memory usage when performing inverse RST can be reduced by a ratio of R / N. Also, compared to the number of multiplication operations when using a normal inverse transformation matrix (NxN), using a simplified inverse transformation matrix can reduce the number of multiplication operations by a ratio of R / N (NxR).

[0146] Meanwhile, the transform set configuration shown in Table 2 can also be applied to an 8x8 RST. That is, the 8x8 RST can be applied according to the transform set in Table 2. Since one transform set is composed of two or three transforms (kernels) depending on the intra-frame prediction mode, it can be configured to select one of up to four transforms, including cases where a secondary transform is not applied. When a secondary transform is not applied, the transform can be considered to have been applied with an identity matrix. If the four transforms are assigned indices 0, 1, 2, and 3 (for example, index 0 can be assigned to the identity matrix, i.e., when a secondary transform is not applied), a syntax element called a transform index or an lfnst index can be signaled for each block of transform coefficients to specify the transform to be applied. That is, for an 8x8 upper left block, an 8x8 RST can be specified in the RST configuration via the transform index, or an 8x8 lfnst can be specified when an LFNST is applied. The 8x8 lfnst and 8x8 RST refer to a transform that can be applied to an 8x8 region contained within a block of transform coefficients when W and H of the target block are all equal to or greater than 8, and the 8x8 region may be the upper left 8x8 region within the block of transform coefficients. Similarly, the 4x4 lfnst and 4x4 RST refer to a transform that can be applied to a 4x4 region contained within a block of transform coefficients when W and H of the target block are all equal to or greater than 4, and the 4x4 region may be the upper left 4x4 region within the block of transform coefficients.

[0147] Meanwhile, according to one embodiment of this document, during the encoding process, only 48 pieces of data, rather than a 16x64 transformation kernel matrix, can be selected for the 64 pieces of data constituting an 8x8 region, thereby applying a maximum 16x48 transformation kernel matrix. Here, "maximum" means that for an mx48 transformation kernel matrix that can generate m coefficients, the maximum value of m is 16. That is, when RST is performed by applying an mx48 transformation kernel matrix (m≦16) to an 8x8 region, 48 pieces of data can be input and m coefficients can be generated. When m is 16, 48 pieces of data can be input and 16 coefficients can be generated. That is, when 48 pieces of data form a 48x1 vector, the 16x1 vector can be generated by multiplying the 16x48 matrix and the 48x1 vector in order. Then, the 48 pieces of data constituting the 8x8 region can be properly arranged to form a 48x1 vector. In this case, when a matrix operation is performed by applying a maximum 16x48 transform kernel matrix, 16 modified transform coefficients are generated, and the 16 modified transform coefficients can be arranged in the upper left 4x4 area according to the scanning order, and the upper right 4x4 area and the lower left 4x4 area can be filled with 0s.

[0148] A transposed matrix of the above-described transform kernel matrix can be used for the inverse transform in the decoding process. That is, when an inverse RST or an LFNST is performed in the inverse transform process executed in the decoding device, input coefficient data to which the inverse RST is applied is configured as a one-dimensional vector in a predetermined arrangement order, and the modified coefficient vector obtained by multiplying the one-dimensional vector by the matrix of the inverse RST on the left side can be arranged in a two-dimensional block in a predetermined arrangement order.

[0149] To summarize, when RST or LFNST is applied to an 8x8 region during the transform process, a matrix operation is performed on 48 transform coefficients in the upper left, upper right, and lower left regions of the 8x8 region, excluding the lower right region, of the transform coefficients of the 8x8 region, and a 16x48 transform kernel matrix. For the matrix operation, the 48 transform coefficients are input into a one-dimensional array. After this matrix operation, 16 modified transform coefficients are derived, and the modified transform coefficients may be arranged in the upper left region of the 8x8 region.

[0150] Conversely, when the inverse RST or LFNST is applied to an 8x8 region in the inverse transform process, 16 transform coefficients corresponding to the upper left side of the 8x8 region among the transform coefficients of the 8x8 region are input in a one-dimensional array form according to the scanning order and may be subjected to a matrix operation with a 48x16 transform kernel matrix. That is, the matrix operation in this case can be expressed as (48x16 matrix) * (16x1 transform coefficient vector) = (48x1 modified transform coefficient vector). Here, an nx1 vector can be interpreted as an nx1 matrix and therefore may be expressed as an nx1 column vector. Also, * indicates a matrix multiplication operation. When this matrix operation is performed, 48 modified transform coefficients can be derived, and the 48 modified transform coefficients can be arranged in the upper left, upper right, and lower left regions of the 8x8 region, excluding the lower right region.

[0151] On the other hand, when the second-order inverse transform is performed based on the RST, the inverse transform unit 235 of the encoding apparatus 200 and the inverse transform unit 322 of the decoding apparatus 300 may include an inverse RST unit that derives modified transform coefficients based on the inverse RST for the transform coefficients, and an inverse linear transform unit that derives residual samples for the current block based on an inverse linear transform for the modified transform coefficients. The inverse linear transform refers to the inverse transform of the linear transform applied to the residual. In this document, deriving transform coefficients based on a transform may refer to deriving transform coefficients by applying the transform.

[0152] The above-mentioned non-separable transform, LFNST, will be described in detail as follows: LFNST can include a forward transform performed by an encoding device and an inverse transform performed by a decoding device.

[0153] The encoding device applies a forward primary (core) transform, and then applies a forward secondary transform using the derived result (or part of the result) as input.

[0154]

number

[0155] In Equation 9, x and y are the input and output of the quadratic transformation, respectively, and G is a matrix representing the quadratic transformation, where the transform basis vector is composed of a column vector. In the case of the backward LFNST, when the dimension of the transformation matrix G is expressed as [number of rows × number of columns], in the case of the forward LFNST, transposing the matrix G is expressed as G. T It becomes a dimension of.

[0156] For the backward LFNST, the dimensions of the matrix G are [48x16], [48x8], [16x16], and [16x8], where the [48x8] and [16x8] matrices are submatrices obtained by sampling eight transformation basis vectors from the left side of the [48x16] and [16x16] matrices, respectively.

[0157] On the other hand, in the case of forward LFNST, the matrix G T The dimensions of are [16x48], [8x48], [16x16], and [8x16], where the [8x48] and [8x16] matrices are submatrices obtained by sampling eight transformation basis vectors from the top of the [16x48] and [16x16] matrices, respectively.

[0158] Therefore, in the case of forward LFNST, the input x can be a [48x1] vector or a [16x1] vector, and the output y can be a [16x1] vector or an [8x1] vector. Since the output of a forward linear transform in video coding and decoding is two-dimensional (2D) data, in order to construct a [48x1] or [16x1] vector as the input x, the 2D data output from the forward transform must be appropriately arranged to construct a one-dimensional vector.

[0159] 7 shows an example of a sequence for arranging output data of a forward linear transform into a one-dimensional vector. The left diagrams of (a) and (b) of FIG. 7 show a sequence for creating a [48x1] vector, and the right diagrams of (a) and (b) of FIG. 7 show a sequence for creating a [16x1] vector. In the case of LFNST, 2D data is sequentially arranged in the sequence shown in (a) and (b) of FIG. 7 to obtain a one-dimensional vector x.

[0160] The arrangement direction of the output data of the forward linear transform may be determined according to the intra prediction mode of the current block. For example, if the intra prediction mode of the current block is horizontally aligned with respect to the diagonal direction, the output data of the forward linear transform may be arranged in the order of (a) of Figure 7, and if the intra prediction mode of the current block is vertically aligned with respect to the diagonal direction, the output data of the forward linear transform may be arranged in the order of (b) of Figure 7.

[0161] As an example, an ordering different from that shown in (a) and (b) of Figures 7 can be applied, and in order to derive the same result (y vector) as when the ordering shown in (a) and (b) of Figures 7 is applied, the column vectors of matrix G can be rearranged to match that ordering. In other words, the column vectors of G can be rearranged so that each element constituting the x vector is always multiplied by the same transformation base vector.

[0162] Since the output y derived through Equation 9 is a one-dimensional vector, if a configuration that processes the result of a forward quadratic transform as input, for example, a configuration that performs quantization or residual coding, requires two-dimensional data as input data, the output y vector of Equation 9 must be appropriately arranged into 2D data again.

[0163] FIG. 8 is a diagram showing an example of the order in which output data of the forward quadratic transform is arranged into a two-dimensional vector.

