Patent Publication Number: US-2023134294-A1

Title: Coding of information about transform kernel set

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 17/556,099, filed on Dec. 20, 2021, which is a continuation pursuant to 35 U.S.C. § 119(e) of International Application PCT/KR2020/007599, with an international filing date of Jun. 11, 2020, which claims the benefit of U.S. Provisional Patent Application No. 62/863,812, filed on Jun. 19, 2019, the contents of which are hereby incorporated by reference herein in their entirety. 
    
    
     BACKGROUND OF THE DISCLOSURE 
     Field of the disclosure 
     The present disclosure relates to an image coding technology, and more particularly, to the coding of information about a transform kernel set. 
     Related Art 
     Recently, the demand for high resolution, high quality image/video such as 4K, 8K or more Ultra High Definition (UHD) image/video is increasing in various fields. As the image/video resolution or quality becomes higher, relatively more amount of information or bits are transmitted than for conventional image/video data Therefore, if image/video data are transmitted via a medium such as an existing wired/wireless broadband line or stored in a legacy storage medium, costs for transmission and storage are readily increased. 
     Moreover, interests and demand are growing for virtual reality (VR) and artificial reality (AR) contents, and immersive media such as hologram; and broadcasting of images/videos exhibiting image/video characteristics different from those of an actual image/video, such as game images/videos, are also growing. 
     Therefore, a highly efficient image/video compression technique is required to effectively compress and transmit, store, or play high resolution, high quality images/videos showing various characteristics as described above. 
     SUMMARY 
     According to an embodiment of the present document, a method and an apparatus for enhancing image/video coding efficiency are provided. 
     According to an embodiment of the present document, a method and an apparatus for coding an MTS index in video coding are provided. 
     According to an embodiment of the present document, a method and an apparatus for signaling MTS index information are provided. 
     According to an embodiment of the present document, a method and an apparatus for signaling information representing a transform kernel set to be applied to a current block among a plurality of transform kernel sets are provided. 
     According to an embodiment of the present document, a method and an apparatus for context coding or bypass coding with respect to bins for an MTS index are provided. 
     According to an embodiment of the present document, a video/image decoding method performed by a decoding apparatus is provided. 
     According to an embodiment of the present document, a decoding apparatus for performing videolimage decoding is provided. 
     According to an embodiment of the present document, a video/image encoding method performed by an encoding apparatus is provided. 
     According to an embodiment of the present document, an encoding apparatus for performing video/image encoding is provided. 
     According to an embodiment of the present document, a computer-readable digital storage medium storing encoded video/image information generated according to the video/image encoding method disclosed in at least one of the embodiments of this document is provided. 
     According to an embodiment of the present document, a computer-readable digital storage medium storing encoded information or encoded video/image information causing a. decoding apparatus to perform the video/image decoding method disclosed in at least one of the embodiments of this document is provided. 
     According to the present document, the overall image/video compression efficiency can be enhanced. 
     According to the present document, the MTS index information can be efficiently signaled. 
     According to the present document, complexity of the coding system can be lowered by efficiently coding the MTS index information. 
     Effects that can be obtained through a detailed example of the present document are not limited to the effects enumerated above. For example, there may be various technical effects that can be understood or induced by a person having ordinary skill in the related art from the present document. Accordingly, the detailed effects of the present document are not limited to those explicitly stated in the present document, but may include various effects that can be understood or induced from the technical features of the present document. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    schematically illustrates an example of a video/image coding system to which the present document is applicable. 
         FIG.  2    is a diagram schematically explaining the configuration of a video/image encoding apparatus to which the present document is applicable. 
         FIG.  3    is a diagram schematically explaining the configuration of a video/image; decoding apparatus to which the present document is applicable. 
         FIG.  4    schematically illustrates a multi-transform technique according to an embodiment of the present document. 
         FIG.  5    exemplarily illustrates intra directional modes in 65 prediction directions. 
         FIGS.  6  and  7    are diagrams explaining RST according to an embodiment of the present document. 
         FIG.  8    exemplarily illustrates context-adaptive binary arithmetic coding (CABAL) for encoding syntax elements. 
         FIGS.  9  and  10    schematically illustrate a video/image encoding method and an example of related components according to embodiment(s) of the present document. 
         FIGS.  11  and  12    schematically illustrate a video/image decoding method and an example of related components according to embodiment(s) of the present document. 
         FIG.  13    illustrates an example of a content streaming system to which embodiments disclosed in the present document are applicable. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     The present disclosure may be modified in various forms, and specific embodiments thereof will be described and illustrated in the drawings. However, the embodiments are not intended for limiting the disclosure. The terms used in the following description are used to merely describe specific embodiments, but are not intended to limit the disclosure. An expression of a singular number includes an expression of the plural number, so long as it is clearly read differently. The terms such as “include” and “have” are intended to indicate that features, numbers, steps, operations, elements, components, or combinations thereof used in the following description exist and it should be thus understood that the possibility of existence or addition of one or more different features, numbers, steps, operations, elements, components, or combinations thereof is not excluded. 
     In addition, each configuration of the drawings described in this document is an independent illustration for explaining functions as features that are different from each other, and does not mean that each configuration is implemented by mutually different hardware or different software. For example, two or more of the configurations can be combined to form one configuration, and one configuration can also be divided into multiple configurations. Without departing from the gist of this document, embodiments in which configurations are combined and/or separated are included in the scope of claims. 
     Hereinafter, examples of the present embodiment will be described in detail with reference to the accompanying drawings. In addition, like reference numerals are used to indicate like elements throughout the drawings, and the same descriptions on the like elements will be omitted. 
     This document relates to video/image coding. For example, methods/embodiments disclosed in this document may be related to the versatile video coding (V VC) standard (ITU-T Rec. H.266), the next-generation video/image coding standard after VVC, or other video coding related standards (e.g., high efficiency video coding (HEVC) standard (ITU-T Rec. H.265), essential video coding (EVC) standard, AVS2 standard, and the like). 
     This document suggests various embodiments of video/image coding, and the above embodiments may also be performed in combination with each other unless otherwise specified. 
     In this document, a video may refer to a series of images over time. A picture generally refers to the unit representing one image at a particular time frame, and a slice/tile refers to the unit constituting a part of the picture in terms of coding. A slice/tile may include one or more coding tree units (CTUs). One picture may consist of one or more slices/tiles. One picture may consist of one or more tile groups. One tile group may include one or more tiles. 
     A pixel or a pel may mean a smallest unit constituting one picture (or image). Also, ‘sample’ may be used as a term corresponding to a pixel. A sample may generally represent a pixel or a value of a pixel, and may represent only a pixel/pixel value of a luma component or only a pixel/pixel value ofa chroma component. 
     A unit may represent a basic unit of image processing. The unit may include at least one of a specific region of the picture and information related to the region. One unit may include one luma block and two chroma (ex. cb, cr) blocks. The unit may be used interchangeably with terms such as block or area in some cases. In a general case, an MxN block may include samples (or sample arrays) or a set (or array) of transform coefficients of M columns and N rows. Alternatively, the sample may mean a pixel value in the spatial domain, and when such a pixel value is transformed to the frequency domain, it may mean a transform coefficient in the frequency domain. 
     In this document, the term “/” and “,” should be interpreted to indicate “and/or.” For instance, the expression “A/B” may mean “A and/or B.” Further, 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.” 
     Further, in the document, the term “of”p 9  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.”1411 In the present specification, “at least one of A and B” may mean “only A”, “only B”, or “both A and B”. Further, in the present specification, the expression “at least one of A or B” or “at least one of A and/or B” may be interpreted the same as “at least one of A and B”. 
     Further, in the present specification, “at least one of A, B and C” may mean “only A”. “only B”, “only C”, or “any combination of A, B and C”. Further, “at least one of A, B or C” or “at least one of A, B and/or C” may mean “at least one of A, B and C”. 
     Further, the parentheses used in the present specification may mean “for example”. Specifically, in the case that “prediction (intra prediction)” is expressed, it may be indicated that “intra prediction” is proposed as an example of “prediction”. In other words, the term “prediction” in the present specification is not limited to “intra prediction”, and it may be indicated that “intra prediction” is proposed as an example of “prediction”. Further, even in the case that “prediction (i.e., intra. prediction)” is expressed, it may be indicated that “intra prediction” is proposed as an example of “prediction”. 
     In the present specification, technical features individually explained in one drawing may be individually implemented, or may be simultaneously implemented. 
       FIG.  1    illustrates an example of a video/image coding system to which the disclosure of the present document may be applied. 
     Referring to FIG I, a video/image coding system may include a source device and a reception device. The source device may transmit encoded Video/image: information or data to the reception device through a digital storage medium or network in the form of a file or streaming. 
     The source device may include a video source, an encoding apparatus, and a transmitter. The receiving device may include a receiver, a decoding apparatus, and a renderer. The encoding apparatus may be called a video/image encoding apparatus, and the decoding apparatus may be called a video/image decoding apparatus. The transmitter may be included in the encoding apparatus. The receiver may be included in the decoding apparatus. The renderer may include a display, and the display may be configured as a separate device or an external component 
     The video source may acquire video image through a process of capturing, synthesizing, or generating the video/image. The video source may include a video/image capture device and/or a video/image generating device. The video/image capture device may include, for example, one or more cameras, video/image archives including previously captured video/images, and the like. The video/image generating device may include, for example, computers, tablets and smartphones, and may (electronically) generate video/images. For example, a virtual video/image may be generated through a computer or the like. In this case, the video/image capturing process may be replaced by a process of generating related data. 
     The encoding apparatus may encode input video/image. The encoding apparatus may perform a series of procedures such as prediction, transform, and quantization for compaction and coding efficiency. The encoded data (encoded video/image information) may be output in the form of a bitstream. 
     The transmitter may transmit the encoded image/image information or data output in the form of a bitstream to the receiver of the receiving device through a digital storage medium or a network in the form of a file or streaming. The digital storage medium may include various storage mediums such as USB, SD, CD, MD, Biu-ray, HDD, SSD, and the like. The transmitter may include an element for generating a media file through a predetermined file format and may include an element for transmission through a broadcast/communication network. The receiver may receive/extract the bitstream and transmit the received bitstream to the decoding apparatus. 
     The decoding apparatus may decode the video/image by performing a series of procedures such as dequantization, inverse transform, and prediction corresponding to the operation of the encoding apparatus. 
     The renderer may render the decoded video/image. The rendered video/image may be displayed through the display. 
       FIG.  2    is a diagram schematically illustrating the configuration of a video/image encoding apparatus to which the disclosure of the present document may be applied. Hereinafter, what is referred to as the video encoding apparatus may include an image encoding apparatus. 
     Referring to  FIG.  2   , the encoding apparatus  200  may include and be configured with 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 subtra.ctor  231 . The adder  250  may be called a reconstructor or reconstructed block generator. The image partitioner  210 , the predictor  220 , the residual processor  230 , the entropy encoder  240 , the adder  250 , and the filter  260 , which have been described above, may be configured by one or more hardware components (e.g., encoder chipsets or processors) according to an embodiment. In addition, the memory  270  may include a decoded picture buffer (DPB), and may be configured by a digital storage medium. The hardware component may further include the memory  270  as an internal/external component. 
