Patent Publication Number: US-2022239942-A1

Title: Apparatus and method for encoding motion vector determined using adaptive motion vector resolution, and apparatus and method for decoding motion vector

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This is a continuation application of U.S. application Ser. No. 16/622,157, filed Dec. 12, 2019, which is a National Stage of International Application No. PCT/KR2018/003800, filed Mar. 30, 2018, which claims priority under 35 U.S.C. § 119 from U.S. Provisional Application No. 62/529,566, filed Jul. 7, 2017 the contents of all of which are incorporated herein by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to video encoding and decoding fields. More particularly, the present disclosure relates to a method and apparatus for encoding a motion vector of a video, and a method and apparatus for decoding a motion vector of a video. 
     BACKGROUND ART 
     In video encoding and decoding methods, in order to encode an image, one picture may be split into macroblocks and each of the macroblocks may be encoded by using inter prediction or intra prediction. 
     Inter prediction refers to a method of compressing an image by removing temporal redundancy between pictures, a representative example of which is motion estimation encoding. In motion estimation encoding, each block of a current picture is predicted by using at least one reference picture. A reference block that is most similar to a current block is found within a predetermined search range by using a predetermined evaluation function. 
     A current block is predicted based on a reference block, and a residual block obtained by subtracting from the current block a prediction block generated as a prediction result is encoded. In this case, in order to more accurately perform prediction, interpolation is performed on a search range of the reference picture, sub-pel-unit pixels smaller than integer-pel-unit pixels may be generated, and inter prediction may be performed on the generated sub-pel-unit pixels. 
     In a codec such as H.264 advanced video coding (AVC) and high efficiency video coding (HEVC), in order to predict a motion vector of a current block, a motion vector of previously encoded blocks adjacent to the current block or blocks included in a previously encoded picture is used as a prediction motion vector of the current block. 
     DESCRIPTION OF EMBODIMENTS 
     Solution to Problem 
     A method of decoding a motion vector, according to an embodiment, may include: obtaining information indicating a motion vector resolution (MVR) of a current block from a bitstream, selecting one candidate block from among at least one candidate block, based on the MVR of the current block; and obtaining a motion vector of the current block corresponding to the MVR, by using a motion vector of the determined one candidate block as a prediction motion vector of the current block. 
     Advantageous Effects of Disclosure 
     An apparatus and method of encoding a motion vector and an apparatus and method of decoding a motion vector according to an embodiment may efficiently encode and decode an image at a low bit rate by representing a residual motion vector based on a motion vector resolution that is adaptively determined. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       A brief explanation of each drawing is provided to more fully understand the accompanying drawings. 
         FIG. 1  is a block diagram illustrating a configuration of a motion vector encoding apparatus, according to an embodiment. 
         FIG. 2  is a flowchart for describing a motion vector encoding method, according to an embodiment. 
         FIG. 3  is a block diagram illustrating a configuration of a motion vector decoding apparatus, according to an embodiment. 
         FIG. 4  is a flowchart for describing a motion vector decoding method, according to an embodiment. 
         FIG. 5  is a diagram for describing at least one candidate block mapped in a one-to-one (1:1) manner to at least one candidate motion vector resolution (MVR). 
         FIG. 6  is a diagram illustrating a mapping relationship between at least one candidate MVR and at least one candidate block. 
         FIG. 7  is a diagram for describing interpolation for determining a motion vector according to various MVRs. 
         FIG. 8  is a diagram illustrating positions of pixels that may be indicated by motion vectors according to a ¼ pixel unit MVR, a ½ pixel unit MVR, a 1 pixel unit MVR, and a 2 pixel unit MVR when an available minimum MVR is the ¼ pixel unit MVR. 
         FIGS. 9A and 9B  are diagrams for describing a method of adjusting a prediction motion vector. 
         FIG. 10  is a diagram illustrating syntax for describing a process of obtaining an MVR index of a current block. 
         FIG. 11  is a block diagram of a video decoding apparatus for decoding an image based on at least one from among block shape information and split shape information, according to an embodiment. 