[0164] In the case of LFNST, the output values ​​can be arranged in a 2D block according to a predetermined scan order. Figure 8(a) shows that when the output y is a [16x1] vector, the output values ​​are arranged in 16 positions of the 2D block according to a diagonal scan order. Figure 8(b) shows that when the output y is an [8x1] vector, the output values ​​are arranged in 8 positions of the 2D block according to a diagonal scan order, and the remaining 8 positions are filled with 0. X in Figure 8(b) indicates that it is filled with 0.

[0165] As another example, depending on the configuration for performing quantization or residual coding, the order in which the output vector y is processed may be performed according to a preset order, so the output vector y may not be arranged in a 2D block as shown in Figure 8. However, in the case of residual coding, data coding may be performed in units of 2D blocks (e.g., 4x4) such as CG (Coefficient Group), and in this case, data may be arranged in a specific order such as the diagonal scan order of Figure 8.

[0166] Meanwhile, the decoding device can arrange two-dimensional data output through an inverse quantization process, etc., for inverse transformation according to a preset scanning order to form a one-dimensional input vector y. The input vector y can be output to the input vector x according to the following equation:

[0167]

number

[0168] For the reverse LFNST, the output vector x can be derived by multiplying the input vector y, which is a [16x1] or [8x1] vector, by the G matrix. For the reverse LFNST, the output vector x can be a [48x1] or [16x1] vector.

[0169] The output vector x is arranged in two-dimensional blocks in the order shown in FIG. 7 and arranged into two-dimensional data, and such two-dimensional data becomes the input data (or part of the input data) for the inverse linear transformation.

[0170] Therefore, the inverse quadratic transform is generally the opposite process to the forward quadratic transform, and in the case of the inverse transform, unlike the forward transform, the inverse quadratic transform is applied first, and then the inverse linear transform is applied.

[0171] Inverse LFNST allows you to select one of eight [48x16] matrices or eight [16x16] matrices as the transformation matrix G. Whether to apply a [48x16] or [16x16] matrix depends on the size and shape of the block.

[0172] Also, the eight matrices may be derived from four transform sets as shown in Table 2 above, and each transform set may consist of two matrices. Which transform set to use among the four transform sets is determined depending on the intra prediction mode. More specifically, the transform set is determined based on an extended intra prediction mode value, taking into account a wide angle intra prediction mode (WAIP). Which of the two matrices constituting the selected transform set is selected is determined through index signaling. More specifically, the transmitted index value may be 0, 1, or 2, where 0 indicates that LFNST is not applied and 1 and 2 indicate one of the two transform matrices constituting the transform set selected based on the intra prediction mode value.

[0173] FIG. 9 is a diagram illustrating a wide-angle intra prediction mode according to one embodiment of this document.

[0174] General intra prediction mode values ​​can range from 0 to 66 and from 81 to 83, and as shown, intra prediction mode values ​​extended by WAIP can range from -14 to 83. Values ​​from 81 to 83 indicate CCLM (Cross Component Linear Model) modes, and values ​​from -14 to -1 and values ​​from 67 to 80 indicate intra prediction mode values ​​extended by applying WAIP.

[0175] When the width of the current block to be predicted is greater than its height, the reference pixel on the top is generally closer to the position inside the block to be predicted. Therefore, predicting in the bottom-left direction may be more accurate than predicting in the top-right direction. Conversely, when the height of the block is greater than its width, the reference pixel on the left is generally closer to the position inside the block to be predicted. Therefore, predicting in the top-right direction may be more accurate than predicting in the bottom-left direction. Therefore, it may be advantageous to apply remapping, i.e., mode index conversion, to the wide-angle intra prediction mode index.

[0176] When wide-angle intra prediction is applied, information for existing intra prediction may be signaled, and after the information is parsed, the information may be remapped with the index of the wide-angle intra prediction mode. Therefore, the total number of intra prediction modes for a specific block (e.g., a non-square block of a specific size) may not be changed, i.e., the total number of intra prediction modes is 67, and the coding of the intra prediction modes for the specific block may not be changed.

[0177] Table 3 below shows a process of deriving a modified intra mode by remapping an intra prediction mode with a wide-angle intra prediction mode.

[0178] [Table 3]

[0179] In Table 3, the extended intra prediction mode value is finally stored in the predModeIntra variable, ISP_NO_SPLIT indicates that the CU block is not divided into sub-partitions using the Intra Sub Partitions (ISP) technology currently adopted in the VVC standard, and the cIdx variable values ​​of 0, 1, and 2 refer to the luma, Cb, and Cr components, respectively. The Log2 function in Table 3 returns a log value with a base of 2, and the Abs function returns an absolute value.

[0180] The variable predModeIntra indicating the intra prediction mode, the height and width of the transform block, etc. are used as input values ​​for the wide angle intra prediction mode mapping process, and the output value is the modified intra prediction mode predModeIntra. The height and width of the transform block or coding block become the height and width of the current block for intra prediction mode remapping. At this time, the variable whRatio reflecting the ratio of height to width can be set to Abs(Log2(nW / nH)).

[0181] For non-square blocks, the intra prediction mode can be modified in two distinct cases.

[0182] First, if all of the following conditions are met: (1) the width of the current block is greater than the height; (2) the intra prediction mode before modification is equal to or greater than 2; and (3) the intra prediction mode is (8+2*whRatio) when the variable whRatio is greater than 1, and is less than the value derived from 8 when the variable whRatio is equal to or less than 1 [predModeIntra is less than (whRatio>1)?(8+2*whRatio):8], the intra prediction mode is set to a value 65 greater than the intra prediction mode [predModeIntra is set equal to (predModeIntra+65)].

[0183] If the above is not the case, and all of the following conditions are met: (1) the height of the current block is greater than the width, (2) the intra prediction mode before modification is equal to or less than 66, and (3) the intra prediction mode is greater than the value derived from (60-2*whRatio) when the variable whRatio is greater than 1 and 60 when the variable whRatio is equal to or less than 1 [predModeIntra is greater than (whRatio>1)?(60-2*whRatio):60], then the intra prediction mode is set to a value 67 less than the intra prediction mode [predModeIntra is set equal to (predModeIntra-67)].

[0184] The above-mentioned Table 2 shows how transform sets are selected based on the intra prediction mode value extended by WAIP in LFNST. As shown in FIG. 9, modes 14 to 33 and modes 35 to 80 are symmetrical to each other in terms of prediction direction with mode 34 as the center. For example, mode 14 and mode 54 are symmetrical to each other with respect to the direction corresponding to mode 34 as the center. Therefore, the same transform set is applied to modes located in symmetrical directions, and this symmetry is also reflected in Table 2.

[0185] However, it is assumed that the input data to the forward LFNST for mode 54 is symmetrical to the input data to the forward LFNST for mode 14. For example, for modes 14 and 54, two-dimensional data is rearranged into one-dimensional data according to the arrangement orders shown in Figures 7(a) and 7(b), respectively, and it can be seen that the ordering patterns shown in Figures 7(a) and 7(b) are symmetrical about the direction indicated by mode 34 (diagonal direction).

[0186] On the other hand, as described above, whether to apply a [48x16] matrix or a [16x16] matrix to LFNST is determined by the size and shape of the block to be transformed.

[0187] Figure 10 shows the shapes of blocks to which LFNST is applied, where (a) shows a 4x4 block, (b) shows 4x8 and 8x4 blocks, (c) shows a 4xN or Nx4 block where N is 16 or greater, (d) shows an 8x8 block, and (e) shows an MxN block where M≧8, N≧8, and N>8 or M>8.

[0188] In Fig. 10, blocks with thick frames indicate the regions to which LFNST is applied. For the blocks in Fig. 10(a) and (b), LFNST is applied to the top-left 4x4 region, and for the block in Fig. 10(c), LFNST is applied to each of the two consecutive 4x4 regions in the top-left corner. In Fig. 10(a), (b), and (c), LFNST is applied in units of 4x4 regions, so this type of LFNST will be referred to as "4x4 LFNST" below, and the transformation matrix that can be applied is a [16x16] or [16x8] matrix based on the matrix dimensions for G in Equation 9 and Equation 10.

[0189] More specifically, a [16x8] matrix is ​​applied to the 4x4 block (4x4TU or 4x4CU) in (a) of Figure 10, and a [16x16] matrix is ​​applied to the blocks in (b) and (c) of Figure 10. This is to match the worst-case computational complexity with 8 multiplications per sample.