     The image partitioner  210  may split an input image (or, picture, frame) input to the encoding apparatus  200  into one or more processing units. As an example, the processing unit may be called a coding unit (CU). In this case, the coding unit may be recursively split according to a Quad-tree binary-tree ternary-tree (QTBTIT) structure from a coding tree unit (CTU) or the largest coding unit (LCU). For example, one coding unit may be split into a. plurality of coding units of a deeper depth based on a quad-tree structure, a binary--tree structure, and/or a ternary-tree structure. In this case, for example, the quad-tree structure is first applied and the binary-tree structure and/or the ternary-tree structure may be later applied. Alternatively, the binary-tree structure may also be first applied. A coding procedure according to the present disclosure may be performed based on a final coding unit which is not split any more. In this case, based on coding efficiency according to image chara.cteri sties or the like, the maximum coding unit may be directly used as the final coding unit, or as necessary, the coding unit may be recursively split into coding units of a deeper depth, such that a coding unit having an optimal size may be used as the final codinu unit. Here, the coding procedure may include a. 
     procedure such as prediction, transform, and reconstruction to be described later. As another example, the processing unit may further include a prediction unit (PU) or a transform unit (TU). In this case, each of the prediction unit and the transform unit may be split or partitioned from the aforementioned final coding unit. The prediction unit may be a unit of sample prediction, and the transform unit may be a unit for inducing a transform coefficient and/or a unit for inducing a residual signal from the transform coefficient. 
     The unit may be interchangeably used with the term such as a block or an area in some cases. Generally, an MxN block may represent samples composed of M columns and N rows or a group of transform coefficients. The sample may generally represent a pixel or a value of the pixel, and may also represent only the pixel/pixel value of a luma component, and also represent only the pixel/pixel value of a chroma component. The sample may be used as the term corresponding to a pixel or a peal configuring one picture (or image). 
     The subtractor  231  may generate a residual signal (residual block, residual samples, or residual sample array) by subtracting a prediction signal (predicted block, prediction samples, or prediction sample array) output from the predictor  220  from an input image signal (original block, original samples, or original sample array), and the generated residual signal is transmitted to the transformer  232 . The predictor  220  may perform prediction for a processing target block (hereinafter, referred to as a “current block”), and generate a predicted block including prediction samples for the current block. The predictor  220  may determine whether intra prediction or inter prediction is applied on a current block or in a CU unit. As described later in the description of each prediction mode, the predictor may generate various kinds of information related to prediction, such as prediction mode information, and transfer the generated information to the entropy encoder  240 . The information on the prediction may be encoded in the entropy encoder  240  and output in the form of a bitstream. 
     The intra predictor  222  may predict a current block with reference to samples within a current picture. The referenced samples may be located neighboring to the current block, or may also be located away from the current block according to the prediction mode. The prediction modes in the intra prediction may include a plurality of non-directional modes and a plurality of directional modes. The non-directional mode may include, for example, a DC mode or a planar mode. The directional mode may include, for example,  33  directional prediction modes or  65  directional prediction modes according to the fine degree of the prediction direction. However, this is illustrative and the directional prediction modes which are more or less than the above number may be used according to the setting. The intra predictor  222  may also determine the prediction mode applied to the current block using the prediction mode applied to the neighboring block. 
     The inter predictor  221  may induce a predicted block of the current block based on a reference block (reference sample array) specified by a motion vector on a reference picture. At this time, in order to decrease the amount of motion information transmitted in the inter prediction mode, the motion information may be predicted in units of a block, a sub-block, or a sample based on the correlation of the motion information between the neighboring block and the current block. The motion information may include a motion vector and a reference picture index. The motion information may further include inter prediction direction (L0 prediction, L1 prediction. Bi prediction, or the like) information. In the case of the inter prediction, the neighboring block may include a spatial neighboring block existing within the current picture and a temporal neighboring block existing in the reference picture. The reference picture including the reference block and the reference picture including the temporal neighboring block may also be the same as each other, and may also be different from each other. The temporal neighboring block may be called the name such as a collocated reference block, a collocated CU (colCU), or the like, and the reference picture including the temporal neighboring block may also be called a collocated picture (colPic). For example, the inter predictor  221  may configure a motion information candidate list based on the neighboring blocks, and generate information indicating what candidate is used to derive the motion vector and/or the reference picture index of the current block. The inter prediction may be performed based on various prediction modes, and for example, in the case of a skip mode and a merge mode, the inter predictor  221  may use the motion information of the neighboring block as the motion information of the current block. In the case otthe skip mode, the residual signal may not be transmitted unlike the merge mode. A motion vector prediction (MVP) mode may indicate the motion vector of the current block by using the motion vector of the neighboring block as a motion vector predictor, and signaling a motion vector difference. 
     The predictor  220  may generate a prediction signal based on various prediction methods described below. For example, the predictor may not only apply intra prediction or inter prediction to predict one block but also simultaneously apply both intra prediction and inter prediction. This may be called combined inter and intra prediction (CIIP). In addition, the predictor may perform an intra block copy (IBC) for prediction of a block. The intra block copy may be used for content image/moving image coding of a game or the like, for example, screen content coding (SCC). The IBC basically performs prediction in the current picture, but may be performed similarly to inter prediction in that a reference block is derived in the current picture. That is, the IBC may use at least one of inter prediction techniques described in the present document. 
     The prediction signal generated through the inter predictor  221  and/or the intra predictor  222  may be used to generate a reconstructed signal or to generate a residual signal. The transformer  232  may generate transform coefficients by applying a transform technique to the residual signal, For example, the transform technique may include at least one of a discrete cosine transform (DCT), a discrete sine transform (DST), a graph-based transform (GBT), or a conditionally non-linear transform (CNT). Here, the GBT means transform obtained from a graph when relationship information between pixels is represented by the graph. The CNT refers to the transform obtained based on a prediction signal generated using all previously reconstructed pixels. In addition, the transform process may be applied to square pixel blocks having the same size, or may be applied to blocks having a variable size rather than a square. 
     The quantizer  233  may quantize the transform coefficients and transmit them to the entropy encoder  240 , and the entropy encoder  240  may encode the quantized signal (information on the quantized transform coefficients) and output a bitstream. The information on the quantized transform coefficients may be referred to as residual information. The quantizer  233  may rearrange block type quantized transform coefficients into a one-dimensional vector form based on a coefficient scanning order, and generate information on the quantized transform coefficients based on the quantized transform coefficients in the one-dimensional vector form. The entropy encoder  240  may perform various encoding methods such as, for example, exponential Golomb, context-adaptive variable length coding (CAVLC), context-adaptive binary arithmetic coding (CABAC), and the like. The entropy encoder  240  may encode information necessary for video/image reconstruction together with or separately from the quantized transform coefficients (e.g., values of syntax elements and the like). Encoded information (e.g., encoded video/image information) may be transmitted or stored in the unit of a network abstraction layer (NAL) in the form of a bitstream. 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). In addition, the videolimage information may further include general constraint information. In the present document, information and/or syntax elements being signaled/transmitted to be described later may be encoded through the above-described encoding procedure, and be included in the bitstream. The bitstream may be transmitted through a network, or may be 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 USB, SD, CD, DVD, Blu-ray, HDD, SSD, and the like. A transmitter (not illustrated) transmitting a signal output from the entropy encoder  240  and/or a storage unit (not illustrated) storing the signal may be configured as an internal/external element of the encoding apparatus  200 , and alternatively, the transmitter may be included in the entropy encoder  240 . 
     The quantized transform coefficients output from the quantizer  233  may be used to generate a prediction signal. For example, the residual signal (residual block or residual samples) may be reconstructed by applying dequantization and inverse transform to the quantized transform coefficients through the dequantizer  234  and the inverse transformer  235 . The adder  250  adds the reconstructed residual signal to the prediction signal output from the predictor  220  to generate a reconstructed signal (reconstructed picture, reconstructed block, reconstructed samples, or reconstructed sample array). If there is no residual for the processing target block, such as a case that a 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 a next processing target block in the current picture, and may be used for inter prediction of a next picture through filtering as described below, 
     Meanwhile, luma mapping with chroma scalingscaling (LMCS) may be applied during a picture encoding and/or reconstruction process. 
     The filter  260  may improve subjective/objective image quality by applying filtering to the reconstructed signal. For example, the filter  260  may generate a modified reconstructed picture by applying various filtering methods to the reconstructed picture, and store the modified reconstructed picture in the memory  270 , specifically, in a DPB of the memory  270 . The various filtering methods may include, for example, deblocking filtering, a sample adaptive offset (SAO), an adaptive loop filter, a bilateral filter, and the like. The filter  260  may generate various kinds of information related to the filtering, and transfer the generated information to the entropy encoder  290  as described later in the description of each filtering method. The information related to the filtering may be encoded by the entropy encoder  290  and output in the form of a bitstream. The modified reconstructed picture transmitted to the memory  270  may be used as a. eference picture in the inter predictor  221 . When the inter prediction is applied through the encoding apparatus, prediction mismatch between the encoding apparatus  200  and the decoding apparatus can be avoided and encoding efficiency can be improved. 
     The DPB of the memory  270  may store the modified reconstructed picture for use as the reference picture in the inter predictor  221 . The memory  270  may store motion information of a block from which the motion information in the current picture is derived (or encoded) andlor motion information of blocks in the picture, having already been reconstructed. The stored motion information may be transferred to the inter predictor  221  to be utilized as motion information of the spatial neighboring block or motion information of the temporal neighboring block. The memory  270  may store reconstructed samples of reconstructed blocks in the current picture, and may transfer the reconstructed samples to the intra predictor  222 . 
       FIG.  3    is a diagram for schematically explaining the configuration of a video/image decoding apparatus to which the disclosure of the present document may be applied. 
     Referring to  FIG.  3   , the decoding apparatus  300  may include and configured with 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  322 . The entropy decoder  310 , the residual processor  320 , the predictor  330 , the adder  340 , and the filter  350 , which have been described above, may be configured by one or more hardware components (e.g., decoder chipsets or processors) according to an embodiment. Further, the memory  360  may include a decoded picture buffer (DFB), and may be configured by a digital storage medium. The hardware component may further include the memory  360  as an internal/external component.  1701  When the bitstream including the video/image information is input, the decoding apparatus  300  may reconstruct the image in response to a process in which the video/image information is processed in the encoding apparatus illustrated in  FIG.  2   . For example, the decoding apparatus  300  may derive the units/blocks based on block split-related information acquired from the bitstream. The decoding apparatus  300  may perform decoding using the processing unit applied to the encoding apparatus. Therefore, the processing unit for the decoding may be, for example, a. coding unit, and the coding unit may be split according to the quad-tree structure, the binary-tree structure, and/or the ternary-tree structure from the coding tree unit or the maximum coding unit. One or more transform units may be derived from the coding unit. In addition, the reconstructed image signal decoded and output through the decoding apparatus  300  may be reproduced through a reproducing apparatus. 