         FIG. 12  is a block diagram of a video encoding apparatus for encoding an image based on at least one from among block shape information and split shape information, according to an embodiment. 
         FIG. 13  illustrates a process in which a current coding unit is split to determine at least one coding unit, according to an embodiment. 
         FIG. 14  illustrates a process of determining at least one coding unit by splitting a non-square coding unit, according to an embodiment. 
         FIG. 15  illustrates a process of splitting a coding unit based on at least one of block shape information and split shape information, according to an embodiment. 
         FIG. 16  illustrates a method of determining a predetermined coding unit from among an odd number of coding units, according to an embodiment. 
         FIG. 17  illustrates an order of processing a plurality of coding units when the plurality of coding units are determined by splitting a current coding unit, according to an embodiment. 
         FIG. 18  illustrates a process of determining that a current coding unit is to be split into an odd number of coding units, when the coding units are not processable in a predetermined order, according to an embodiment. 
         FIG. 19  illustrates a process of determining at least one coding unit by splitting a first coding unit, according to an embodiment. 
         FIG. 20  illustrates that a shape into which a second coding unit is splittable is restricted when the second coding unit having a non-square shape, which is determined by splitting a first coding unit, satisfies a predetermined condition, according to an embodiment. 
         FIG. 21  illustrates a process of splitting a square coding unit when split shape information indicates that the square coding unit is not to be split into four square coding units, according to an embodiment. 
         FIG. 22  illustrates that a processing order between a plurality of coding units may be changed depending on a process of splitting a coding unit, according to an embodiment. 
         FIG. 23  illustrates a process of determining a depth of a coding unit as a shape and size of the coding unit change, when the coding unit is recursively split such that a plurality of coding units are determined, according to an embodiment. 
         FIG. 24  illustrates depths that are determinable based on shapes and sizes of coding units, and part indexes (PIDs) for distinguishing the coding units, according to an embodiment. 
         FIG. 25  illustrates that a plurality of coding units are determined based on a plurality of predetermined data units included in a picture, according to an embodiment. 
         FIG. 26  illustrates a processing block serving as a unit for determining a determination order of reference coding units included in a picture, according to an embodiment. 
         FIG. 27  illustrates coding units determinable per picture when a combination of shapes into which a coding unit is splittable is different per picture, according to an embodiment. 
         FIG. 28  illustrates various shapes of a coding unit determinable based on split shape information representable as a binary code, according to an embodiment. 
         FIG. 29  illustrates other shapes of a coding unit determinable based on split shape information representable as a binary code, according to an embodiment. 
         FIG. 30  is a block diagram of a video encoding and decoding system for performing loop filtering. 
         FIG. 31  illustrates an example of filtering units included in a largest coding unit and filtering performing information of a filtering unit, according to an embodiment. 
         FIG. 32  illustrates a process of performing merging or splitting between coding units determined according to a predetermined encoding method, according to an embodiment. 
         FIG. 33  illustrates an index according to a Z-scan order of a coding unit, according to an embodiment. 
         FIG. 34  is a diagram of a reference sample for intra prediction of a coding unit, according to an embodiment. 
     
    
    
     BEST MODE 
     A method of decoding a motion vector according to an embodiment includes: obtaining information indicating a motion vector resolution (MVR) of a current block from a bitstream; selecting one candidate block from among at least one candidate block, based on the MVR of the current block; and obtaining a motion vector of the current block corresponding to the MVR, by using a motion vector of the determined one candidate block as a prediction motion vector of the current block. 
     A method of decoding a motion vector according to an embodiment includes: obtaining information indicating one candidate block for a current block from a bitstream; determining one candidate motion vector resolution (MVR) from among at least one candidate MVR as an MVR of the current block, based on the information indicating the one candidate block; and obtaining a motion vector of the current block corresponding to the MVR, by using a motion vector of the one candidate block as a prediction motion vector of the current block. 
     The MVR of the current block may be determined from among at least one candidate MVR. 