[0190] In (d) and (e) of FIG. 10, LFNST is applied to the upper-left 8x8 region, and such LFNST will be referred to as "8x8 LFNST" hereinafter. A [48x16] or [48x8] matrix can be used as the transformation matrix. In the case of forward LFNST, a [48x1] vector (the x vector in Equation 9) is input as input data, so not all sample values ​​in the upper-left 8x8 region are used as input values ​​for the forward LFNST. That is, as seen in the left-hand order of FIG. 7(a) or the left-hand order of FIG. 7(b), the bottom-right 4x4 block is left as is, and a [48x1] vector can be constructed based on samples belonging to the remaining three 4x4 blocks.

[0191] A [48x8] matrix can be applied to the 8x8 block (8x8TU or 8x8CU) in Figure 10(d), and a [48x16] matrix can be applied to the 8x8 block in Figure 10(e), again to match the worst-case computational complexity to 8 multiplications per sample.

[0192] Depending on the block shape, the corresponding forward LFNST (4x4LFNST or 8x8LFNST) is applied to generate 8 or 16 output data (the y vector in Equation 9, an [8x1] or [16x1] vector). In the forward LFNST, the matrix G T Due to the characteristics of the algorithm, the number of output data is equal to or less than the number of input data.

[0193] FIG. 11 is a diagram showing an example of the arrangement of output data from the forward LFNST, showing blocks in which the output data from the forward LFNST is arranged according to the block shape.

[0194] The shaded area in the upper left corner of the block shown in Figure 11 corresponds to the area where the output data of the forward LFNST is located, with locations marked with 0 indicating samples filled with 0 values, and the remaining area indicating areas that are not changed by the forward LFNST. In areas that are not changed by the LFNST, the output data of the forward linear transform remains unchanged.

[0195] As mentioned above, the dimensions of the transformation matrix applied vary depending on the block shape, and therefore the number of output data also varies. As shown in Figure 11, the output data of the forward LFNST may not fill the entire upper-left 4x4 block. In Figures 11(a) and 11(d), a [16x8] matrix and a [48x8] matrix are applied to the block indicated by the thick line or a partial area within the block, respectively, and an [8x1] vector is generated as the output of the forward LFNST. That is, according to the scan order shown in Figure 8(b), only eight output data positions are filled as shown in Figures 11(a) and 11(d), and the remaining eight positions are filled with zeros. In the case of the block to which the LFNST is applied in Figure 10(d), the two 4x4 blocks on the upper right and lower left adjacent to the upper-left 4x4 block are also filled with zeros, as shown in Figure 11(d).

[0196] As described above, the LFNST index is basically signaled to specify whether to apply LFNST and the transformation matrix to be applied. As shown in Figure 11, when LFNST is applied, the number of output data from the forward LFNST may be equal to or less than the number of input data, so areas filled with zero values ​​occur as follows:

[0197] 1) As shown in Figure 11(a), in the 4x4 block on the upper left, the 8th position in the scan order and after, that is, the 9th to 16th samples

[0198] 2) As shown in (d) and (e) of FIG. 11, a [48x16] matrix or a [48x8] matrix is ​​applied to the two 4x4 blocks adjacent to the upper left 4x4 block or the second and third 4x4 blocks in the scan order.

[0199] Therefore, if non-zero data is found by checking the above 1) and 2), it is certain that the LFNST has not been applied, and signaling of the LFNST index can be omitted.

[0200] For example, in the case of LFNST adopted in the VVC standard, signaling of the LFNST index is performed after residual coding, so that the encoding device can determine whether non-zero data (significant coefficients) exist at all positions within a TU or CU block through residual coding. Therefore, the encoding device can determine whether to perform signaling for the LFNST index based on whether non-zero data exists, and the decoding device can determine whether to parse the LFNST index. If non-zero data does not exist in the areas specified in 1) and 2), signaling of the LFNST index is performed.

[0201] Since a truncated unary code is applied as the binarization method for the LFNST index, the LFNST index consists of a maximum of two bins, and the binary codes for the possible LFNST index values ​​of 0, 1, and 2 are assigned as 0, 10, and 11, respectively. In the LFNST currently adopted by VVC, context-based CABAC coding (regular coding) is applied to the first bin, and bypass coding is applied to the second bin. The total number of contexts for the first bin is two, with (DCT-2, DCT-2) applied as the primary transform pair in the horizontal and vertical directions. One context is assigned when the luma and chroma components are coded using a dual-tree type, and the other context is applied for the remaining cases. The coding of such LFNST indexes is shown in the table below.

[0202] [Table 4]

[0203] On the other hand, the following simplification method can be applied to the adopted LFNST.

[0204] (i) As an example, the number of output data for the forward LFNST can be limited to a maximum of 16.

[0205] In the case of (c) of Figure 10, 4x4 LFNST can be applied to each of the two adjacent 4x4 regions on the upper left side, generating a maximum of 32 LFNST output data. If the number of output data for forward LFNST is limited to a maximum of 16, 4x4 LFNST can be applied only to the single 4x4 region on the upper left side of a 4xN / Nx4 (N≧16) block (TU or CU), and LFNST can be applied only once to all blocks in Figure 10. This simplifies the implementation of video coding.

[0206] As an example, Figure 12 shows that the number of output data items for the forward LFNST is limited to a maximum of 16. As shown in Figure 12, when LFNST is applied to the upper-leftmost 4x4 region of a 4xN or Nx4 block where N is 16 or greater, the number of output data items for the forward LFNST is 16.

[0207] (ii) As an example, zero-out can be applied to areas where LFNST is not applied. In this document, zero-out can mean filling the values ​​of all positions belonging to a specific area with 0. In other words, zero-out can be applied to areas that remain unchanged by LFNST and retain the results of the forward linear transform. As mentioned above, LFNST is divided into 4x4 LFNST and 8x8 LFNST, so zero-out can be divided into two types ((ii)-(A) and (ii)-(B)) as follows.

[0208] (ii)-(A) When 4x4 LFNST is applied, regions to which 4x4 LFNST is not applied can be zeroed out. Figure 13 illustrates zeroing out in a block to which 4x4 LFNST is applied, according to an example.

[0209] As shown in FIG. 13, for blocks to which 4x4 LFNST is applied, i.e., for blocks (a), (b), and (c) in FIG. 11, even areas to which LFNST is not applied can be filled with 0.

[0210] On the other hand, (d) of FIG. 13 shows that when the maximum value of the output of the forward LFNST is limited to 16 as in FIG. 12, zeroing out is performed on the remaining blocks to which the 4x4 LFNST is not applied.

[0211] (ii)-(B) When an 8x8 LFNST is applied, regions to which the 8x8 LFNST is not applied can be zeroed out. Figure 14 illustrates zeroing out in a block to which the 8x8 LFNST is applied, according to an example.

[0212] As shown in FIG. 14, for 8x8 blocks to which LFNST is applied, i.e., for the blocks (d) and (e) in FIG. 11, the entire area up to the area to which LFNST is not applied can be filled with 0.

[0213] (iii) The zero-out method proposed in (ii) above may change the area filled with zeros when LFNST is applied. Therefore, the zero-out method proposed in (ii) above can check whether non-zero data exists in a wider area than the LFNST method in FIG. 11.

[0214] For example, when (ii)-(B) is applied, it is possible to check whether non-zero data exists in the areas filled with zero values ​​in (d) and (e) of FIG. 11 as well as in the areas further filled with zeros in FIG. 14, and then perform signaling for the LFNST index only if non-zero data does not exist.

[0215] Of course, even when the zero-out proposed in (ii) above is applied, it is possible to check whether non-zero data exists, just like the existing LFNST index signaling. That is, it is possible to check whether non-zero data exists for blocks filled with zeros in Figure 11 and apply LFNST index signaling. In this case, zero-out is performed only in the encoding device, and the decoding device does not assume this zero-out. In other words, it is possible to perform LFNST index parsing by checking whether non-zero data exists only in areas explicitly marked with zeros in Figure 11.

[0216] Alternatively, according to another example, zeroing out can be performed as shown in Fig. 15. Fig. 15 is a diagram showing zeroing out in an 8x8 block to which LFNST is applied, according to another example.

[0217] As shown in Figures 13 and 14, zeroing out can be applied to all areas other than the area to which LFNST is applied, or it can be applied to only a partial area as shown in Figure 15. It is also possible to apply zeroing out only to areas other than the 8x8 area in the upper left of Figure 15, and not to apply zeroing out to the 4x4 block in the lower right inside the 8x8 area in the upper left.

[0218] Various embodiments can be derived by applying combinations of the simplification methods ((i), (ii)-(A), (ii)-(B), and (iii)) to the LFNST. Of course, the combinations of the simplification methods are not limited to the following examples, and any combination can be applied to the LFNST.