     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 through the entropy decoder  310 . For example, the entropy decoder  310  may parse the bitstream to derive information (e.g., video/image: information) necessary for image reconstruction (or picture reconstruction). 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). In addition, the video/image information may further include general constraint information. The decoding apparatus may further decode picture based on the information on the parameter set and/or the general constraint information. Signaled/received information and/or syntax elements described later in this document may be decoded may decode the decoding procedure and obtained from the bitstream. For example, the entropy decoder  310  decodes the information in the bitstream based on a coding method such as exponential Golomb coding, CAVLC, or CABAC, and output syntax elements required for image reconstruction and quantized values of transform coefficients for residual. More specifically, the CABAC entropy decoding method may receive a bin corresponding to each syntax element in the bitstream, determine a context model by using a decoding target syntax element information, decoding information of a decoding target block or information of a symbol/bin decoded in a previous stage, and perform an arithmetic decoding on the bin by predicting a probability of occurrence of a bin according to the determined context model, and generate a symbol corresponding to the value of each syntax element. In this case, the CABAC entropy decoding method may update the context model by using the information of the decoded symbol/bin for a context model of a next symbol/bin after determining the context model. The information related to the prediction among the information decoded by the entropy decoder  310  may be provided to the predictor  330 , and information on the residual on which the entropy decoding has been performed in the entropy decoder  310 , that is, the quantized transform coefficients and related parameter information, may be input to the dequantizer  321 . In addition, information on filtering among information decoded by the entropy decoder  310  may be provided to the filter  350 . Meanwhile, a receiver (not illustrated) for receiving a signal output from the encoding apparatus may be further configured as an internal/external element of the decoding apparatus  300 , or the receiver may be a constituent element of the entropy decoder  310 . Meanwhile, the decoding apparatus according to the present document may be referred to as a video/image/picture decoding apparatus, and the decoding apparatus may be classified 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 decoder  310 , and the sample decoder may include at least one of the dequantizer  321 , the inverse transformer  322 , the predictor  330 , the adder  340 , the filter  350 , and the memory  360 . 
     The dequantizer  321  may dequantize the quantized transform coefficients to output the transform coefficients. The dequantizer  321  may rearrange the quantized transform coefficients in a two-dimensional block form. In this case, the rearrangement may be performed based on a coefficient scan order performed by the encoding apparatus. The dequantizer  321  may perform dequantization for the quantized transform coefficients using a quantization parameter (e.g., quantization step size information), and acquire the transform coefficients. 
     The inverse transformer  322  inversely transforms the transform coefficients to acquire the residual signal (residual block, residual sample array). 
     The predictor  330  may perform the prediction of the current block, and generate a predicted block including the prediction samples of the current block. The predictor may determine whether the intra prediction is applied or the inter prediction is applied to the current block based on the information about prediction output from the entropy decoder  310 , and determine a specific intra/inter prediction mode. 
     The predictor may generate a prediction signal based on various prediction methods described below. For example, the predictor may not only apply intra prediction or inter prediction to predict one block but also simultaneously apply intra prediction and inter prediction. This may be called combined inter and intra prediction (CLIP). In addition, the predictor may perform an intra block copy (IBC) for prediction of a block. The intra block copy may be used for content image/moving image coding of a game or the like, for example, screen content coding (SCC). The IBC basically performs prediction in the current picture, but may be performed similarly to inter prediction in that a reference block is derived in the current picture. That is, the IBC may use at least one of inter prediction techniques described in the present document. 
     The intra predictor  332  may predict the current block by referring to the samples in the current picture. The referred samples may be located in the neighborhood of the current block, or may be located apart from the current block according to the prediction mode. In intra prediction, prediction modes may include a plurality of non-directional modes and a plurality of directional modes. The intra predictor  332  may determine the prediction mode to be applied to the current block by using the prediction mode applied to the neighboring block. 
     The inter predictor  331  may derive a predicted block for the current block based on a reference block (reference sample array) specified by a motion vector on a reference picture. In this case, in order to reduce the amount of motion information being transmitted in the inter prediction mode, motion information may be predicted in the unit of blocks, subblocks, or samples based on correlation of motion information between the neighboring block 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 inter prediction direction (L0 prediction, L1 prediction, Bi prediction, and the like). In case of inter prediction, the neighboring block may include a spatial neighboring block existing in the current picture and a temporal neighboring block existing in the reference picture. For example, the inter predictor  331  may construct a motion information candidate list based on neighboring blocks, and derive a motion vector of the current block and/or a reference picture index based on the received candidate selection information. Inter prediction may be performed based on various prediction modes, and the information on the prediction may include information indicating a mode of inter prediction for the current block. 
     The adder  340  may generate a reconstructed signal (reconstructed picture, reconstructed block, or reconstructed sample array) by adding the obtained residual signal to the prediction signal (predicted block or predicted sample array) output from the predictor  330 . if there is no residual for the processing target block, such as a case that a skip mode is applied, the predicted block may be used as the reconstructed block. 
     The adder  340  may be called a reconstructor or a reconstructed block generator. The generated reconstructed signal may be used for the intra prediction of a next block to be processed in the current picture, and as described later, may also be output through filtering or may also be used for the inter prediction of a next picture. 
     Meanwhile, a lama mapping with chrorna scaling (LMCS) may also be applied in the picture decoding process. 
     The filter  350  may improve subjective/objective image quality by applying filtering to the reconstructed signal. For example, the filter  350  may generate a modified reconstructed picture by applying various filtering methods to the reconstructed picture, and store the modified reconstructed picture in the memory  360 , specifically, in a DPB of the memory  360 . The various filtering methods may include, for example, deblocking filtering, a sample adaptive offset, an adaptive loop filter, a bilateral filter, and the like. 
     The (modified) reconstructed picture stored in the DPB of the memory  360  may be used as a reference picture in the inter predictor  331 . The memory  360  may store the motion information of the block from which the motion information in the current picture is derived (or decoded) and/or the motion information of the blocks in the picture having already been reconstructed. The stored motion information may be transferred to the inter predictor  331  so as to be utilized as the motion information of the spatial neighboring block or the motion information of the temporal neighboring block. The memory  360  may store reconstructed samples of reconstructed blocks in the current picture, and transfer the reconstructed samples to the intra predictor  332 . 
     In the present specification, the embodiments described in the predictor  330 , the dequmtizer  321 , the inverse transformer  322 . and the filter  350  of the decoding apparatus  300  may also be applied in the same manner or corresponding to the predictor  220 , the dequantizer  234 , the inverse transformer  235 , and the filter  260  of the encoding apparatus  200 . 
     Meanwhile, as described above, in performing video coding, prediction is performed to improve compression efficiency. Through this, a predicted block including prediction samples for a current block as a block to be coded (i.e., a coding target block) may be generated. Here, the predicted block includes prediction samples in a spatial domain (or pixel domain). The predicted block is derived in the same manner in an encoding apparatus and a decoding apparatus, and the encoding apparatus may signal information (residual information) on residual between the original block and the predicted block, rather than an original sample value of an original block, to the decoding apparatus, thereby increasing image coding efficiency. The decoding apparatus may derive a residual block including residual samples based on the residual information, add the residual block and the predicted block to generate reconstructed blocks including reconstructed samples, and generate a reconstructed picture including the reconstructed blocks. 
     The residual information may be generated through a transform and quantization procedure. For example, the encoding apparatus 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 related residual information to the decoding apparatus (through a bit stream). Here, the residual information may include value information of the quantized transform coefficients, location information, a transform technique, a transform kernel, a quantization parameter, and the like. The decoding apparatus may perform dequanti zation/in verse transform procedure based on the residual information and derive residual samples (or residual blocks). The decoding apparatus may generate a reconstructed picture based on the predicted block and the residual block. Also, for reference for inter prediction of a picture afterward, the encoding apparatus may also dequantize/inverse-transform the quantized transform coefficients to derive a residual block and generate a reconstructed picture based thereon. 
       FIG.  4    schematically illustrates a multi-transform technique according to the present document. 
     Referring to  FIG.  4   , a transformer may correspond to the transformer in the encoding apparatus of  FIG.  2    as described above, and an inverse transformer may correspond to the inverse transformer in the encoding apparatus of  FIG.  2   , or the inverse transformer in the decoding apparatus of  FIG.  3    as described above. 
     The transformer may derive (primary) transform coefficients by performing, primary transform based on residual sample (residual sample array) in a residual block (S 410 ). Such primary transform may be referred to as a core transform. Here, the primary transform may be based on multiple transform selection (MTS), and in case that the multi-transform is applied as the primary transform, it may be referred to as multi core transform. 
     For example, the multi core transform may represent a transform method by additionally using discrete cosine transform (DCT) type 2 (DCT-II), discrete sine transform (DST) type 7 (DST-VII), DCT type 8 (DCT-VIII), and/or DST type 1 (DST-I). That is, the multi core transform may represent a transform method for transforming a residual signal (or residual block) of a spatial domain into transform coefficients (or primary transform coefficients) of a frequency domain based on a plurality of transform kernels selected among the DCT type 2, the DST type 7, the DCT type 8, and the DST type 1. Here, the primary transform coefficients may be called temporary transform coefficients on the transformer side. 
     In other words, in case that the existing transform method is applied, transform of the spatial domain for the residual signal (or residual block) into the frequency domain may be applied based on the DCT type 2, and the transform coefficients may be generated. However, unlike this, in case that the multi core transform is applied, transform of the spatial domain for the residual signal (or residual block) into the frequency domain may be applied based on the DCT type 2, DST type 7, DCT type 8, and/or DST type 1, and the transform coefficients (or primary transform coefficients) may be generated. Here, the DCT type 2, DST type 7, DCT type 8, and DST type 1 may be called the transform type, transform kernel, or transform core. The DCT/DST transform types may be defined based on basis functions. 
     In case that the multi core transform is performed, a vertical transform kernel and/or a horizontal transform kernel for a target block may be selected among the transform kernels, a vertical transform for the target block may be performed based on the vertical transform kernel, and a horizontal transform for the target block may be performed based on the horizontal transform kernel. Here, the horizontal transform may represent a transform for horizontal components of the target block, and the vertical transform may represent a transform for vertical components of the target block. The vertical transform kernel/horizontal transform kernel may be adaptively determined based on the prediction mode and/or transform index of the target block (CU or subblock) including the residual block. 
     Further, for example, in case of performing primary transform by applying MTS, specific basis functions may be configured to specified values, and in case of the vertical transform or horizontal transform, the mapping relationship for the transform kernel may be configured by combining what basis functions are applied. For example, in case that the horizontal direction transform kernel is represented by trTypeHor, and the vertical direction transform kernel is represented by trTypeVer, the trIypeHor or trTypeVer having a value of 0 may be configured as DCT2, and the trTypeHor or trIypeVer having a value of 1 may be configured as DST7. The trTypeHor or trTypeVer having a value of 2 may be configured as DCTS. 
     Alternatively, for example, in order to indicate any one of a plurality of transform kernel sets, MTS index may be encoded, and MTS index information may be signaled to the decoding apparatus. Here, the MTS index may be represented as tu_mts_idx syntax element or mts_idx syntax element. For example, if the MTS index is 0, it may be represented that trTypeHor and trTypeVer values are all 0, and (trTypeHor, trTypeVer)=(DCT2, DCT2). If the MTS index is 1, it may be represented that trTypeHor and trIypeVer values are all 1, and (trTypeHor, trTypeVer)=(DST7, DST7). If the MTS index is 2, it may be represented that the trTypeHor value is 2, and the trTypeVer value is 1, and (trTypeHor, trTypeVer) =(DCTS, DST7). If the MTS index is 3, it may be represented that the trTypeHor value is 1, and the trTypeVer value is 2, and (trTypeHor, trTypeVer)=(DST7, DCTS). If the MTS index is 4, it may be represented that the trTypeHor and trTypeVer values are all 2, and (trTypeHor, trTypeVer)=(DCTS, DCTS). For example, the transform kernel set according to the MTS index may be represented as in the following table. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 MTS index 
                 0 
                 1 
                 2 
                 3 
                 4 
               