     The at least one candidate MVR and the at least one candidate block may be mapped in a one-to-one (1:1) manner. 
     The method may further include, based on information about at least one from among the current block, a previously decoded block, a current slice, a previously decoded slice, a current picture, and a previously decoded picture, determining a number and a type of the at least one candidate MVR. 
     The method may further include, based on information about at least one from among the current block, a previously decoded block, a current slice, a previously decoded slice, a current picture, and a previously decoded picture, determining a position of the at least one candidate block to be mapped to the at least one candidate MVR. 
     The determining of the MVR of the current block may include: obtaining an index indicating the MVR of the current block from the bitstream; and determining a candidate MVR corresponding to the obtained index from among the at least one candidate MVR as the MVR of the current block. 
     The method may further include, when a motion vector does not exist in the one candidate block, determining a motion block of a block other than the at least one candidate block as the prediction motion vector. 
     The method may further include, when candidate blocks having a same motion vector exist among the at least one candidate block mapped to at least one candidate MVR selectable for the current block, replacing some from among the candidate blocks having the same motion vector with a block other than the at least one candidate block. 
     The obtaining of the motion vector of the current block may include, when the MVR of the current block is higher than a minimum MVR from among at least one candidate MVR, upscaling a residual motion vector obtained from the bitstream. 
     The obtaining of the motion vector of the current block may include, when the MVR of the current block is higher than a minimum MVR from among at least one candidate MVR, adjusting the prediction motion vector. 
     The adjusting may include: downscaling the prediction motion vector, based on a difference between the MVR of the current block and the minimum MVR; when the downscaled prediction motion vector does not indicate an integer pixel unit, changing the downscaled prediction motion vector to indicate the integer pixel unit; and obtaining the adjusted prediction motion vector by upscaling the changed downscaled prediction motion vector. 
     An apparatus for decoding a motion vector includes: an obtainer configured to obtain information indicating a motion vector resolution (MVR) of a current block from a bitstream; and a prediction decoder configured to determine one candidate block from among at least one candidate block based on the MVR of the current block and obtain a motion vector of the current block corresponding to the MVR by using a motion vector of the determined one candidate block as a prediction motion vector of the current block. 
     A method of encoding a motion vector includes: determining a motion vector resolution (MVR) of a current block; determining one candidate block from among at least one candidate block, based on the determined MVR; obtaining a motion vector of the current block according to the determined MVR; and generating a bitstream including at least one from among information indicating the MVR and information indicating the one candidate block, and a residual motion vector between the motion vector of the current block and a motion vector of the one candidate block. 
     A bitstream stored in a storage medium includes: information indicating a motion vector resolution (MVR) of a current block or information indicating one candidate block for the current block; and information corresponding to a residual motion vector obtained by using a motion vector of the current block determined according to the MVR and a motion vector of the one candidate block, wherein the information indicating the MVR of the current block and the information indicating the one candidate block for the current block are mapped to each other. 
     MODE OF DISCLOSURE 
     As the present disclosure allows for various changes and numerous embodiments, exemplary embodiments will be illustrated in the drawings and described in detail in the written description. However, this is not intended to limit the present disclosure to particular modes of practice, and it is to be appreciated that all changes, equivalents, and replaces that do not depart from the spirit and technical scope of the present disclosure are encompassed in the present disclosure. 
     In the description of the present disclosure, certain detailed explanations of the related art are omitted when it is deemed that they may unnecessarily obscure the essence of the present disclosure. Also, numbers (e.g., first and second) used in the description of embodiments of the disclosure are intended to merely distinguish one component from another. 
     When a component is referred to as being “connected” or “accessed” to or by any other component, it should be understood that the component may be directly connected or accessed to or by the other component, but another new component may also be interposed between them, unless otherwise specifically indicated. 
     Regarding an element with a suffix such as ‘unit’ or ‘module’, two or more elements may be combined into one element or one element may be divided into two or more elements according to functions. In addition, each of respective components to be described below may additionally perform some or all functions among functions which other components take charge of in addition to a primary function which each component takes charge of and some functions among primary functions which the respective components take charge of may be exclusively performed by other components. 