[0219] Embodiment 1

[0220] -Limit the number of output data for forward LFNST to a maximum of 16 (i)

[0221] -When 4x4 LFNST is applied, zero out all areas where 4x4 LFNST is not applied. (ii)-(A)

[0222] -When 8x8 LFNST is applied, zero out all areas where 8x8 LFNST is not applied. (ii)-(B)

[0223] -After checking whether non-zero data exists in the area filled with existing 0 values ​​and the area filled with 0 by additional zero-out ((ii)-(A), (ii)-(B)), signaling LFNST indexing only if non-zero data does not exist (iii)

[0224] In the first embodiment, when LFNST is applied, the region where non-zero output data can exist is limited to the interior of the upper left 4x4 region. More specifically, in the cases of (a) in Figure 13 and (a) in Figure 14, the 8th position in the scan order is the (most) last position where non-zero data can exist, and in the cases of (b) and (c) in Figure 13 and (b) in Figure 14, the 16th position in the scan order (i.e., the position on the lower right edge of the upper left 4x4 block) is the (most) last position where non-zero data can exist.

[0225] Therefore, when LFNST is applied, whether or not to signal the LFNST index can be determined after checking whether non-zero data exists at a position where the residual coding process is not allowed (a position beyond the last position).

[0226] Below is a table showing the LFNST process according to embodiment 1.

[0227] [Table 5]

[0228] [Table 6]

[0229] Tables 5 and 6 show the decoding process for (ii) and (iii) of the LFNST simplification method.

[0230] According to the top part of Table 5, if the index of the sub-block in which the last non-zero coefficient exists is greater than 0 and the width and height of the transform block are all greater than 4 [(lastSubBlock>0 && log2TbWidth>=2 && log2TbHeight>=2)], or the position of the last non-zero coefficient within the sub-block in which the last non-zero coefficient exists is greater than 7 and the size of the transform block is 4x4 or 8x8 [(lastScanPos>7 && (log2TbWidth==2||log2TbHeight==3) && log2TbWidth==log2TbHeight)], the flag variable lfnstZeroOutSigCoeffFlag for LFNST zero-out is set to 1.

[0231] That is, the first condition is that a non-zero coefficient is derived in an area other than the upper left area of ​​the transform block where LFNST can be applied (i.e., a significant coefficient is derived in a sub-block other than the upper left sub-block (4x4)), and when the first condition is met, the flag variable lfnstZeroOutSigCoeffFlag for LFNST zero-out is set to 1. In this case, since the size of the transform block is 4x4 or greater, this indicates that zero-out will be performed on the transform block to which 4x4 LFNST and 8x8 LFNST are applied.

[0232] The second condition is that when LFNST is applied to a 4x4 block and an 8x8 block, the last position where a non-zero coefficient can exist is the eighth position, as shown in (a) and (d) of Figure 11. Therefore, when starting from 0, if a non-zero coefficient exists beyond the seventh position, the flag variable lfnstZeroOutSigCoeffFlag is set to 1.

[0233] In this way, when the flag variable lfnstZeroOutSigCoeffFlag is set to 1, lfnst_idx, which is signaled at the coding unit level when lfnstZeroOutSigCoeffFlag is 0 as shown in Table 6, is not signaled.

[0234] By way of another example, when the first or second condition in Table 5 is met, the flag variable lfnstZeroOutSigCoeffFlag is set to 0, and lfnst_idx can be signaled when lfnstZeroOutSigCoeffFlag is 1.

[0235] [Table 7-1] [Table 7-2] [Table 7-3]

[0236] Referring to Table 7, the variable nonZeroSize, which indicates the size or number of non-zero variables on which a matrix operation is performed to apply an LFNST, is set to 8 or 16. If the width and height of the transform block are 4 or 8, that is, the length of the output data of the forward LFNST or the input data of the reverse LFNST for 4x4 blocks and 8x8 blocks as shown in Figure 11 is 8. For all other blocks, the length of the output data of the forward LFNST or the input data of the reverse LFNST is 16 [nonZeroSize=((nTbW==4 && nTbH==4)||(nTbW==8 && nTbH==8))?8:16]. In other words, when a forward LFNST is applied, the maximum number of output data is limited to 16.

[0237] The input data for such a backward LFNST can be arranged two-dimensionally by diagonal scanning [xC=DiagScanOrder[log2LfnstSize][log2LfnstSize][x][0], yC=DiagScanOrder[log2LfnstSize][log2LfnstSize][x][1]]. The above description shows the decoding process for (i) of the LFNST simplification method.

[0238] In addition, the variables nonZeroW and nonZeroH, which indicate the width and height of the upper left block where non-zero transform coefficients to be input to the inverse linear transform may exist, are derived as 4 if the width or height of the transform block is 4 when the lfnst index is not 0, and as 8 in other cases [nonZeroW=(nTbW==4||nTbH==4)?4:8, nonZeroH=(nTbW==4||nTbH==4)?4:8]. This means that areas of the transform block other than the 4x4 and 8x8 areas to which lfnst is applied are zeroed out and filled with zeros. This part shows the decoding process for (ii) of the LFNST simplification method.

[0239] Embodiment 2

[0240] -Limit the number of output data for forward LFNST to a maximum of 16 (i)

[0241] In embodiment 2), the zero-out method proposed in (ii) is not applied, and an LFNST index signaling method is applied that does not check whether non-zero data exists. That is, only the zero-out method proposed in FIG. 11 is checked, and the LFNST index is signaled based on this. In the case of FIG. 11(c), the number of output data is 32, which is different from embodiment 2 (i.e., embodiment 2 is as shown in FIG. 12), but it is the same as FIG. 11(c) in that no zero-out occurs, except that the output data is located in the upper left 4x4 block.

[0242] As shown in Figure 12, 4x4 LFNST is applied only to the upper left 4x4 region, and a [16x16] matrix is ​​applied to this region, so when forward LFNST is applied, no region is filled with zeros. Because the region that is checked for the presence of non-zero data remains unchanged, the LFNST index signaling method that does not check for the presence of non-zero data can be applied as is.

[0243] [Table 8-1] [Table 8-2]

[0244] Referring to Table 8, the variable nonZeroSize, which indicates the size or number of non-zero variables on which a matrix operation is performed to apply LFNST, is set to 8 or 16. If the width and height of the transform block are 4 or 8, that is, the length of the output data of the forward LFNST or the input data of the reverse LFNST for 4x4 blocks and 8x8 blocks as shown in Figure 11 is 8. For all other blocks, the length of the output data of the forward LFNST or the input data of the reverse LFNST is 16 [nonZeroSize=((nTbW==4 && nTbH==4)||(nTbW==8 && nTbH==8))?8:16]. In other words, when a forward LFNST is applied, the maximum number of output data is limited to 16.

[0245] The input data for such a backward LFNST can be arranged two-dimensionally according to diagonal scanning [xC = DiagScanOrder[log2LfnstSize][log2LfnstSize][x][0], yC = DiagScanOrder[log2LfnstSize][log2LfnstSize][x][1]]. The part described with reference to Table 8 shows the decoding process for (i) of the LFNST simplification method.

[0246] Embodiment 3

[0247] -When 8x8 LFNST is applied, zero out all areas where 8x8 LFNST is not applied. (ii)-(B)

[0248] - After checking whether non-zero data exists in the area filled with existing zero values ​​(the zero-out area shown in FIG. 11) and the area filled with zeros by additional zero-out ((ii)-(B)), signaling LFNST indexing only if non-zero data does not exist (iii)

[0249] [Table 9]

[0250] Table 9 changes the conditions at the top of Table 5. The size of the transform block to which the first condition, where the flag variable lfnstZeroOutSigCoeffFlag for LFNST zero-out is set to 1, is applied has been changed from 4x4 to 8x8. This change in the size of the transform block indicates that zero-out is performed only on transform blocks to which 8x8 LFNST is applied.

[0251] The syntax syntax for the coding unit for the third embodiment is as shown in Table 6.

[0252] [Table 10]

[0253] In this embodiment, since zeroing out of LFNST is performed on transform blocks having width and height of 8 or more on which 8x8 LFNST is performed, as shown in Table 10, the variables nonZeroW and nonZeroH indicating the width and height of a block including non-zero transform coefficients input to the inverse linear transform can be derived as 8 for transform blocks having width and height of 8 or more when the lfnst index is greater than 0 [(lfnst_idx[xTbY][yTbY]>0 && nTbW>=8 && nTbH>=8)?8, (lfnst_idx[xTbY][yTbY]>0 && nTbW>=8 && nTbH>=8)?8]. In other words, this means that areas of the transform block other than the 8x8 area on which lfnst is performed are zeroed out and filled with 0. This part shows the decoding process for (ii)-(B) of the LFNST simplification method.