               
                   
                   
               
             
            
               
                   
                 trTypeHor 
                 0 
                 1 
                 2 
                 1 
                 7 
               
               
                   
                 trTypeVer 
                 0 
                 1 
                 1 
                 2 
                 2 
               
               
                   
                   
               
            
           
         
       
     
     The transformer may derive modified (secondary) transform coefficients by performing secondary transform based on the (primary) transform coefficients (S 420 ). The primary transform may be a transform of the spatial domain into the frequency domain, and the secondary transform may represent a transform into a more compressive expression by using a correlation existing between the (primary) transform coefficients. 
     For example, the secondary transform may include a non-separable transform. In this case, the secondary transform may be called a non-separable secondary transform (NSST) or a mode-dependent non-separable secondary transform (MDNSST). The non-separable secondary transform may represent a transform for generating modified transform coefficients (or secondary transform coefficients) for the residual signal by secondarily transforming the (primary) transform coefficients derived through the primary transform based on a non-separable transform matrix. Here, the vertical transform and the horizontal transform may not be separately (or independently) applied with respect to the (primary) transform coefficients based on the non-separable transform matrix, but may be applied all at once. 
     In other words, the non-separable secondary transform may represent a transform method for rearranging, for example, two-dimensional signals (transform coefficients) to one-dimensional signal through a specifically determined direction (e.g., row-first direction or column-first direction), without separating the (primary) transform coefficients into vertical components and horizontal components, and then generating modified transform coefficients (or secondary transform coefficients) based on the non-separable transform matrix. 
     For example, the row-first direction (or order) may represent an arrangement of an MxN block in a line in the order of a first row to an N-th row and the column-first direction (or order) may represent an arrangement of an MxN block in a line in the order of a first column to an M-th column. Here, M and N may represent a width (W) and a height (H) of the block, and may be all positive integers. 
     For example, the non-separable secondary transform may be applied to a top-left area of the block composed of (primary) transform coefficients (hereinafter, transform coefficient block). For example, if the width (W) and the height (H) of the transform coefficient block are all equal to or larger than 8, 8×8 non-separable secondary transform may be applied to the top-left 8×8 area of the transform coefficient block. Further, if the width (W) and the height (H) of the transform coefficient block are all equal to or larger than 4 and smaller than 8, 4×4 non-separable secondary transform may be applied to the top-left min (8, W)×min (8, H) area of the transform coefficient block. However, embodiments are not limited thereto, and for example, even if a condition that the width (W) and the height (H) of the transform coefficient block are all equal to or larger than 4 is satisfied, the 4×4 non-separable secondary transform may be applied to the top-left min (8, W)×min (8, H) area of the transform coefficient block. 
     Specifically, for example, in case that a 4×4 input block is used, the non-separable secondary transform may be performed as follows. 
     The 4×4 input block X may be represented as follows. 
     
       
         
           
             
               
                 
                   X 
                   = 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             00 
                           
                         
                         
                           
                             X 
                             01 
                           
                         
                         
                           
                             X 
                             02 
                           
                         
                         
                           
                             X 
                             03 
                           
                         
                       
                       
                         
                           
                             X 
                             10 
                           
                         
                         
                           
                             X 
                             11 
                           
                         
                         
                           
                             X 
                             12 
                           
                         
                         
                           
                             X 
                             13 
                           
                         
                       
                       
                         
                           
                             X 
                             20 
                           
                         
                         
                           
                             X 
                             21 
                           
                         
                         
                           
                             X 
                             22 
                           
                         
                         
                           
                             X 
                             23 
                           
                         
                       
                       
                         
                           
                             X 
                             30 
                           
                         
                         
                           
                             X 
                             31 
                           
                         
                         
                           
                             X 
                             32 
                           
                         
                         
                           
                             X 
                             33 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                         
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     For example, the vector form of the X may be represented as follows. 
         ={X 00  X 01  X 02  X 03  X 10  X 11  X 1 X 13  X 20  X 21  X 22  X 23  X 30  X 31  X 32  X 33 } T   [Equation 2]
 
     Referring to Equation 2,   may represent the vector X, and the two-dimensional block of the X in Equation 1 may be rearranged and represented as the one-dimensional vector in accordance with the row-first order. 
     In this case, the secondary non-separable transform may be calculated as follows. 
         = T·         [Equation 3]
 
     Here,   may represent a transform coefficient vector, and T may represent 16×16 (non-separable) transform matrix. 
     Based on Equation 3,   having a size of 16×1 may be derived, and   may be reorganized as 4×4 block through a scan order (horizontal, vertical, or diagonal). However, the above-described calculation is exemplary, and in order to reduce calculation complexity of the non-separable secondary transform, hypercube-givens transform (HyGT) and the like may be used to calculate the non-separable secondary transform. 
     Meanwhile, in the non-separable secondary transform, a transform kernel (or transform core or transform type) may be selected in a mode dependent manner. Here, the mode may include an intra prediction mode and/or an ter prediction mode. 
     For example, as described above, the non-separable secondary transform may be performed based on the 8×8 transform or 4×4 transform determined based on the width (W) and the height (H) of the transform coefficient block. For example, if the W and H are all equal to or larger than 8, the 8×8 transform may represent a transform that can be applied to the 8×8 area included inside the corresponding transform coefficient block, and the 8×8 area may be the top-left 8×8 area inside the corresponding transform coefficient block. Further, similarly, if the W and H are all equal to or larger than 4, the 4×4 transform may represent a transform that can be applied to the 4×4 area included inside the corresponding transform coefficient block, and the 4×4 area may be the top-left 4×4 area inside the corresponding transform coefficient block. For example, an 8×8 transform kernel matrix may be a 64×64/16×64 matrix, and a 4×4 transform kernel matrix may be a 16×16/8×16 matrix. 
     In this case, for mode-based transform kernel selection, two non-separable secondary transform kernels per transform set for the non-separable secondary transform may be configured with respect to all of the 8×8 transform and the 4×4 transform, and four transform sets may be provided. That is, four transform sets may be configured with respect to the 8 ×8 transform, and four transform sets may be configured with respect to 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. 
     However, the size of the transform, the number of sets, and the number of transform kernels in the set are exemplary, and a size excluding the 8×8 or 4×4 may be used, or n sets may be configured, or k transform kernels may be included in each set. Here, n and k may be positive integers. 
     For example, the transform set may be called an NSST set, and the transform kernel in the NSST set may be called an NSST kernel. For example, selection of a specific set among the transform sets may be performed based on the intra prediction mode of the target block (CU or subblock). 
     For example, the intra prediction mode 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 No. 0 planar intra prediction mode and No. 1 DC intra prediction mode, and the directional intra prediction modes may include 65 (No. 2 to No. 66) intra prediction modes. However, this is exemplary, and the embodiment according to the present document may be applied even to a case that a different number of intra prediction modes is provided. Meanwhile, in some cases, No. 67 intra prediction mode may be further used, and the No. 67 intra prediction mode may represent a linear model (IrM) mode. 
       FIG.  5    exemplarily illustrates intra directional rnodes in  65  prediction directions. 
     Referring to  FIG.  5   , modes may be divided into intra prediction modes having horizontal directionality and intra prediction modes having vertical directionality around No.  34  intra prediction mode having top-left diagonal prediction direction. In  FIG.  5   , H and V may mean the horizontal directionality and the vertical directionality, respectively, and numerals of −32 to 32 may represent displacements in the unit of 1/32 on a sample grid position. This may represent an offset for a mode index value. 
     For example, No. 2 to No. 33 intra prediction modes may have the horizontal directionality, and. No. 34 to No. 66 intra prediction modes have the vertical directionality. Meanwhile, technically speaking, No, 34 intra prediction mode may be considered to have neither the horizontal directionality nor the vertical directionality, but may be classified to belong to the horizontal directionality from the viewpoint of determining the transform set of the secondary transform. This is because input data is transposed and used with respect to the vertical direction modes being symmetrical around the No. 34 intra prediction mode, and an input data arrangement method for the horizontal direction mode is used with respect to the No. 34 intra prediction mode. Here, transposing of the input data may mean configuration of N×M data in a manner that rows become columns and columns become rows with respect to two-dimensional block data M×N. 
     Further, No. 18 intra prediction mode and No. 50 intra prediction mode may represent a horizontal intra prediction mode and a vertical intra prediction mode, respectively, and No. 2 intra prediction mode may be called top-right diagonal intra prediction mode since prediction is made in the top-right direction with a left reference pixel. In the same context, No. 34 intra prediction mode may be called a bottom-right diagonal intra prediction mode, and No. 66 intra prediction mode may be called a bottom-left diagonal intra prediction mode. 
     Meanwhile, if it is determined that a specific set is used for non-separable transform, one of k transform kernels in the specific set may be selected through the non-separable secondary transform index. For example, the encoding apparatus may derive the non-separable secondary transform index representing a specific transform kernel based on a rate-distortion (RD) check, and may signal the non-separable secondary transform index to the decoding apparatus. For example, the decoding apparatus may select one of the k transform kernels in the specific set based on the non-separable secondary transform index. For example, an NSST index having a value of 0 may represent a first non-separable secondary transform kernel, an NSST index having a value of I may represent a second non-separable secondary transform kernel, and an NSST index having a value of 2 may represent a third non-separable secondary transform kernel. Alternatively, an NSST index having a value of 0 may represent that the first non-separable secondary transform is not applied to the target block, and an NSST index having a value of 1 to 3 may indicate the three transform kernels as above. 
     The transformer may perform the non-separable secondary transform based on the selected transform kernels, and may obtain modified (secondary) transform coefficients. The modified transform coefficients may be derived as quantized transform coefficients through the above-described quantizer, and may be encoded to be signaled to the decoding apparatus and may be transferred to the dequantizer/inverse transformer in the encoding apparatus. 
     Meanwhile, if the secondary transform is omitted as described above, the (primary) transform coefficients that are outputs of the primary (separable) transform may be derived as the quantized transform coefficients through the quantizer as described above, and may be encoded to be signaled to the decoding apparatus and may be transferred to the dequantizer/inverse transformer in the encoding apparatus. 
     Referring again to  FIG.  4   , the inverse transformer may perform a series of procedures in reverse order to the procedures performed by the above-described transformer. The inverse transformer may receive (dequantized) transform coefficients, derive (primary) transform coefficients by performing secondary (inverse) transform (S 450 ), and obtain a residual block (residual samples) by performing primary (inverse) transform with respect to the (primary) transform coefficients (S 460 ). Here, the primary transform coefficients may be called modi fled transform coefficients on the inverse transformer side. As described above, the encoding apparatus and; or the decoding apparatus may generate a reconstructed block based on the residual block and a predicted block, and may generate a reconstructed picture based on this. 
     Meanwhile, the decoding apparatus may further include a secondary inverse transform application/non-application determiner (or element for determining whether to apply the secondary inverse transform) and a. secondary inverse transform determiner (or element for determining the secondary inverse transform). For example, the secondary inverse transform application/non-application determiner may determine whether to apply the secondary inverse transform. For example, the secondary inverse transform may be NSST or RST, and the secondary inverse transform application/non-application determiner may determine whether to apply the secondary inverse transform based on a secondary transform flag parsed or obtained from a bitstream. Alternatively, for example, the secondary inverse transform application/non-application determiner may determine whether to apply the secondary inverse transform based on the transform coefficient of the residual block. 
     The secondary inverse transform determiner may determine the secondary inverse transform. In this case, the secondary inverse transform determiner may determine the secondary inverse transform being applied to the current block based on the NSST (or RST) transform set designated in accordance with the intra prediction mode. Alternatively, a secondary transform determination method may be determined depending on a primary transform determination method. Alternatively, various combinations of the primary transform and the secondary transform may be determined in accordance with the intra prediction mode. For example, the secondary inverse transform determiner may determine an area to which the secondary inverse transform is applied based on the size of the current block. 
     Meanwhile, if the secondary (inverse) transform is omitted as described above, the residual block (residual samples) may be obtained by receiving the (dequantized) transform coefficients and performing the primary (separable) inverse transform. As described above, the encoding apparatus and/or the decoding apparatus may generate a reconstructed block based on the residual block and the predicted block, and may generate a reconstructed picture based on this. 
     Meanwhile, in the present document, in order to reduce a computation amount and a memory requirement amount being accompanied by the non-separable secondary transform, a reduced secondary transform (RST) having a reduced size of the transform matrix (kernel) may be applied on the concept of NSST. 
     In the present document, the RST may mean a (simplification) transform being performed with respect to the residual samples for the target block based on the transform matrix of which the size is reduced in accordance with a simplification factor. In case of performing this, the computation amount being required during the transform may be reduced due to the reduction of the size of the transform matrix. That is, the RST may be used to solve the computation complexity issue occurring during the transform of a block having a large size or on-separable transform. 
     For example, the RST may be referred to as various terms, such as reduced transform, reduced secondary transform, reduction transform, simplified transform, or simple transform, and names to which the RST is referred are not limited to the enumerated examples. Further, the RST is mainly performed in a low-frequency domain including coefficients that are not 0 in the transform block, and thus may be called a low-frequency non-separable transform (LFNST). 
     Meanwhile, in case that the secondary inverse transform is performed based on the RST, the inverse transformer  235  of the encoding apparatus  200  and the inverse transformer  322  of the decoding apparatus  300  may include an inverse RST unit deriving modified transform coefficients based on the inverse RST for the transform coefficients, and an inverse primary transformer deriving residual samples for the target block based on the inverse primary transform for the modified transform coefficients. The inverse primary transform means an inverse transform of the primary transform having been applied to the residual. In the present document, derivation of the transform coefficients based on the transform may mean derivation of the transform coefficients by applying the corresponding transform. 
       FIGS.  6  and  7    are diagrams explaining RST according to an embodiment of the present document. 
     For example,  FIG.  6    may be a figure explaining that a forward reduced transform is applied, and  FIG.  7    may be a figure explaining that an inverse reduced transform is applied. In the present document, the target block may represent the current block, a residual block, or a transform block of which coding is performed. 
     For example, in the RST, an N-dimensional vector may be mapped on an R-dimensional vector located in another space, and a reduced transform matrix may be determined. Here, N and R may be positive integers, and R may be smaller than N. N may mean a square of a length of one side of a block to which transform is applied or the total number of transform coefficients corresponding to the block to which the transform is applied, and a simplification factor may mean an R/N value. The simplification factor may be referred to as various terms, such as reduced factor, reduction factor, simplified factor, or simple factor. Meanwhile, R may be referred to as a reduced coefficient, and in some cases, the simplification factor may mean the R. Further, in some cases, the simplification factor may mean the N/R value. 
     For example, the simplification factor or the reduced coefficient may be signaled through the bitstream, but is not limited thereto. For example, predefined values for the simplification factor or the reduced coefficient may be stored in the encoding apparatus  200  and the decoding apparatus  300 , and in this case, the simplification factor or the reduced coefficient may not be separately signaled. 
     For example, the size (R×N) of the simplification transform matrix may be smaller than the size (NxN) of a regular transform matrix, and may be defined as in the following equation. 
     