     Also, the term ‘image’ or picture’ used herein may refer to a still image of a video, or a moving image, i.e., a video itself. 
     Also, the term ‘sample’ used herein refers to data that is assigned to a sampling location of an image and is to be processed. For example, pixels in an image of a spatial domain or transform coefficients in a transform domain may be samples. A unit including one or more samples may be defined as a block. 
     Also, the term ‘current block’ used herein may refer to a block of a largest coding unit, a coding unit, a prediction unit, or a transform unit of a current image to be encoded or decoded. 
     Also, the term ‘MVR’ used herein may refer to the precision of a position of a pixel that may be indicated by a motion vector determined through inter prediction from among pixels included in a reference image (or an interpolated reference image). When an MVR has an N pixel unit (N is a rational number), it means that a motion vector may have the precision of an N pixel unit. For example, an MVR of ¼ pixel unit may mean that a motion vector may indicate a pixel position of a ¼ pixel unit (i.e., a subpixel unit) in an interpolated reference image, and an MVR of 1 unit pixel may mean that a motion vector may indicate a pixel position corresponding to a 1 pixel unit (i.e., an integer pixel unit) in an interpolated reference image. 
     Also, the term ‘candidate MVR’ used herein refers to one or more MVRs that may be selected as an MVR of a block, and the term ‘candidate block’ refers to one or more blocks that are mapped to a candidate MVR and may be used as a block for a prediction motion vector of a block to be inter predicted. 
     Also, the term ‘pixel unit’ used herein may be interchangeably used with the terms ‘pixel precision’ and ‘pixel accuracy’. 
     An apparatus and method of encoding a motion vector and an apparatus and method of decoding a motion vector according to an embodiment will be described with reference to  FIGS. 1 through 4 . 
     A motion vector encoding apparatus  10  and a motion vector encoding method may be included in a video encoding apparatus  200  and method and method described below. Also, a motion vector decoding apparatus  30  and a motion vector decoding method may be included in a video decoding apparatus  100  and method described below. 
       FIG. 1  is a block diagram illustrating a configuration of the motion vector encoding apparatus  10 , according to an embodiment. 
     Inter prediction in video encoding refers to a prediction method using a similarity between a current image and another image. A reference block similar to a current block of the current image is detected from a reference image that is decoded earlier than the current image, and a distance between the current block and the reference block is represented by using a motion vector. Also, a difference of pixel values between the current block and the reference block may be represented as residual data. Accordingly, information output via inter prediction of the current block is not image information of the current block, but may be an index, a motion vector, and residual data indicating the reference block, thereby improving encoding and decoding efficiency. 
     The motion vector encoding apparatus  10  according to an embodiment may encode a motion vector used for inter prediction for each block of each image of a video. 
     A type of a block may be a square shape or a rectangular shape, or may be an arbitrary geometrical shape. A block according to an embodiment is not limited to a data unit of a certain size, and may include a largest coding unit, a coding unit, a prediction unit, and a transform unit from among coding units according to a tree structure. 
     Video encoding and decoding methods based on the coding units according to the tree structure will be described below with reference to  FIGS. 11 through 34 . 
     As shown in  FIG. 1 , the motion vector encoding apparatus  10  according to an embodiment may include a prediction encoder  11  and a generator  13 . As described above, the motion vector encoding apparatus  10  may be included in the video encoding apparatus  200  of  FIG. 12 , and the prediction encoder  11  may be included in an encoder  220  of the video encoding apparatus  200  and the generator  13  may be included in a bitstream generator  210  of the video encoding apparatus  200 . 
     The motion vector encoding apparatus  10  may perform encoding on a motion vector by performing inter prediction in a block unit split from a picture. 
     Regarding a current block including a coding unit or a prediction unit split from the coding unit, the motion vector encoding apparatus  10  according to an embodiment may search for a prediction block most similar to the current block in a reference image through motion estimation, and may determine a motion vector indicating motion information between the current block and the prediction block. 