[0254] Embodiment 4

[0255] -When 8x8 LFNST is applied, zero out all areas where 8x8 LFNST is not applied. (ii)-(B)

[0256] The LFNST index signaling method that does not check whether non-zero data exists can be applied as is. That is, the zero-out in (ii)-(B) is performed by the encoding device, and the decoding device can signal the LFNST index by assuming that non-zero data may exist in the corresponding zero-out region. In this case, only the zero-out shown in FIG. 11 is checked, and the LFNST index is signaled based on this.

[0257] Embodiment 5

[0258] -Limit the number of output data for forward LFNST to a maximum of 16 (i)

[0259] -When 8x8 LFNST is applied, zero out all areas where 8x8 LFNST is not applied. (ii)-(B)

[0260] - Check whether non-zero data exists in the area filled with existing zero values ​​(the remaining zero-out area in FIG. 11 except for FIG. 11(c)). FIG. 12 applies instead of FIG. 11(c), but zero-out does not apply) and the area filled with zeros due to additional zero-out ((ii)-(B)). Signal LFNST indexing only if non-zero data does not exist. (iii)

[0261] In this embodiment, the syntax syntax for residual coding is shown in Table 9 of the third embodiment, and the syntax syntax for coding units is shown in Table 6 of the first embodiment.

[0262] According to Table 9, the size of the transform block to which the first condition, in which the flag variable lfnstZeroOutSigCoeffFlag for zero-out of LFNST is set to 1, is applied, is 8x8. This limitation on the size of the transform block indicates that zero-out is performed only on transform blocks to which 8x8 LFNST is applied.

[0263] [Table 11-1] [Table 11-2]

[0264] Referring to Table 11, the variable nonZeroSize, which indicates the size or number of non-zero variables on which a matrix operation is performed to apply an LFNST, is set to 8 or 16. If the width and height of the transform block are 4 or 8, that is, as shown in Figure 11, the length of the output data of the forward LFNST or the input data of the reverse LFNST for a 4x4 block and an 8x8 block is 8. For all other blocks, the length of the output data of the forward LFNST or the input data of the reverse LFNST is 16 [nonZeroSize=((nTbW==4 && nTbH==4)||(Tb==8 && nTbH==8))?8:16]. In other words, when a forward LFNST is applied, the maximum number of output data is limited to 16.

[0265] The input data for such a backward LFNST can be arranged two-dimensionally according to diagonal scanning [xC=DiagScanOrder[log2LfnstSize][log2LfnstSize][x][0], yC=DiagScanOrder[log2LfnstSize][log2LfnstSize][x][1]]. The above description shows the decoding process for (i) of the LFNST simplification method.

[0266] In addition, in this embodiment, since zeroing out of LFNST is performed on transform blocks having a width and height of 8 or more on which an 8x8 LFNST is performed, as shown in Table 11, the variables nonZeroW and nonZeroH indicating the width and height of a block including non-zero transform coefficients input to the inverse linear transform can be derived as 8 for a transform block having a width and height of 8 or more when the lfnst index is greater than 0 [(lfnst_idx[xTbY][yTbY]>0 && nTbW >= 8 && nTbH >= 8)?8, (lfnst_idx[xTbY][yTbY]>0 && nTbW >= 8 && nTbH >= 8)?8]. In other words, this means that areas of the transform block other than the 8x8 area on which lfnst is performed are zeroed out and filled with zeros. This part shows the decoding process for (ii)-(B) of the LFNST simplification method.

[0267] Example 6

[0268] -Limit the number of output data for forward LFNST to a maximum of 16 (i)

[0269] -When 8x8 LFNST is applied, zero out all areas where 8x8 LFNST is not applied. (ii)-(B)

[0270] The LFNST index signaling method that does not check whether non-zero data exists can be applied as is. That is, the zero-out in (ii)-(B) is performed by the encoding device, and the decoding device can signal the LFNST index by assuming that non-zero data may exist in the corresponding zero-out area. In this case, only the remaining zero-out areas in Figure 11, excluding Figure 11(c), are checked, and the LFNST index is signaled based on the check.

[0271] In the fourth and sixth embodiments, zeroing out is performed only in the encoding device, and the decoding device parses the lfnst index without taking the zeroing out into consideration, so the specification text for the LFNST index is not changed.

[0272] In the case of the zero-out method proposed in (ii), the amount of data ultimately generated when both the linear transform and the LFNST are applied is reduced, thereby reducing the amount of calculation required to perform the entire transform process. In other words, when the LFNST is applied, zero-out is also applied to the output data of the forward linear transform that exists in areas where the LFNST is not applied, so there is no need to generate data for areas that will be zeroed out when the forward linear transform is performed. Therefore, the amount of calculation required to generate this data can be reduced. Additional effects of the zero-out method proposed in (ii) can be summarized as follows.

[0273] First, as mentioned above, the amount of computation required to perform the entire transformation process is reduced.

[0274] In particular, when (ii)-(B) is applied, the amount of calculations in the worst case is reduced, making the transform process lighter.In addition, while a large amount of calculations is generally required to execute a large-size linear transform, when (ii)-(B) is applied, the number of data derived as a result of executing the forward LFNST can be reduced to 16 or less, and the effect of reducing the amount of transform calculations increases further as the size of the entire block (TU or CU) increases.

[0275] Second, the overall amount of computation required for the conversion process is reduced, which can reduce the power consumption required to perform the conversion.

[0276] Third, it reduces the latency involved in the conversion process.

[0277] A quadratic transform such as LFNST adds computational complexity to an existing linear transform, thereby increasing the overall latency associated with the execution of the transform. In particular, in the case of intra prediction, reconstruction data of neighboring blocks is used in the prediction process, so the increase in latency due to the quadratic transform during encoding leads to an increase in latency until reconstruction, which can lead to an increase in the overall latency of intra prediction encoding.

[0278] However, when the zero-out technique presented in (ii) is applied, the latency of the primary transform can be significantly reduced when LFNST is applied, so the latency of the entire transform execution remains the same or even decreases, making it easier to implement the encoding device.

[0279] The following drawings are created to explain a specific example of the present specification. The names of specific devices and names of specific signals / messages / fields shown in the drawings are provided for illustrative purposes only, and the technical features of the present specification are not limited to the specific names used in the following drawings.

[0280] FIG. 16 is a flowchart illustrating the operation of a video decoding device according to one embodiment of the present document.

[0281] Each step disclosed in Figure 16 may be performed by the decoding apparatus 300 disclosed in Figure 3. More specifically, S1610 and S1640 may be performed by the entropy decoding unit 310 disclosed in Figure 3, S1620 may be performed by the inverse quantization unit 321 disclosed in Figure 3, S1630, S1650, and S1660 may be performed by the inverse transform unit 322 disclosed in Figure 3, and S1670 may be performed by the addition unit 340 disclosed in Figure 3. In addition, the operations of S1610 to S1670 are based on some of the contents described above with reference to Figures 4 to 15. Therefore, detailed descriptions that overlap with the contents described above with reference to Figures 3 to 15 will be omitted or simplified.

[0282] A decoding device 300 according to one embodiment receives a bitstream including residual information and can derive residual information, e.g., quantized transform coefficients, for a current block, i.e., a transform block to be transformed, from the bitstream (S1610).

[0283] More specifically, the decoding apparatus 300 may decode information on quantized transform coefficients for a current block from a bitstream and derive quantized transform coefficients for a target block based on the information on the quantized transform coefficients for the current block. The information on the quantized transform coefficients for the target block may be included in a Sequence Parameter Set (SPS) or a slice header, and may include at least one of information on whether a simplified transform (RST) is applied, information on a simplification factor, information on a minimum transform size to apply the simplified transform, information on a maximum transform size to apply the simplified transform, a simplified inverse transform size, and information on a transform index indicating one of the transform kernel matrices included in the transform set.

[0284] The decoding apparatus 300 may derive transform coefficients by performing inverse quantization on the quantized transform coefficients for the current block (S1620).

[0285] The derived transform coefficients may be two-dimensionally arranged in the current block, and the decoding device may derive non-zero data, i.e., information on non-zero significant coefficients, in the current block through such residual coding. That is, the decoding device may obtain information on the last position of non-zero significant coefficients in the current block.