       
         
           
             
               
                 
                   
                     T 
                     RxN 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             t 
                             11 
                           
                         
                         
                           
                             t 
                             12 
                           
                         
                         
                           
                             t 
                             13 
                           
                         
                         
                           … 
                         
                         
                           
                             t 
                             
                               1 
                               ⁢ 
                               N 
                             
                           
                         
                       
                       
                         
                           
                             t 
                             21 
                           
                         
                         
                           
                             t 
                             22 
                           
                         
                         
                           
                             t 
                             23 
                           
                         
                         
                             
                         
                         
                           
                             t 
                             
                               2 
                               ⁢ 
                               N 
                             
                           
                         
                       
                       
                         
                             
                         
                         
                           ⋮ 
                         
                         
                             
                         
                         
                           ⋱ 
                         
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             t 
                             
                               R 
                               ⁢ 
                               1 
                             
                           
                         
                         
                           
                             t 
                             
                               R 
                               ⁢ 
                               2 
                             
                           
                         
                         
                           
                             t 
                             
                               R 
                               ⁢ 
                               3 
                             
                           
                         
                         
                           … 
                         
                         
                           
                             t 
                             RN 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                         
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     For example, the matrix T in the reduced transform block illustrated in  FIG.  6    may represent the matrix T R×N  of Equation 4. As shown in  FIG.  6   , in case that the residual samples for the target block is multiplied by the simplification transform matrix T R×N , the transform. coefficients for the target block may be derived. 
     For example, in case that the size of the block to which the transform is applied is 8×8, and R is 16 (i.e., R/N=16/64 =1/4), the RST according to  FIG.  6    may be expressed by a matrix operation as in Equation 5 below. In this case, the memory and the multiplication operation may be reduced to about ¼ by the simplification factor.  11391  In the present document, the matrix operation may be understood as an operation of obtaining a column vector by placing the matrix on the left side of the column vector and multiplying the matrix and the column vector. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             t 
                             
                               1 
                               , 
                               1 
                             
                           
                         
                         
                           
                             t 
                             
                               1 
                               , 
                               2 
                             
                           
                         
                         
                           
                             t 
                             
                               1 
                               , 
                               3 
                             
                           
                         
                         
                           … 
                         
                         
                           
                             t 
                             
                               1 
                               , 
                               64 
                             
                           
                         
                       
                       
                         
                           
                             t 
                             
                               2 
                               , 
                               1 
                             
                           
                         
                         
                           
                             t 
                             
                               2 
                               , 
                               2 
                             
                           
                         
                         
                           
                             t 
                             
                               2 
                               , 
                               3 
                             
                           
                         
                         
                             
                         
                         
                           
                             t 
                             
                               2 
                               , 
                               64 
                             
                           
                         
                       
                       
                         
                             
                         
                         
                           ⋮ 
                         
                         
                             
                         
                         
                           ⋱ 
                         
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             t 
                             
                               16 
                               , 
                               1 
                             
                           
                         
                         
                           
                             t 
                             
                               16 
                               , 
                               2 
                             
                           
                         
                         
                           
                             t 
                             
                               16 
                               , 
                               3 
                             
                           
                         
                         
                           … 
                         
                         
                           
                             t 
                             
                               16 
                               , 
                               64 
                             
                           
                         
                       
                     
                     ] 
                   
                   × 
                   
                     [ 
                     
                       
                         
                           
                             r 
                             1 
                           
                         
                       
                       
                         
                           
                             r 
                             2 
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             r 
                             64 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                         
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation  5 , ri to r 64  may represent residual samples for the target block. 
     Alternatively, for example, they may be transform coefficients generated by applying the primary transform. Based on the result of the operation of Equation  5 , transform coefficients Ci for the target block may be derived. 
     For example, in case that R is  16 , transform coefficients ci to cio for the target block may be derived. If the transform matrix having a size of  64  × 64  (NxN) through application of a regular transform rather than the RST is multiplied by the residual samples having a size of  64 x  1  (Nx 1 ),  64  (N) transform coefficients for the target block may be derived, but since the RST is applied. only  16  (N) transform coefficients for the target block may be derived. Since the total number of transform coefficients for the target block is reduced from N to R, the amount of data that the encoding apparatus  200  transmits to the decoding apparatus  300  may be reduced, and thus transmission efficiency between the encoding apparatus  200  and the decoding apparatus  300  may be increased. 
     In consideration of the size of the transform matrix, since the size of the regular transform matrix is  64  × 64  (NxN), and the size of the simplification transform matrix is reduced to 16×64 (R×N), the memory usage when performing the RST can be reduced in an RN ratio as compared with a case that the regular transform is performed. Further, as compared with the number (N×N) of multiplication operations when using the regular transform matrix, the usage of the simplification transform matrix can reduce the number of multiplication operations (R×N) in the R/N ratio. 
     In an embodiment, the transformer  232  of the encoding apparatus  200  may derive the transform coefficients for the target block by performing primary transform and RST-based secondary transform of the residual samples for the target block. The transform coefficients may be transferred to the inverse transformer of the decoding apparatus  300 , and the inverse transformer  322  of the decoding apparatus  300  may derive the modified transform coefficients based on inverse reduced secondary transform (RST) for the transform coefficients, and may derive the residual samples for the target block based on the inverse primary transform of the modified transform coefficients. 
     The size of the inverse RST matrix T N×R  according to an embodiment may be N×R that is smaller than the size N×N of the regular inverse transform matrix, and may be in transpose relationship with the simplification transform matrix T R×N  illustrated in Equation 4. 
     The matrix T 1  in the reduced inverse transform block illustrated in  FIG.  7    may represent an inverse RST matrix T R×N   T . Here, the superscript T may represent the transpose. As shown in  FIG.  7   , in case that the transform coefficients for the target block is multiplied by the inverse RST matrix T R×N   T , the modified transform coefficients for the target block or the residual samples for the target block may be derived. The inverse RST matrix T R×N   T  may be expressed as (T R×N ) T   N×R . 
     More specifically, in case that the inverse RST is applied as the secondary inverse transform, the modified transform coefficients for the target block may be derived by multiplying the transform coefficients for the target block by the inverse RST matrix T R×N   T . Meanwhile, the inverse RST may be applied as the inverse primary transform, and in this case, the residual samples fo the target block may be derived by multiplying the transform coefficients for the target block by the inverse RST matrix T R×N   T . 
     In an embodiment, in case that the size of the block to which the inverse transform is applied is 8×8, and R is 16 (i.e. =16/64=1/4), the RST according to  FIG.  7    may be expressed by a matrix operation as in Equation 6 below. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             t 
                             
                               1 
                               , 
                               1 
                             
                           
                         
                         
                           
                             t 
                             
                               2 
                               , 
                               1 
                             
                           
                         
                         
                             
                         
                         
                           
                             t 
                             
                               16 
                               , 
                               1 
                             
                           
                         
                       
                       
                         
                           
                             t 
                             
                               1 
                               , 
                               2 
                             
                           
                         
                         
                           
                             t 
                             
                               2 
                               , 
                               2 
                             
                           
                         
                         
                           … 
                         
                         
                           
                             t 
                             
                               16 
                               , 
                               2 
                             
                           
                         
                       
                       
                         
                           
                             t 
                             
                               1 
                               , 
                               3 
                             
                           
                         
                         
                           
                             t 
                             
                               2 
                               , 
                               3 
                             
                           
                         
                         
                             
                         
                         
                           
                             t 
                             
                               16 
                               , 
                               3 
                             
                           
                         
                       
                       
                         
                             
                         
                         
                           ⋮ 
                         
                         
                           ⋱ 
                         
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             t 
                             
                               1 
                               , 
                               64 
                             
                           
                         
                         
                           
                             t 
                             
                               2 
                               , 
                               64 
                             
                           
                         
                         
                           … 
                         
                         
                           
                             t 
                             
                               16 
                               , 
                               64 
                             
                           
                         
                       
                     
                     ] 
                   
                   × 
                   
                     [ 
                     
                       
                         
                           
                             c 
                             1 
                           
                         
                       
                       
                         