     In an embodiment, the prediction encoder  11  may select one candidate MVR from among at least one candidate MVR as an MVR of the current block, and may determine a motion vector of the current block according to the selected MVR. The prediction encoder  11  may use a motion vector of a candidate block mapped to the selected MVR of the current block from among at least one candidate block as a prediction motion vector of the current block. 
     In an embodiment, the prediction encoder  11  may select one candidate block for the current block from among the at least one candidate block, and may determine one candidate MVR mapped to the selected candidate block from among the at least one candidate MVR as an MVR of the current block. 
     In an embodiment, a one-to-one (1:1) mapping relationship or a correspondence relationship between the at least one candidate MVR and the at least one candidate block may be preset in the motion vector encoding apparatus  10 . When the at least one candidate MVR and the at least one candidate block are mapped in a 1:1 manner, it may mean that when one candidate MVR from among the at least one candidate MVR is determined as an MVR of the current block, a position of one candidate block to be used as a prediction motion vector of the current block is accordingly determined, and in contrast, when one candidate block to be used as a prediction motion vector of the current block is determined from among the at least one candidate block, one candidate MVR is accordingly determined as an MVR of the current block. That is, in an embodiment of the present disclosure, it would be understood that one candidate block is allocated to each of the at least one candidate MVR. 
     The at least one candidate MVR may include at least one from among an MVR of ⅛ pixel unit, an MVR of ¼ pixel unit, an MVR of ½ pixel unit, an MVR of 1 pixel unit, an MVR of 2 pixel unit, an MVR of 4 pixel unit, and an MVR of 8 pixel unit. However, a candidate MVR is not limited to the above examples, and MVRs having various values may be included in the candidate MVR. 
     In the present specification, when a first MVR is higher than a second MVR, it means that a pixel unit of the first MVR is higher than a pixel unit of the second MVR. For example, an MVR of 1 pixel unit is higher than an MVR of ½ pixel unit, and an MVR of ½ pixel unit is higher than an MVR of ¼ pixel unit. In fact, although prediction when a motion vector is determined by using an MVR of ¼ pixel unit is more accurate than that when a motion vector is determined by using an MVR of 1 pixel unit, the present specification will describe a size difference of each MVR based on a size of a pixel unit of each MVR for convenience of explanation. 
     The at least one candidate block may be selected from among blocks including spatial blocks and temporal blocks associated with the current block. The spatial blocks associated with the current block may include at least one block spatially adjacent to the current block. The temporal blocks may include a block located at the same position as the current block in a reference image having a picture order count (POC) different from a POC of the current block and at least one block spatially adjacent to the block at the same position. 
     In an embodiment, when the at least one candidate MVR includes an MVR of ¼ pixel unit, an MVR of ½ pixel unit, an MVR of 1 pixel unit, and an MVR of 2 pixel unit and the at least one candidate block includes a left block, an upper block, a left upper block, and an upper left block, a mapping relationship or a correspondence relationship between (the MVR of ¼ pixel unit and the left block), (the MVR of ½ pixel unit and the upper block), (the MVR of 1 pixel unit and the left upper block), and (the MVR of 2 pixel unit and the upper left block) may be set in the motion vector encoding apparatus  10 . Accordingly, when the MVR of ¼ pixel unit is selected as an MVR of the current block, the prediction encoder  11  may accordingly use a motion vector of the left block as a prediction motion vector of the current block. Also, when the upper block is selected as a prediction motion vector of the current block, the prediction encoder  11  may accordingly determine the MVR of ½ pixel unit as an MVR of the current block. 
     In an embodiment, the prediction encoder  11  may determine the number and a type of selectable candidate MVRs in a block unit, a slice unit, or a picture unit, based on information about at least one from among a current block, a previously encoded block, a current slice, a previously encoded slice, a current picture, and a previously encoded picture. The prediction encoder  11  may determine one candidate MVR from among the selectable candidate MVRs for the current block determined in the block unit, the slice unit, or the picture unit as an MVR of the current block. 