[0286] The transform coefficients derived based on the residual information in S1620 may be dequantized transform coefficients as described above, or may be quantized transform coefficients. That is, the transform coefficients may be data that can be checked for non-zero data in the current block, regardless of whether they can be quantized or not.

[0287] For example, the decoding apparatus may determine whether a significant coefficient exists in a second region other than the first region at the upper left of the current block (S1630).

[0288] The first region can be derived based on the size of the current block.

[0289] For example, if the size of the current block is 4x4 or 8x8, the first region may be from the upper left side of the current block to the 8th sample position in the scanning direction.

[0290] If the size of the current block is 4x4 or 8x8, eight pieces of data are output through the forward LFNST, and the eight transform coefficients received by the decoding device can be arranged from the upper left side of the current block to the eighth sample position in the scanning direction, as shown in (a) of Figure 13 and (a) of Figure 14.

[0291] Also, if the size of the current block is not 4x4 or 8x8, the first region may be the 4x4 region at the upper left of the current block. If the size of the current block is not 4x4 or 8x8, 16 data are output through the forward LFNST, and therefore the 16 transform coefficients received by the decoding device may be arranged in the 4x4 region at the upper left of the current block, as shown in (b) to (d) of Figure 13 and (b) of Figure 14.

[0292] Meanwhile, the transform coefficients that can be arranged in the first region can be arranged along the diagonal scan direction as shown in FIG.

[0293] Also, by way of example, the transform coefficients for a block to which LFNST is applied may be up to 16.

[0294] If the decoding device determines that there are no valid coefficients in the second region excluding the first region, that is, if there are no valid coefficients after checking the valid coefficients up to the second region of the current block, the decoding device can parse the LFNST index from the bitstream (S1640).

[0295] As described above, when the forward LFNST is performed by the encoding apparatus, the remaining area of ​​the current block, excluding the transform coefficients by the LFNST, can be zeroed out.

[0296] Therefore, if there is a valid coefficient in the second region, the LFNST is not applied, so the LFNST index is not signaled and the decoding device does not parse the LFNST index.

[0297] The LFNST index information is received as syntax information, which is received as a binary-coded bin string containing 0s and 1s.

[0298] The LFNST index syntax element in this embodiment can indicate whether an inverse LFNST or an inverse non-separable transform is applied, and which of the transform kernel matrices is included in the transform set. If the transform set includes two transform kernel matrices, the value of the Transform Index syntax element can be three.

[0299] That is, according to one embodiment, the value of the syntax element for the LFNST index may include 0, which indicates that the inverse LFNST is not applied to the current block, 1, which indicates the first transformation kernel matrix among the transformation kernel matrices, or 2, which indicates the second transformation kernel matrix among the transformation kernel matrices.

[0300] Once the LFNST index is parsed, the decoding device may apply the LFNST matrix to the transform coefficients of the first region to derive modified transform coefficients (S1650).

[0301] The inverse transform unit 332 of the decoding device 300 can determine a transform set based on a mapping relationship according to the intra prediction mode applied to the current block, and perform an inverse LFNST, i.e., an inverse non-separable transform, based on the transform set and the value of a syntax element for the LFNST index.

[0302] As described above, multiple transform sets can be determined depending on the intra prediction mode of the transform block to be transformed, and inverse LFNST can be performed based on one of the transform kernel matrices, i.e., LFNST matrices, included in the transform set indicated by the LFNST index. A matrix applied to inverse LFNST may be called an inverse LFNST matrix or an LFNST matrix, and such a matrix may be named any name as long as it is in a transpose relationship with the matrix used for forward LFNST.

[0303] In one example, the inverse LFNST matrix may be a non-square matrix with fewer columns than rows.

[0304] Meanwhile, a predetermined number of modified transform coefficients may be derived based on the size of the current block. For example, if the height and width of the current block are 8 or more, 48 modified transform coefficients may be derived as shown on the left side of Figure 7. If the width and height of the current block are less than 8, i.e., if the width and height of the current block are 4 or more but less than 8, 16 modified transform coefficients may be derived as shown on the right side of Figure 7.

[0305] As shown in FIG. 7, the 48 modified transform coefficients can be arranged in the 4x4 areas on the upper left, upper right, and lower left of the 8x8 area on the upper left of the current block, and the 16 modified transform coefficients can be arranged in the 4x4 area on the upper left of the current block.

[0306] The 48 modified transform coefficients and the 16 modified transform coefficients may be arranged vertically or horizontally according to the intra prediction mode of the current block. For example, if the intra prediction mode is a horizontal direction (modes 2 to 34 in FIG. 9) based on a diagonal direction (mode 34 in FIG. 9), the modified transform coefficients may be arranged horizontally, i.e., in a row-major order, as shown in (a) of FIG. 7. If the intra prediction mode is a vertical direction (modes 35 to 66 in FIG. 9) based on a diagonal direction, the modified transform coefficients may be arranged horizontally, i.e., in a column-major order, as shown in (b) of FIG. 7.

[0307] In one embodiment, S1650 may include the steps of decoding a transform index, determining whether a condition for applying an inverse RST is met based on the transform index, i.e., the LFNST index, selecting a transform kernel matrix, and, if the condition for applying the inverse LFNST is met, applying the inverse LFNST to the transform coefficients based on the selected transform kernel matrix and / or a simplification factor. In this case, the size of the simplified inverse transform matrix may be determined based on the simplification factor.

[0308] Referring to S1650, it can be seen that residual samples for a current block are derived based on the inverse LFNST of the transform coefficients of the current block. Considering the size of the inverse transform matrix, the size of a typical inverse transform matrix is ​​NxN, while the size of the inverse LFNST matrix is ​​reduced to NxR. Therefore, compared to performing a conventional transform, memory usage when performing the inverse LFNST can be reduced by a ratio of R / N. Furthermore, compared to the number of multiplication operations required when using a typical inverse transform matrix (NxN), the number of multiplication operations can be reduced by a ratio of R / N (NxR) when using the inverse LFNST matrix. Furthermore, since only R transform coefficients need to be decoded when applying the inverse LFNST, compared to the number of transform coefficients required when applying a conventional inverse transform (N), the total number of transform coefficients for the current block is reduced from N to R, thereby improving decoding efficiency. In summary, S1650 can improve the (inverse) transform efficiency and decoding efficiency of the decoding device 300 through the inverse LFNST.

[0309] The decoding apparatus 300 according to an embodiment may derive residual samples for the current block based on the inverse linear transform of the modified transform coefficients (S1660).

[0310] On the other hand, if LFNST is not applied, only the first inverse transform procedure based on MTS can be applied in the inverse transform procedure. That is, the decoding device determines whether LFNST is applied to the current block as in the above-described embodiment, and if LFNST is not applied, it can derive residual samples from the transform coefficients through the first inverse transform.

[0311] As shown in FIG. 16, if there are significant coefficients in the second region excluding the first region in the upper left corner of the current block, it is determined that LFNST has not been applied, and the decoding device can derive residual samples from the transform coefficients through a first-order inverse transform.

[0312] The primary inverse transform procedure may be referred to as an inverse primary transform procedure or an inverse MTS transform procedure. Such an MTS-based primary inverse transform procedure may also be omitted in some cases.

[0313] In addition, a simplified inverse transform can be applied to the inverse linear transform, or a normal separable transform can be used.

[0314] The decoding apparatus 300 according to an embodiment may generate a reconstructed picture based on the residual sample for the current block and the predicted sample for the current block (S1670).

[0315] The following drawings are created to explain a specific example of the present specification. The names of specific devices and names of specific signals / messages / fields shown in the drawings are provided for illustrative purposes only, and the technical features of the present specification are not limited to the specific names used in the following drawings.

[0316] FIG. 17 is a flowchart illustrating the operation of a video encoding device according to one embodiment of the present document.

[0317] The steps disclosed in FIG. 17 may be performed by the encoding apparatus 200 disclosed in FIG. 2. More specifically, S1710 may be performed by the prediction unit 220 disclosed in FIG. 2, S1720 may be performed by the subtraction unit 231 disclosed in FIG. 2, S1730 to S1750 may be performed by the transformation unit 232 disclosed in FIG. 2, and S1760 may be performed by the quantization unit 233 and entropy encoding unit 240 disclosed in FIG. 2. In addition, the operations of S1710 to S1760 are based on some of the contents described above with reference to FIGS. 4 to 15. Therefore, detailed descriptions that overlap with those described above with reference to FIGS. 2 and 4 to 15 will be omitted or simplified.