                           
                             c 
                             2 
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             c 
                             16 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                         
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 6, c 1  to c 16  may represent transform coefficients for the target block. r j  representing the modified transform coefficients for the target block or the residual samples for the target block may be derived based on the result of the operation of Equation 6. That is, r i  to rx representing the modified transform coefficients for the target block or the residual samples for the target block may be derived. 
     In consideration of the size of the inverse transform matrix, since the size of the regular inverse transform matrix is 64×64 (N×N), and the size of the simplification inverse transform matrix is reduced to 64×16 (N×R), the memory usage when performing the inverse RST can be reduced in an ratio as compared with a case that the regular inverse transform is performed. Further, as compared with the number (N×N) of multiplication operations when using the regular inverse transform matrix, the usage of the simplification inverse transform matrix can reduce the number of multiplication operations (N×R) in the R/N ratio. 
     Meanwhile, transform sets may be configured and applied even with respect to 8×8 RST. That is, the corresponding 8×8 RST may be applied in accordance with the transform set. Since one transform set is composed of two or three transform kernels in accordance with the intra prediction mode, it may be configured to select one of four transforms at maximum including even a case that the secondary transform is not applied. In the transform when the secondary transform is not applied, it may be considered that an identity matrix has been applied. If it is assumed that an index of 0, 1, 2, or 3 is given for four transforms (e.g., No. 0 index may be allocated to a case that the identity matrix, that is, secondary transform, is not applied), the transform to be applied may be designated by signaling a syntax element that is an NSST index to every transform coefficient block. That is, through the NSST index, 8×8 NSST may be designated for an 8×8 top-left block, and in the RST configuration, 8×8 RST may be designated. The 8×8 NSST and the 8×8 RST may represent transforms capable of being applied to the 8×8 area included inside the corresponding transform coefficient block in case that the W and the H of the target block that becomes the target of the transform are all equal to or larger than 8, and the 8×8 area may be the top-left 8 ×8 area inside the corresponding transform coefficient block. Similarly, the 1×4 NSST and the 4 ×4 RST may represent transforms capable of being applied to the 4 ×4 area included inside the corresponding transform coefficient block in case that the W and the H of the target block are all equal to or larger than 4, and the 4×4 area may be the top-left 4×4 area inside the corresponding transform coefficient block. 
     Meanwhile, for example, the encoding apparatus may derive the bitstream by encoding the value of the syntax element or the quantized values of the transform coefficient for the residual based on various coding methods, such as exponential Golomb, context-adaptive variable length coding (CAVLC), context-adaptive binary arithmetic coding (CABAC), and the like. Further, the decoding apparatus may derive the value of the syntax element or the quantized values of the transform coefficient for the residual based on various coding methods, such as exponential Golomb encoding, CAVLC, CABAC, and the like. 
     For example, the above-described coding methods may be performed as the contents to be described later. 
       FIG.  8    exemplarily illustrates context-adaptive binary arithmetic coding (CABAC) for encoding a syntax element. 
     For example, in a CABAC coding process, if an input signal is a syntax element that is not a binary value, a value of the input signal may be transformed into a binary value through binarization. Further, if the input signal is already the binary value (i.e., if the value of the input signal is the binary value), the binarization may not be performed, but the input signal may be used as it is. Here, each binary number 0 or 1 constituting the binary value may be called a bin. For example, if a binary string after the binarization is 110, each of 1, 1, and 0 may be represented as one bin. The bin(s) for one syntax element may represent the value of the syntax element. The binarization may be based on various binarization method, such as a truncated rice binarization process or a fixed-length binarization process, and the binarization method for a target syntax element may be predefined. The binarization procedure may be performed by a. binarizer in an entropy encoder. 
     Thereafter, the binarized bins of the syntax element may be input to a regular coding engine or a bypass coding engine. The regular coding engine of the encoding apparatus may allocate a context model that reflects a probability value with respect to the corresponding bin, and encode the corresponding bin based on the allocated context model. The regular coding engine of the encoding apparatus may update the context model for the corresponding bin after performing coding with respect to the respective bins. The bins being coded as the above-described contents may be represented as context-coded bins. 
     Meanwhile, in case that the binarized bins of the syntax element are input to the bypass coding engine, they may be coded as follows. For example, the bypass coding engine of the encoding apparatus may omit a procedure for estimating probability with respect to the input bin and a procedure for updating a probability model having been applied to the bin after the coding. In case that the bypass coding is applied, the encoding apparatus may code the input bin by applying regular probability distribution instead of allocating, the context model, and through this, the coding speed can be improved. The bin being coded as the above-described. contents may be represented as a bypass bin. 
     Entropy decoding may represent a process for performing the same process as the above-described entropy encoding in reverse order. 
     The decoding apparatus (entropy decoder) may decode encoded image/video information. The image/video information may include partitioning-related information, prediction-related information (e.g., inter/intra, prediction division information, infra prediction mode information, inter prediction mode information, and the like), residual information, or in-loop filtering-related information, or may include various syntax elements thereabout. The entropy coding may be performed in the unit of a syntax element. 
     The decoding apparatus may perform binarization of target syntax elements. Here, the binarization may be based on various binarization methods, such as a truncated rice binarization process ora fixed-length binarization process, and the binarization method for the target syntax element may be predefined. The decoding apparatus may derive available bin strings (bin string candidates) for available values of the target syntax elements through the binarization procedure. The binarization procedure may be performed by the hinarizer in the entropy decoder. 
     The decoding apparatus may compare the derived bin string with available bin strings for the corresponding syntax elements while sequentially decoding or parsing the respective bins for the target syntax elements from input bit(s) in the bitstream. If the derived bin string is equal to one of the available bin strings, the value corresponding to the corresponding bin string is derived as the value of the corresponding syntax element. If not, the decoding apparatus may re-perform the above-described procedure after further parsing the next bit in the bitstream. Through such a process, it is possible to perform signaling of specific information (or specific syntax element) in the bitstream using a variable length bit even without using a start bit or an end bit of the corresponding information. Through this, a relatively smaller bit may be allocated with respect to a smaller value, and thus an overall coding efficiency can be enhanced. 
     The decoding apparatus may perform context model-based or bypass-based decoding of the respective bins in the bin string from the bitstream based on an entropy coding technique, such as CABAC or CAVLC. 
     In case that the syntax element is decoded based on the context model, the decoding apparatus may receive the bin corresponding to the syntax element through the bitstream, max determine a context model using the syntax element and decoding information of the decoding target block or the neighboring block or symbol/bin information decoded in the previous stage, and may derive the syntax element value by performing arithmetic decoding of the bin through prediction of the probability of occurrence of the received bin in accordance with the determined context model. Thereafter, the context model of the bin being next decoded may be updated based on the determined context model. 
     The context model may be allocated and updated by context-coded (regularly coded) bins, and the context model may be indicated based on context index (ctxIdx) or context index increment (ctxInc). Ctxldx may be derived based on ctxInc. Specifically, for example, the ctxIdx representing the context model for each of the regularly coded bins may be derived by the sum of ctxInc and context index offset (ctxIdxOffset). For example, the ctxInc may be differently derived by bins. The ctxIdx 0 ffset may be represented as the lowest value of the ctxIdx. Generally, the ctxidxOffset may be a value being used to distinguish the same from context models for other syntax elements, and the context model for one syntax element may be divided or derived based on the ctxInc. 
     In the entropy encoding procedure, it may be determined whether to perform encoding through the regular coding engine or to perform encoding through the bypass coding engine, and accordingly, a coding path may be switched. Entropy decoding may perform the same process as the entropy encoding in reverse order. 
     Meanwhile, for example, in case that the syntax element is bypass-decoded, the decoding apparatus may receive the bin corresponding to the syntax element through the bitstream, and may decode the input bin by applying regular probability distribution. In this case, the decoding apparatus may omit a procedure of deriving the context model of the syntax element and a procedure of updating the context model applied to the bin after the decoding. 
     Meanwhile, an embodiment of the present document may propose a scheme for signaling an MTS index. Here, the MTS index, as described above, may represent any one of a plurality of transform kernel sets, and the MTS index may be encoded and MTS index information may be signaled to the decoding apparatus. The decoding apparatus may obtain the MTS index by decoding the MTS index information, and may determine a transform kernel set to be applied based on the MTS index. The MTS index may be represented as a to nits idx syntax element or an mts_idx syntax element. For example, the MTS index may be binarized using Rice-Goln b parameter 0 th  order, but may be binarized based on truncated rice. In case of the binarization based on the truncated rice, an input parameter cMax may have the value of 4, and cRiceParam may have the value of 0. For example, the encoding apparatus may derive bin(s) for the MTS index by binarizing the MTS index, derive MTS index information (bit(s) for MTS index) by encoding the derived bin(s), and signal the MTS index information to the decoding apparatus. The decoding apparatus may derive the bin(s) for the MTS index by decoding the MTS index information, and derive the MTS index by comparing the derived bin(s) for the MTS index with candidate bin(s) for the MTS index. 
     For example, the MTS index (e.g., tu_mts_idx syntax element or mts_ids syntax element) may be context-coded based on the context model or context index with respect to all bins. In this case, a context index increment (ctixInc) for context coding of the MTS index or ctxInc according to the bin location may be allocated or determined as in Table 2. Further, a context model may be selected according to the bin location as in Table 2. 
     
       
         
           
               
               
             
               
                   
                 TABLE 2 
               
             
            
               
                   
                   
               
               
                   
                 binIdx 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Syntax element 
                 0 
                 1 
                 2 
                 3 
                 4 
                 &gt;=5 
               
               
                   
               
               
                 tu_mts_idx[ ][ ] 
                 cqtDepth 
                 6 
                 7 
                 8 
                 na 
                 Na 
               
               
                   
               
            
           
         
       
     
     Referring to Table 2, the ctxInc for No. 0 bin (first bin) may be allocated based on cqtDepth. Here, the cqtDepth may represent a quad-tree depth for the current block, and may be derived as one value of 0 to 5. That is, the ctxInc for the 0 th  bin may be allocated with one value of 0 to 5 according to the cqtDepth. Further, the ctxInc for No. 1 bin (second bin) may be allocated with 6, the ctxInc for No. 2 bin (third bin) may be allocated with 7, and the ctxInc for No. 3 bin (fourth bin) may be allocated with 8. That is, No. 0 bin to No. 3 bin may be allocated with ctxInc having different values. Here, the different ctxinc value may represent different context models, and in this case, 9 context models for the MTS index coding may be provided. 
     Further, for example, the MTS index (e.g., tu_mts_idx syntax element or mts_idx syntax element) may be bypass-coded with respect to all bins as in Table 3. In this case, 0 context model for the MTS index coding may be provided. 
     
       
         
           
               
               
             
               
                   
                 TABLE 3 
               
             
            
               
                   
                   
               
               
                   
                 binIdx 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Syntax element 
                 0 
                 1 
                 2 
                 3 
                 4 
                 &gt;=5 
               
               
                   
               
               
                 tu_mts_idx[ ][ ] 
                 bypass 
                 bypass 
                 bypass 
                 bypass 
                 na 
                 na 
               
               
                   
               
            
           
         
       
     
     Further, for example, the MTS index (e.g., tu nits idx syntax element or mts idx syntax element) may be context-coded based on the context model or the context index with respect to N0. 0 bin (first bin) as in Table 4, and may be bypass-coded with respect to the remaining bins. That is, the ctxInc for No. 0 bin (first bin) may be allocated with 0. In this case, one context model for the MTS index coding may be provided. 
     