     For example, the prediction encoder  11  may differently determine at least one candidate MVR selectable for the current block and at least one candidate MVR selectable for a subsequent block. For example, an MVR of ¼ pixel unit and an MVR of ½ pixel unit may be determined as the at least one candidate MVR selectable for the current block, and an MVR of 1 pixel unit and an MVR of 2 pixel unit may be determined as the at least one candidate MVR for the subsequent block. Alternatively, only one MVR may be determined as a candidate MVR for any block. 
     For example, when the selectable at least one candidate MVR is determined in the block unit, the prediction encoder  11  may compare a size of the current block with a pre-determined size and may cause only one MVR to be included in the candidate MVR or may cause a plurality of MVRs to be included in the candidate MVR. Alternatively, when the selectable at least one candidate MVR is determined in the block unit, the prediction encoder  11  may determine the number and a type of the candidate MVR selectable for the current block based on an MVR of a previously encoded neighboring block. 
     Also, for example, when the selectable at least one candidate MVR is determined in the slice or picture unit, the prediction encoder  11  may determine the number and a type of candidate MVRs selectable for the current slice or the current picture according to a type of a slice or a picture. Also, for example, when the selectable at least one candidate MVR is determined in the slice or picture unit, the prediction encoder  11  may determine the number and a type of the candidate MVR selectable for the current slice or the current picture according to whether the slice or the picture is referred to by another slice or picture. 
     In an embodiment, the prediction encoder  11  may determine a position of at least one candidate block mapped to each of at least one candidate MVR in a block unit, a slice unit, or a picture unit, based on information about at least one from among a current block, a previously encoded block, a current slice, a previously encoded slice, a current picture, and a previously encoded picture. 
     For example, the prediction encoder  11  may differently determine at least one candidate block selectable for the current block and at least one candidate block selectable for a subsequent block. For example, when the position of the selectable candidate block is determined in the block unit, an upper block and a left block may be respectively mapped to an MVR of 1 pixel unit and an MVR of 2 pixel unit corresponding to candidate MVRs of the current block and an upper left block and a left lower block may be respectively mapped to an MVR of 1 pixel unit and an MVR of 2 pixel unit corresponding to candidate MVRs of the subsequent block. 
     In an embodiment, the number and a type of at least one candidate MVR and a position of at least one candidate block to be respectively mapped to the at least one candidate MVR may be fixed and set as a default for a video to be encoded. 
     In an embodiment, the prediction encoder  11  may determine one candidate MVR from among at least one candidate MVR as an MVR of a current block, and may determine a motion vector of the current block according to the MVR of the current block. 
     In order to determine the motion vector of the current block, the prediction encoder  11  may interpolate a reference image by using a minimum MVR from among the at least one candidate MVR. 
     In an embodiment, when a candidate MVR of smallest pixel unit (i.e., a minimum MVR) from among the at least one candidate MVR has a 1/n pixel unit (n is a natural number), the prediction encoder  11  may generate a subpixel of 1/n pixel unit from an integer pixel of the reference image for motion estimation, and may determine the motion vector of the current block indicating a subpixel of maximum 1/n pixel unit according to the MVR of the current block. 
     Determining a motion vector by using an MVR of small pixel unit according to characteristics of a current image may always be less efficient than determining a motion vector by using an MVR of large pixel unit. A case where a motion vector is determined by using an MVR of small pixel unit may require more bits to represent a size of a motion vector (or a residual motion vector) and may be less efficient in terms of a bit rate than a case where a motion vector is determined by using an MVR of large pixel unit. Accordingly, for example, an MVR may be adaptively determined according to a resolution of an image to reduce a bit rate and minimize a decrease in the quality of a reconstructed image. 
     The prediction encoder  11  according to an embodiment may adaptively determine an MVR of a current block, and may determine a motion vector by using a pixel unit of the determined MVR. For example, when a pixel unit of the MVR of the current block is ½, the prediction encoder  11  may determine a motion vector indicating a pixel of ½ pixel unit in a reference image interpolated according to a minimum MVR. 