[0318] The encoding apparatus 200 according to an embodiment may derive prediction samples based on the intra prediction mode applied to the current block (S1710).

[0319] The encoding apparatus 200 according to an embodiment may derive residual samples for the current block based on the predicted samples (S1720).

[0320] The encoding apparatus 200 according to an embodiment may derive transform coefficients for the current block based on a linear transform of the residual samples (S1730).

[0321] The primary transform can be performed via multiple transform kernels, where the transform kernel can be selected based on the intra-prediction mode.

[0322] The encoding apparatus 200 may determine whether to perform a quadratic transform or a non-separable transform, specifically an LFNST, on the transform coefficients for the current block.

[0323] If it is determined that LFNST is to be performed, the encoding apparatus 200 may derive modified transform coefficients for the current block based on the transform coefficients of the first region in the upper left corner of the current block and a predetermined LFNST matrix (S1740).

[0324] The encoding apparatus 200 may determine a transform set based on a mapping relationship according to an intra-prediction mode applied to the current block, and perform an LFNST, i.e., a non-separable transform, based on one of two LFNST matrices included in the transform set.

[0325] As described above, multiple transform sets can be determined depending on the intra prediction mode of the transform block to be transformed. The matrix applied to LFNST has a transpose relationship with the matrix used in backward LFNST.

[0326] In one example, the LFNST matrix may be a non-square matrix with fewer rows than columns.

[0327] The first region may be derived based on the size of the current block. For example, if the height and width of the current block are 8 or more, the first region may be the 4x4 regions at the upper left, upper right, and lower left of the 8x8 region at the upper left of the current block as shown on the left side of Fig. 7. If the height and width of the current block are not 8 or more, the first region may be the 4x4 region at the upper left of the current block as shown on the right side of Fig. 7.

[0328] The transform coefficients of the first region may be arranged one-dimensionally in the vertical or horizontal direction according to the intra prediction mode of the current block for multiplication with the LFNST matrix.

[0329] The 48 modified transform coefficients or the 16 modified transform coefficients of the first region may be arranged vertically or horizontally according to the intra prediction mode of the current block. For example, if the intra prediction mode is a horizontal direction (modes 2 to 34 in FIG. 9) based on a diagonal direction (mode 34 in FIG. 9), the transform coefficients may be arranged horizontally, i.e., in a row-major order, as shown in (a) of FIG. 7. If the intra prediction mode is a vertical direction (modes 35 to 66 in FIG. 9) based on a diagonal direction, the transform coefficients may be arranged horizontally, i.e., in a column-major order, as shown in (b) of FIG. 7.

[0330] In one embodiment, LFNST may be performed based on a simplified transformation matrix or a transformation kernel matrix, where the simplified transformation matrix may be a non-square matrix with fewer rows than columns.

[0331] In one example, S1740 may include determining whether a condition for applying LFNST is met, generating and encoding an LFNST index based on the determination, selecting a transformation kernel matrix, and, if the condition for applying LFNST is met, applying LFNST to the residual samples based on the selected transformation kernel matrix and / or a simplification factor. In this case, the size of the simplified transformation kernel matrix may be determined based on the simplification factor.

[0332] Referring to S1740, it can be seen that transform coefficients for a current block are derived based on LFNST for residual samples. Considering the size of the transform kernel matrix, the size of a conventional transform kernel matrix is ​​NxN, while the size of a simplified transform matrix is ​​reduced to NxR. Therefore, compared to performing a conventional transform, memory usage can be reduced by a ratio of R / N when performing RST. Furthermore, compared to the number of multiplication operations (NxN) when using a conventional transform kernel matrix, the number of multiplication operations can be reduced by a ratio of R / N (RxN) when using a simplified transform kernel matrix. Furthermore, since only R transform coefficients are derived when RST is applied, the total number of transform coefficients for a current block is reduced from N to R, compared to the number of transform coefficients derived when a conventional transform is applied (N). This reduces the amount of data transmitted from the encoding apparatus 200 to the decoding apparatus 300. In summary, according to S1740, the transform efficiency and coding efficiency of the encoding apparatus 200 can be improved through LFNST.

[0333] Meanwhile, according to an example, the encoding apparatus may zero out a second region of the current block in which no modified transform coefficients exist (S1750).

[0334] 13 and 14, the remaining areas of the current block where no modified transform coefficients exist can be processed as all 0. This zeroing reduces the amount of calculation required to perform the entire transform process, reduces the amount of calculation required for the entire transform process, and can reduce power consumption required to perform the transform. In addition, it can reduce latency associated with the transform process and increase video coding efficiency.

[0335] On the other hand, if LFNST is not applied, only the first-order transform procedure based on MTS can be applied to the transform procedure as described above. That is, the encoding apparatus determines whether LFNST is applied to the current block as in the above-described embodiment, and if LFNST is not applied, it can derive transform coefficients from residual samples through first-order transform.

[0336] Such a primary conversion procedure may be referred to as a primary conversion procedure or an MTS conversion procedure. Such an MTS-based primary conversion procedure may also be omitted in some cases.

[0337] According to an embodiment, the encoding apparatus 200 may derive quantized transform coefficients by performing quantization based on modified transform coefficients for a current block, and encode information about the quantized transform coefficients and LFNST indices (S1760). That is, the encoding apparatus may generate residual information including information about the quantized transform coefficients. The residual information may include the above-described transform-related information / syntax elements. The encoding apparatus may encode image / video information including the residual information and output the encoded image / video information in the form of a bitstream.

[0338] More specifically, the encoding apparatus 200 may generate information about the quantized transform coefficients and encode the generated information about the quantized transform coefficients.

[0339] In one example, the information about the quantized transform coefficients may include at least one of information on whether LFNST is applied, information on a simplification factor, information on a minimum transform size to which LFNST is applied, and information on a maximum transform size to which LFNST is applied.

[0340] In addition, the encoding apparatus 200 may encode information on the size of the maximum transform application block, for example, flag information such as sps_max_luma_transform_size_64_flag, at the sequence parameter set level.

[0341] In this document, at least one of quantization / dequantization and / or transform / inverse transform may be omitted. When the quantization / dequantization is omitted, the quantized transform coefficients may be referred to as transform coefficients. When the transform / inverse transform is omitted, the transform coefficients may also be referred to as coefficients or residual coefficients, or may still be referred to as transform coefficients for uniformity of representation.

[0342] Also, in this document, quantized transform coefficients and transform coefficients may be referred to as transform coefficients and scaled transform coefficients, respectively. In this case, residual information may include information about transform coefficients, and the information about the transform coefficients may be signaled via residual coding syntax. Transform coefficients may be derived based on the residual information (or information about the transform coefficients), and scaled transform coefficients may be derived through an inverse transform (scaling) of the transform coefficients. Residual samples may be derived based on an inverse transform (transform) of the scaled transform coefficients. This may also be applied / expressed in other parts of this document.

[0343] In the above-described embodiments, the method is described based on a flowchart as a series of steps or blocks, but this document is not limited to the order of steps, and some steps may occur in a different order or simultaneously with other steps than those described above. Furthermore, those skilled in the art will understand that the steps shown in the flowchart are not exclusive, and other steps may be included, or one or more steps in the flowchart may be deleted without affecting the scope of this document.

[0344] The method according to the present document described above can be implemented in the form of software, and the encoding device and / or decoding device according to the present document can be included in a device that performs video processing, such as a TV, a computer, a smartphone, a set-top box, or a display device.

[0345] In this document, when an embodiment is implemented in software, the methods described above may be implemented with modules (processes, functions, etc.) that perform the functions described above. The modules may be stored in memory and executed by a processor. The memory may be internal or external to the processor and may be coupled to the processor in various well-known ways. The processor may include an application-specific integrated circuit (ASIC), other chipsets, logic circuits, and / or data processing devices. The memory may include read-only memory (ROM), random access memory (RAM), flash memory, a memory card, a storage medium, and / or other storage devices. That is, the embodiments described herein may be implemented and executed on a processor, microprocessor, controller, or chip. For example, the functional units illustrated in each figure may be implemented and executed on a computer, processor, microprocessor, controller, or chip.