       
         
           
               
               
             
               
                   
                 TABLE 4 
               
             
            
               
                   
                   
               
               
                   
                 binIdx 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Syntax element 
                 0 
                 1 
                 2 
                 3 
                 4 
                 &gt;=5 
               
               
                   
               
               
                 tu_mts_idx[ ][ ] 
                 0 
                 bypass 
                 bypass 
                 bypass 
                 na 
                 na 
               
               
                   
               
            
           
         
       
     
     Further, for example, the MTS index (e.g., tu mts idx syntax element or mts_idx syntax element) may be context-coded based on the context model or the context index with respect to No. 0 bin (first bin) and N0. 1 bin (second bin) as in Table 5, and may be bypass-coded coded with respect to the remaining bins. That is, the ctxInc for No. 0 bin (first bin) may be allocated with 0, and the ctxInc for No. 1 bin (second bin) may be allocated with 1. In this case, 2 context models for the MTS index coding may be provided. 
     
       
         
           
               
               
             
               
                   
                 TABLE 5 
               
             
            
               
                   
                   
               
               
                   
                 binIdx 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Syntax element 
                 0 
                 1 
                 2 
                 3 
                 4 
                 &gt;=5 
               
               
                   
               
               
                 tu_mts_idx[ ][ ] 
                 0 
                 1 
                 bypass 
                 bypass 
                 na 
                 na 
               
               
                   
               
            
           
         
       
     
     Further, for example, the MTS index (e.g., tu mts idx syntax element or mts_idx syntax element) may be context-coded based on the context model or the context index with respect to all bins as in Table 6, and may allocate one more with respect to each bin. That is, the ctxInc for No. 0 bin (first bin) may be allocated with 0, and the ctxInc for No. 1 bin (second bin) may be allocated with 1. The ctxInc for No. 2 bin (third bin) may be allocated with 2, and the ctxInc for No. 3 bin (fourth bin) may be allocated with 2. In this case, 4 context models for the MTS index coding may be provided. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 6 
               
             
            
               
                   
                   
               
               
                   
                 binIdx 
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Syntax element 
                 0 
                 1 
                 2 
                 3 
                 4 
                 &gt;=5 
               
               
                   
                   
               
               
                   
                 tu_mts_idx[ ][ ] 
                 0 
                 1 
                 2 
                 3 
                 na 
                 na 
               
               
                   
                   
               
            
           
         
       