     The prediction encoder  11  according to an embodiment may use a motion vector of any of candidate blocks as a prediction motion vector of the current block, or may change the motion vector of any of the candidate blocks and may use the changed motion vector as a prediction motion vector of the current block. 
     In an embodiment, the prediction encoder  11  may adjust a motion vector of a candidate block for the current block based on a difference between the minimum MVR from among available candidate MVRs and the MVR of the current block, and then may determine a motion vector of the current block by using the adjusted motion vector. 
     Because the motion vector of the candidate block is predicted to indicate pixel coordinates in an image interpolated according to the minimum MVR, the motion vector of the candidate block is adjusted to correspond to the MVR of the current block. Also, the reason why the motion vector of the candidate block is adjusted is to represent a residual motion vector in an integer unit as described below. 
     For example, when the MVR of the current block is a 1 pixel unit, the motion vector of the current block has to be determined to indicate a pixel of 1 pixel unit in the image interpolated according to the minimum MVR. However, when the motion vector of the candidate block does not indicate the pixel of 1 pixel unit, the motion vector of the candidate block is adjusted to indicate the pixel of 1 pixel unit. 
     A method of adjusting a motion vector of a candidate block will be described below with reference to  FIGS. 9A and 9B . 
     The prediction encoder  11  determines a motion vector of a current block by using each candidate MVR, by using a motion vector of any of candidate blocks respectively mapped to at least one candidate MVR as a prediction motion vector, and determines one from among the at least one candidate MVR based on a cost. When the cost is calculated, a rate-distortion cost may be used. 
     In order to determine the motion vector of the current block, the prediction encoder  11  may determine a search start position in a reference image by using a motion vector (or an adjusted motion vector) of a candidate block allocated to the each candidate MVR, and may determine the motion vector of the current block according to the each candidate MVR by searching for an optimal reference block according to the each candidate MVR. For example, first, the prediction encoder  11  may perform box search in a search range of 5 pixels around the search start position. Second, the prediction encoder  11  may perform diamond search in various step sizes. Selectively, the prediction encoder  11  may determine an optimal position by performing raster search. 
     The prediction encoder  11  may compare a rate-distortion cost based on a difference value between the motion vector of the current block determined according to the each candidate MVR and the motion vector of the candidate block allocated to the each candidate MVR and may determine a candidate MVR and a candidate block having a minimum cost as an MVR of the current block and a candidate block for a prediction motion vector of the current block. 
     For example, when an MVR of ¼ pixel unit mapped to a left block, an MVR of ½ pixel unit mapped to an upper block, and an MVR of 1 pixel unit mapped to an upper right block are included in the at least one candidate MVR, the prediction encoder  11  may determine the motion vector of the current block in a ¼ pixel unit in a reference image interpolated according to a ¼ pixel unit MVR that is a minimum MVR by using a motion vector of the left block, may determine the motion vector of the current block in a ½ pixel unit in a reference image interpolated according to the ¼ pixel unit MVR by using a motion vector of the upper block, and may determine the motion vector of the current block in a 1 pixel unit in a reference image interpolated according to the ¼ pixel unit MVR by using a motion vector of the upper right block. The prediction encoder  11  may determine one candidate MVR selected based on a cost as the MVR of the current block. 
     In an embodiment, when a motion vector does not exist in a candidate block from among the candidate blocks respectively mapped to the candidate MVRs for the current block, the prediction encoder  11  may exclude the candidate block having no motion vector and may use another block having a motion vector as a candidate block. In this case, the other block newly used as a candidate block may include a block other than the candidate blocks respectively mapped to the candidate MVRs. The prediction encoder  11  may use the motion vector of the other block determined according to the candidate MVR as a prediction motion vector of the current block. When a block is intra predicted, the intra predicted block may be determined to be a block not having a motion vector. 