[0346] In addition, the decoding device and encoding device to which this document is applied may be included in, and may be used to process video signals or data signals, a multimedia broadcast transmitting / receiving device, a mobile communication terminal, a home cinema video device, a digital cinema video device, a surveillance camera, a video interaction device, a real-time communication device such as video communication, a mobile streaming device, a storage medium, a camcorder, a customized video (VoD) service providing device, an over-the-top (OTT) video device, an internet streaming service providing device, a three-dimensional (3D) video device, an image telephone video device, a medical video device, etc. For example, over-the-top (OTT) video devices may include a game console, a Blu-ray player, an internet access TV, a home theater system, a smartphone, a tablet PC, a digital video recorder (DVR), etc.

[0347] Furthermore, the processing method to which this document is applied may be produced in the form of a computer-executable program and stored in a computer-readable recording medium. Multimedia data having a data structure according to this document may also be stored in a computer-readable recording medium. The computer-readable recording medium includes all types of storage devices and distributed storage devices in which computer-readable data is stored. The computer-readable recording medium may include, for example, a Blu-ray Disc (BD), a Universal Serial Bus (USB), a ROM, a PROM, an EPROM, an EEPROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, and an optical data storage device. The computer-readable recording medium may also include media embodied in the form of a carrier wave (e.g., transmission via the Internet). A bitstream generated by the encoding method may be stored in a computer-readable recording medium or transmitted via a wired or wireless communication network. Furthermore, embodiments of this document may be embodied in a computer program product represented by program code, which can be executed by a computer according to embodiments of this document. The program code may be stored on a computer-readable carrier.

[0348] FIG. 18 exemplarily shows a structural diagram of a content streaming system to which this document applies.

[0349] Furthermore, the content streaming system to which this document applies can broadly include an encoding server, a streaming server, a web server, a media storage, a user device, and a multimedia input device.

[0350] The encoding server compresses content input from a multimedia input device such as a smartphone, camera, camcorder, etc. into digital data to generate a bitstream and transmits the bitstream to the streaming server. As another example, if a multimedia input device such as a smartphone, camera, camcorder, etc. directly generates a bitstream, the encoding server may be omitted. The bitstream may be generated by an encoding method or a bitstream generation method to which this document applies, and the streaming server may temporarily store the bitstream during the process of transmitting or receiving the bitstream.

[0351] The streaming server transmits multimedia data to a user device based on a user request via a web server, and the web server acts as an intermediary that informs the user of available services. When a user requests a desired service from the web server, the web server transmits the request to the streaming server, which then transmits the multimedia data to the user. The content streaming system may include a separate control server, which controls commands and responses between devices in the content streaming system.

[0352] The streaming server may receive content from a media storage and / or an encoding server. For example, if content is received from the encoding server, the content may be received in real time. In this case, the streaming server may store the bitstream for a certain period of time to provide a smooth streaming service.

[0353] Examples of the user devices include mobile phones, smartphones, laptop computers, digital broadcasting terminals, personal digital assistants (PDAs), portable multimedia players (PMPs), navigation systems, slate PCs, tablet PCs, ultrabooks, wearable devices (e.g., smartwatches, smart glasses, and head mounted displays (HMDs)), digital TVs, desktop computers, digital signage, etc. Each server in the content streaming system can be operated as a distributed server, and in this case, data received by each server can be processed in a distributed manner.

[0354] The claims described herein may be combined in various ways. For example, technical features of method claims herein may be combined to be embodied as an apparatus, and technical features of apparatus claims herein may be combined to be embodied as a method. Furthermore, technical features of method claims herein and technical features of apparatus claims herein may be combined to be embodied as an apparatus, and technical features of method claims herein and technical features of apparatus claims herein may be combined to be embodied as a method.

Claims

1. A video decoding method performed by a decoding device, comprising: obtaining residual information from the bitstream; deriving transform coefficients for a current block based on the residual information; determining whether a valid coefficient exists in a second region excluding a first region at the upper left of the current block; parsing an LFNST index from the bitstream based on the absence of the significant coefficients in the second region; applying an LFNST matrix derived based on the LFNST index to the transform coefficients of the first region to derive modified transform coefficients; deriving residual samples for the current block based on an inverse linear transform of the modified transform coefficients; generating a reconstructed picture based on residual samples for the current block; the first region is derived based on a size of the current block; Based on the size of the current block being 4x4 or 8x8, the first region is from the upper left side of the current block to an 8th sample position in a scanning direction, If the size of the current block is not 4x4 or 8x8, the first region is a 4x4 region at the upper left of the current block; the predetermined number of modified transform coefficients is derived based on a size of the current block; deriving 48 modified transform coefficients based on the height and width of the current block being equal to or greater than 8; deriving 16 modified transform coefficients based on the width and height of the current block being equal to or greater than 4 and the width or height of the current block being less than 8; The LFNST matrix or the transform coefficients are represented in 8 bits.

2. The video decoding method of claim 1 , wherein the scan direction is a diagonal scan direction.

3. 2. The image decoding method of claim 1, wherein the 48 modified transform coefficients are arranged in 4x4 regions at the upper left, upper right, and lower left of an 8x8 region at the upper left of the current block.

4. The image decoding method of claim 1 , wherein the 16 modified transform coefficients are arranged in a 4×4 region at the upper left corner of the current block.

5. The image decoding method of claim 3 , wherein the 48 modified transform coefficients and the 16 modified transform coefficients are arranged vertically or horizontally according to an intra-prediction mode of the current block.

6. A video encoding method performed by a video encoding apparatus, comprising: deriving a predicted sample for the current block; deriving a residual sample for the current block based on the predicted sample; deriving transform coefficients for the current block based on a linear transform of the residual samples; deriving modified transform coefficients for the current block based on transform coefficients of a first region in an upper left corner of the current block and a predetermined LFNST matrix; zeroing out a second region of the current block where the modified transform coefficients are not present; encoding residual information derived through quantization of the modified transform coefficients and an LFNST index indicating the LFNST matrix; the first region is derived based on a size of the current block; Based on the size of the current block being 4x4 or 8x8, the first region is from the upper left side of the current block to an 8th sample position in a scanning direction, If the size of the current block is not 4x4 or 8x8, the first region is a 4x4 region at the upper left of the current block; the first region is derived based on a size of the current block; The first region is a 4x4 region at the upper left, upper right, and lower left of an 8x8 region at the upper left of the current block, based on the height and width of the current block being equal to or greater than 8; the first region is a 4x4 region on the upper left side of the current block based on the width and height of the current block being equal to or greater than 4 and the width or height of the current block being less than 8; The video encoding method, wherein the LFNST matrix or the transform coefficients are represented by 8 bits.

7. The image encoding method of claim 6 , wherein the transform coefficients in the first region are arranged one-dimensionally vertically or horizontally according to an intra prediction mode of the current block for multiplication with the LFNST matrix.

8. the predetermined number of modified transform coefficients is derived based on a size of the current block; deriving eight modified transform coefficients based on whether the size of the current block is 4x4 or 8x8; The video encoding method of claim 6 , wherein 16 modified transform coefficients are derived based on whether the size of the current block is not 4×4 or 8×8.

9. The image encoding method of claim 8 , wherein the modified transform coefficients are arranged in a diagonal scan direction on the upper left side of the current block.

10. If the size of the current block is 4x4 or 8x8, the modified transform coefficients are arranged from the upper left side of the current block to an 8th sample position in the diagonal scanning direction; The image encoding method of claim 9, wherein if the size of the current block is not 4x4 or 8x8, the modified transform coefficients are arranged in a 4x4 region at the upper left of the current block.

11. obtaining a bitstream, the bitstream is generated by: deriving predicted samples for a current block; deriving residual samples for the current block based on the predicted samples; deriving transform coefficients for the current block based on a linear transform of the residual samples; deriving modified transform coefficients for the current block based on the transform coefficients in a first region at the upper left of the current block and a predetermined LFNST matrix; zeroing out a second region of the current block where the modified transform coefficients do not exist; and encoding residual information derived through quantization of the modified transform coefficients and an LFNST index indicating the LFNST matrix; transmitting the bitstream; the first region is derived based on a size of the current block; Based on the size of the current block being 4x4 or 8x8, the first region is from the upper left side of the current block to an 8th sample position in a scanning direction, If the size of the current block is not 4x4 or 8x8, the first region is a 4x4 region at the upper left of the current block; the first region is derived based on a size of the current block; The first region is a 4x4 region at the upper left, upper right, and lower left of an 8x8 region at the upper left of the current block, based on the height and width of the current block being equal to or greater than 8; the first region is a 4x4 region on the upper left side of the current block based on the width and height of the current block being equal to or greater than 4 and the width or height of the current block being less than 8; A transmission method in which the LFNST matrix or the transform coefficients are represented by 8 bits.

Images