     
     As described above, according to an embodiment, since the number of context models is reduced by applying the bypass coding to all or some of the bins of the MTS index or applying a specific value to the ctxInc although the context coding is applied, the complexity may be lowered, and the output amount of the decoder can be increased. Further, in an embodiment, in case of using context models as described above, the initial value and/or the multi-window size may be variable based on the occurrence statistics for the position of each bin. 
       FIGS.  9  and  10    schematically illustrate a video/image encoding method and an example of related components according to embodiment(s) of the present document. 
     The method disclosed in  FIG.  9    may be performed by the encoding apparatus disclosed in  FIG.  2    or  FIG.  10   . Specifically, for example, S 900  to S 920  of  FIG.  9    may be performed by the residual processor  230  of the encoding apparatus of  FIGS.  10   , and S 930  of  FIG.  9    may be performed by the entropy encoder  240  of the encoding apparatus of  FIG.  10   . Further, although not illustrated in  FIG.  9   , prediction samples or prediction related information may be derived by the predictor  220  of the encoding apparatus of  FIG.  10   , residual information may be derived from the original samples or the prediction samples by the residual processor  230  of the encoding apparatus, and the bitstream may be generated from the residual information or the prediction related information by the entropy encoder  240  of the encoding apparatus. The method disclosed in  FIG.  9    may include the embodiments as described above in the present document. 
     Referring to  FIG.  9   . the encoding apparatus derives the residual samples for the current block (S 900 ). For example, the encoding apparatus may derive the residual samples based on the prediction samples and the original samples. Although not illustrated in  FIG.  9   , in order to generate the prediction samples for the current block, the encoding apparatus may perform intra prediction or inter prediction with respect to the current block in consideration of a rate distortion RD) cost, and may generate the prediction related information including the prediction mode/type information. 
     The encoding apparatus derives the transform coefficients for the current block based on the residual samples (S 910 ). For example, the encoding apparatus may derive transform coefficients by performing transform with respect to the residual samples. Here, the transform may be performed based on a transform kernel or a transform kernel set. For example, the transform kernel set may include a horizontal direction transform kernel and a vertical direction transform kernel. For example, the encoding apparatus may derive the transform coefficients by performing the primary transform with respect to the residual samples. Further, for example, the encoding apparatus may derive temporary transform coefficients by performing the primary transform with respect to the residual samples, and may derive the transform coefficients by performing secondary transform with respect to the temporary transform coefficients. For example, the transform that is performed based on the transform kernel set may be represented as the primary transform. 
     The encoding apparatus generates the MTS index and the residual information based on the transform coefficients (S 920 ). In other words, the encoding apparatus may generate the MTS index and/or the residual information based on the transform coefficients. 
     The MTS index may represent the transform kernel set applied to (the transform coefficients) of the current block among the transform kernel set candidates. Here, the MTS index may be represented as the tri mts idx syntax element or the mts idx syntax element. As described above, the transform kernel set may include the horizontal direction transform kernel and the vertical direction transform kernel, and the horizontal direction transform kernel may be represented as trTypeHor, and the vertical direction transform kernel may be represented as trTy peV er. 
     For example, the trTypeHor and trTypeVer values may be represented by the horizontal direction transform kernel and the vertical direction transform kernel applied to (the transform coefficients) of the current block, and the MTS index may be represented as one of the candidates including 0 to 4 by the trTypeHor and trTypeVer values. 
     For example, if the MTS index is 0, it may be represented that the trTypeHo rand the trTypeVer are all 0. Further, if the MTS index is 1, it may represent that the trTypeHor and the trTypeVer are all 1. Further, if the MTS index is 2, it may represent that the trTypeHor is 2 and the trTypeVer is 1. If the MTS index is 3, it may represent that the trTypeHor is 1 and the trTypeVer is 1. Further, if the MTS index is 4, it may represent that the trTypeHor and the trTypeVer are all 2. For example, if the trTypeHor or trTypeVer value is 0, it may represent that DCT2 is applied to (the transform coefficients) of the current block in the horizontal direction or in the vertical direction, if 1, it may represent that DST7 is applied, and if 2, it may represent that DCTS is applied. That is, each of the transform kernel to be applied in the horizontal direction and the transform kernel to be applied in the vertical direction may be represented as one of the candidates including DCT2, DST7, and DCT8 based on the MTS index. 
     The MTS index may be represented based on the bins of the bin string of the MTS index. In other words, the MTS index may be binarized and represented as (the bins) of the bin string of the MTS index, and (the bins) of the bin string of the MTS index may be entropy-encoded. 
     In other words, at least one of the bins of the bin string of the MTS index, may be represented based on the context coding. Here, the context coding may be performed based on the value of context index increment (ctxInc). Further, the context coding may be performed based on the context index (ctxIdx) or context model. Here, the context index may be represented based on the value of the context index increment. Further, the context index may be represented based on the value of the context index increment and the context index offset (ctxIdxOffset). 
     For example, all of the bins of the bin string of the MTS index may be represented based on the context codling. For example, the ctxInc for the first bin or the 0 th  bin (bin 0) among the bins of the bin string of the MTS index may be represented based on cqtDepth. Here, the cqtDepth may represent a quad-tree depth for the current block, and may be represented as one value among 0 to 5. Further, the ctxInc for the second bin or No. 1 bin (bin 1) may be represented as 6, the ctxInc for the third bin or No. 2 bin (bin 2) may be represented as 7, and the ctxInc for the fourth bin or No. 3 bin (bin 3) may be represented as 8. Further, for example, the ctxInc for the first bin or the 0 th  bin (bin 0) among the bins of the bin string of the MTS index may be represented as 0, the ctxInc for the second bin or No. 1 bin (bin 1) may be represented as 1, the ctxInc for the third bin or No. 2 bin (bin 2) may be represented as 2, and the ctxinc for the fourth bin or No. 3 bin (bin 3) may be represented as 3. That is, the number of context index increment values that can be used for the context coding of the first bin among the bins of the bin string may be one. 
     Further, for example, some of the bins of the bind string of the MTS index may be represented based on the context coding, and the remainders may be represented based on the bypass coding. For example, the cixinc for the first bin or No. 0 bin (bin 0) among the bins of the bin string of the MTS index may be represented as 0, and the remaining bins may be represented based on the bypass coding. Further, for example, the ctxInc for the first bin or No. 0 bin (bin 0) among the bins of the bin string of the MTS index may be represented as 0, the ctxInc for the second bin or No. I bin (bin 1) may be represented as 1, and the remaining bins may be represented based on the bypass coding. That is, the number of context index increment values that can be used for the context coding of the first bin among the bins of the bin string may be one. 
     Further, all of the bins of the bin string of the MTS index may be represented based on the bypass coding. Here, the bypass coding may represent performing of the context coding based on the uniform probability distribution, and since the update procedure of the context coding is omitted, the coding efficiency can be improved. 
     The residual information may represent information that is used to derive the residual samples. Further, for example, the encoding apparatus may perform quantization for the transform coefficients, and the residual information may include information about the residual samples, transform related information, and/or quantization related information. For example, the residual information may include information about the quantized transform coefficients. 
     The encoding apparatus encodes image information including the MTS index and the residual information (S 930 ). For example, the image information may further include prediction related information. For example, the encoding apparatus may generate a bitstream by encoding the image information. The bitstream may be called encoded (image) information. 
     Further, although not illustrated in  FIG.  9   , for example, the encoding apparatus may generate reconstructed samples based on the residual samples and the prediction samples. Further, a reconstructed block and a reconstructed picture may be derived based on the reconstructed samples. 
     For example, the encoding apparatus may generate the bitstream or encoded information by encoding the image information including all or some of the above-described information (or syntax elements). Further, the information may be outputted in the form of a bitstream. Further, the bitstream or the encoded information may be transmitted to the decoding apparatus through the network or storage medium. Further, the bitstream or the encoded information may be stored in a computer readable storage medium, and the bitstream or the encoded information may be generated by the above-described image encoding method. 
       FIGS.  11  and  12    schematically illustrate a video/image decoding method and an example of related components according to embodiment(s) of the present document. 
     The method disclosed in  FIG.  11    may be performed by a decoding apparatus disclosed in  FIG.  3    or  FIG.  12   . Specifically, for example, S 1100  of  FIG.  11    may be performed by the entropy decoder  310  of the decoding apparatus of  FIGS.  12   , and S 1110  and S 1120  of  FIG.  11    may be performed by the residual processor  320  of the decoding apparatus of  FIG.  12   . Further, although not illustrated in  FIG.  11   , the prediction related information or residual information may be derived from the bitstream by the entropy decoder  310  of the decoding apparatus of  FIG.  12   , and the residual samples may be derived from the residual information by the residual processor  320  of the decoding apparatus. The prediction samples may be derived from the prediction related information by the predictor  330  of the decoding apparatus, and the reconstructed block or the reconstructed picture may be derived from the residual samples or the prediction samples by the adder  340  of the decoding apparatus. The method disclosed in  FIG.  11    may include the embodiments described above in the present document 
     Referring to  FIG.  11   , the decoding apparatus obtains the MTS index and the residual information from the bitstream (S 1100 ). For example, the decoding apparatus may obtain the MTS index and/or the residual information by parsing or decoding the bitstream. Here, the bitstream may be called encoded (image) information. 
     The MTS index may represent the transform kernel set to be applied to the current block among the transform kernel set candidates. Here, the MTS index may be represented as the tu_mts_idx syntax element or the mts_idx syntax element. Further, the transform kernel set may include the transform kernel to be applied to the current block in the horizontal direction and the transform kernel to be applied to the current block in the vertical direction. Here, the transform kernel to be applied in the horizontal direction may be represented as trTypeHor, and the transform kernel to be applied in the vertical direction may be represented as trTypeVer. 
     For example, the MTS index may be derived as one of candidates including 0 to 4, and in accordance with the MTS index, each of the trTypeHor and the trTypeVer may be derived as one of 0 to 2. For example, if the MTS index is 0, the trTypeHor and the trTypeVer may be all 0. Further, if the MTS index is 1, the trTypeHor and the trTypeVer may be all I. Further, if the MTS index is 2, the trTypeHor may be 2, and the trTypeVer may be 1. If the MTS index is 3, the trTypeHor may be 1, and the trTypeVer may be 1. Further, if the MTS index is 4, the trTypeHor and the trTypeVer may be all 2. For example, the trTypeVer or trTypeVer value may represent the transform kernel, and if 0, it may represent DCI2, if 1, it may represent DST7, and if 2, it may represent DCIT8. That is, each of the transform kernel to be applied in the horizontal direction and the transform kernel to be applied in the vertical direction may be derived as one of the candidates including DCT2, DST7, and DOTS based on the MTS index. 12031 The MTS index may be derived based on the bins of the bin string of the MTS index. 
     In other words, the MIS index information may be entropy-decoded and may be derived as a binarized MTS index, and the binarized MTS index may be represented as (the bins) of the bin string of the MTS index. 
     In other words, at least one of the bins of the bin string of the MTS index may be derived based on the context coding. Her, the context coding may be performed based on the value of the context index increment (ctxinc). Further, the context coding may be performed based on the context index (ctxIdx) or context model. Here, the context index may be derived based on the value of the context index increment. Further, the context index may be derived based on the value of the context index increment and the context index offset (ctxIdxOffset). 
     For example, all of the bins of the bin string of the MTS index may be derived based on the context codling. For example, the ctxInc for the first bin or the  th  bin (bin 0) among the bins of the bin string of the MTS index may be allocated based on cqtDepth. Here, the cqtDepth may represent a quad-tree depth for the current block, and may be derived as one value among 0 to 5. Further, the ctxinc for the second bin or No. 1 bin (bin 1) may be allocated with 6, the ctxInc for the third bin or No. 2 bin (bin 2) may be allocated with 7, and the ctxInc for the fourth bin or No. 3 bin (bin 3) may be allocated with 8. Further, for example, the ctxInc for the first bin or the 0 th  bin (bin 0) among the bins of the bin string of the MTS index may be allocated with 0, the ctxInc, for the second bin or No. 1 bin (bin 1) may be allocated with I. the ctxInc for the third bin or No. 2 bin (bin 2) may be allocated with 2, and the ctxinc for the fourth bin or No. 3 bin (bin 3) may be allocated with 3. That is, the number of context index increment values that can be used for the context coding of the first bin among the bins of the bin string may be one. 
     Further, for example, some of the bins of the bind string of the MTS index may be derived based on the context coding, and the remainders may be derived based on the bypass coding. For example, the ctxInc for the first bin or No. 0 bin (bin 0) among the bins of the bin string of the MTS index may be allocated with 0, and the remaining bins may be derived based on the bypass coding. Further, for example, the ctxinc for the first bin or No. 0 bin (bin 0) among the bins of the bin string of the MTS index may be allocated with 0, the ctxInc for the second bin or No. 1 bin (bin 1) may be allocated with 1, and the remaining bins may be derived based on the bypass coding. That is, the number of context index increment values that can be used for the context coding of the first bin among the bins of the bin string may be one. 
     Further, all of the bins of the bin string of the MTS index may be derived based on the bypass coding. Here, the bypass coding may represent performing of the context coding based on the uniform probability distribution, and since the update procedure of the context coding is omitted, the coding efficiency can be improved. 
     The residual information may represent information that is used to derive the residual samples, and may include information about the residual samples, inverse transform related information, and/or dequantization related information. For example, the residual information may include information about the quantized transform coefficients. 
     The decoding apparatus derives the transform coefficients for the current block based on the residual information (S 1110 ). For example, the decoding apparatus may derive the quantized transform coefficients for the current block based on the information about the quantized transform coefficients included in the residual information. For example, the decoding apparatus may derive the transform coefficients for the current block by performing dequantization with respect to the quantized transform coefficients. 
     The decoding apparatus generates the residual samples of the current block based on the MTS index and the transform coefficients (S 1120 ). For example, the residual samples may be generated based on the transform kernel set being represented by the transform coefficients and the MTS index. That is, the decoding apparatus may generate the residual samples from the transform coefficients through the inverse transform using the transform kernel set being represented by the MTS index. Here, the inverse transform using the transform kernel set being represented by the MTS index may be included in the primary inverse transform. Further, the decoding apparatus may use not only the primary inverse transform but also secondary inverse transform when generating the residual samples from the transform coefficients. In this case, the decoding apparatus may derive the modified transform coefficients by performing the secondary inverse transform with respect to the transform coefficients, and may generate the residual samples by performing the primary inverse transform with respect to the modified transform coefficients. 
     Although not illustrated in  FIG.  11   , for example, the decoding apparatus may obtain the prediction related information including the prediction modeltype from the bitstream, and may generate the prediction samples for the current block by performing the intra prediction or inter prediction based on the prediction mode/type information. Further, for example, the decoding apparatus may generate the reconstructed samples based on the prediction samples and the residual samples. Further, for example, the reconstructed block or the reconstructed picture may be derived based on the reconstructed samples. 
     For example, the decoding apparatus may obtain image information including all or parts of the above-described pieces of information (or syntax elements) by decoding the bitstream or the encoded information. Further, the bitstream or the encoded information may be stored in a computer readable storage medium, and may cause the above-described decoding method to be performed. 
     Although methods have been described on the basis of a flowchart in which steps or blocks are listed in sequence in the above-described embodiments, the steps of the present document are not limited to a certain order, and a certain step may be performed in a different step or in a different order or concurrently with respect to that described above. Further, it will be understood by those ordinary skilled in the art that the steps of the flowcharts are not exclusive, and another step may be included therein or one or more steps in the flowchart may be deleted without exerting an influence on the scope of the present disclosure. 
     The aforementioned method according to the present disclosure may be in the form of software, and the encoding apparatus and/or decoding apparatus according to the present disclosure may be included in a device for performing image processing, for example, a TV, a computer, a smart phone, a set-top box, a display device, or the like. 
     When the embodiments of the present disclosure are implemented by software, the aforementioned method may be implemented by a module (process or function) which performs the aforementioned function. The module may be stored in a memory and executed. by a processor. The memory may be installed inside or outside the processor and may be connected to the processor via various well-known means. The processor may include Application-Specific Integrated Circuit (ASIC), other chipsets, a logical circuit, and/or a data processing device. The memory may include a Read-Only Memory (ROM), a Random Access Memory (RAM),a flash memory, a memory card, a storage medium, and/or other storage device. In other words, the embodiments according to the present disclosure may be implemented and executed on a processor, a micro-processor, a controller, or a chip. For example, functional units illustrated in the respective figures may be implemented and executed on a computer, a processor, a microprocessor, a controller, or a chip. In this case, information on implementation (for example, information on instructions) or algorithms may be stored in a digital storage medium. 
     In addition, the decoding apparatus and the encoding apparatus to which the embodiment(s) of the present document is applied may be included in a multimedia broadcasting transceiver, a mobile communication terminal, a home cinema video device, a digital cinema video device, a surveillance camera, a video chat device, and a real time communication device such as video communication, a mobile streaming device, a storage medium, a camcorder, a video on demand (VoD) service provider, an Over The Top (OTT) video device, an interne streaming service provider, a  3 D video device, a Virtual Reality (VR) device, an Augment Reality (AR) device, an image telephone video device, a vehicle terminal (for example, a vehicle (including an autonomous vehicle) terminal, an airplane terminal, or a ship terminal), and a medical video device; and may be used to process an image signal or data. For example, the OTT video device may include a game console, a Blu-ray player, an Internet-connected TV, a home theater system, a smartphone, a tablet PC, and a Digital Video Recorder (DVR). 
     In addition, the processing method to which the embodiment(s) of the present document is applied may be produced in the form of a program executed by a computer and may be stored in a computer-readable recording medium. Multimedia data having a data structure according to the embodiment(s) of the present document may also be stored in the computer-readable recording medium. The computer readable recording medium includes all kinds 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 also includes media embodied in the form of a carrier wave (for example, transmission over the Internet), In addition, a bitstream generated by the encoding method may be stored in the computer-readable recording medium or transmitted through a wired or wireless communication network. 
     In addition, the embodiment(s) of the present document may be embodied as a computer program product based on a program code, and the program code may be executed on a computer according to the embodiment(s) of the present document. The program code may be stored on a computer-readable carrier. 
       FIG.  13    illustrates an example of a content streaming system to which embodiments disclosed in the present document are applicable. 
     Referring to  FIG.  13   , the content streaming system to which embodiments disclosed in the present document are applicable may generally include an encoding server, a streaming server, a web server, a media storage, a user device, and a multimedia input device. 
     The encoding server functions to compress to digital data the contents input from the multimedia input devices, such as the smart phone, the camera, the camcorder and the like, to generate a bitstream, and to transmittransamt it to the streaming server. As another example, in a case where the multimedia input device, such as, the smart phone, the camera, the camcorder or the like, 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 the embodiments of the present document is applied. And the streaming server may temporarily store the bitstream in a process of transmitting or receiving the bitstream. 
     The streaming server transmits multimedia data to the user equipment on the basis of a user&#39;s request through the web server, which functions as an instrument that informs a user of what service there is. When the user requests a service which the user wants, the web server transfers the request to the streaming server, and the streaming server transmits multimedia data to the user. In this regard, the contents streaming system may include a separate control server, and in this case, the control server functions to control commands/responses between respective equipment in the content streaming system. 
     The streaming server may receive contents from the media storage and/or the encoding server. For example, in a case the contents are received from the encoding server, the contents may be received in real time. In this case, the streaming server may store the bitstream for a predetermined period of time to provide the streaming service smoothly. 
     For example, the user equipment may include a mobile phone, a smart phone, a laptop computer, a digital broadcasting terminal, a personal digital assistant (PDA), a portable multimedia player (PMP), a navigation, a slate PC, a tablet PC, an ultrabook, a wearable device (e.g., a watch-type terminal (smart watch), a. glass-type terminal (smart glass), a head mounted display (HMD)), a digital TV, a desktop computer, a digital signage or the like. 
     Each of servers in the contents streaming system may be operated as a distributed server, and in this case, data received by each server may be processed in distributed manner. 
     Claims in the present description can be combined in a various way. For example, technical features in method claims of the present description can be combined to be implemented or performed in an apparatus, and technical features in apparatus claims can be combined to be implemented or performed in a method. Further, technical features in method claim(s) and apparatus claim(s) can be combined to be implemented or performed in an apparatus. Further, technical features in method claim(s) and apparatus claim(s) can be combined to be implemented or performed in a method.