     For example, when it is assumed that at least one candidate MVR available for the current block includes the MVR of ¼ pixel unit mapped to the left block, the MVR of ½ pixel unit mapped to the upper block, and the MVR of 1 pixel unit mapped to the upper right block and a motion vector does not exist in the upper right block, the prediction encoder  11  may map the MVR of 1 pixel unit to a block (e.g., an upper left block) other than the at least one candidate block. 
     In an embodiment, when a motion vector does not exist in some candidate blocks from among at least one candidate block mapped to the candidate MVRs, positions and mapping priorities of blocks to be newly mapped may be pre-determined. 
     Also, in an embodiment, when a motion vector does not exist in some candidate blocks from among at least one candidate block mapped to the at least one candidate MVR available for the current block, the prediction encoder  11  may use an arbitrary motion vector (e.g., a zero vector) as a motion vector of the some candidate blocks. 
     Also, in an embodiment, when candidate blocks having the same motion vector exist from among the at least one candidate block mapped to the at least one candidate MVR available for the current block, some from among the candidate blocks having the same motion vector may be replaced by blocks other than the at least one candidate block. For example, when a motion vector of the left block mapped to a ¼ pixel unit MVR and a motion vector of the upper block mapped to a ½ pixel unit MVR are the same, the prediction encoder  11  may replace one block (e.g., the upper block) from among the left block and the upper block with another block (e.g., the upper left block) and may map the replaced block to a candidate MVR (e.g., a ½ pixel resolution). 
     In an embodiment, whether motion vectors of two or more candidate blocks are the same may be determined by adjusting motion vectors of the candidate blocks and then comparing the adjusted motion vectors. 
     When there are a plurality of candidate blocks having the same motion vector, a priority indicating which block from among the plurality of candidate blocks is to be replaced by another block, and positions and priorities of blocks to be newly blocks may be pre-determined. 
     In an embodiment, when a candidate block and a motion vector of a current block are determined, the prediction encoder  11  may obtain a residual motion vector between the motion vector of the current block and a prediction motion vector. 
     The generator  13  may generate a bitstream including at least one from among information indicating an MVR of a current block and information indicating a candidate block used as a prediction motion vector of the current block. As described above, because a candidate MVR and the candidate block have a 1:1 mapping relationship, when the MVR of the current is determined, a position of the candidate block may be accordingly determined, and in contrast, when the candidate block is determined in contrast, the MVR of the current block may be accordingly determined. Accordingly, the generator  13  may generate the bitstream including at least one from among information about the MVR of the current block and information for specifying the candidate block. 
     The generator  13  may cause at least one from among an index indicating the MVR of the current block and an index indicating the candidate block to be included as at least one from among the information indicating the MVR of the current block and the information indicating the candidate block used as the prediction motion vector of the current block. 
     In an embodiment, when an index is allocated in a unary manner to each of candidate MVRs available for the current block and one index is selected by the prediction encoder  11 , the generator  13  may generate a bitstream including the selected index. For example, when the available candidate MVRs include an MVR of ¼ pixel unit, an MVR of ½ pixel unit, an MVR of 1 pixel unit, an MVR of 2 pixel unit, an MVR of 4 pixel unit, and an MVR of 8 pixel unit, the MVR of ¼ pixel unit, the MVR of ½ pixel unit, the MVR of 1 pixel unit, the MVR of 2 pixel unit, the MVR of 4 pixel unit, and the MVR of 8 pixel unit may be respectively represented by indices 0, 10, 110, 1110, 11110, and 11111. 
     In an embodiment, when an index is allocated in a unary manner to each of at least one candidate block respectively mapped to at least one candidate MVR and one index is selected by the prediction encoder  11 , the generator  13  may generate a bitstream including the selected index. For example, when the at least one candidate block includes a left block, an upper block, a left upper block, a left lower block, an upper left block, and an upper right block, the left block, the upper block, the left upper block, the left lower block, the upper left block, and the upper right block may be respectively represented by indices 0, 10, 110, 1110, 11110, and 11111. 
     In an embodiment, when there is one candidate MVR available for a current block, the prediction encoder  11  omits generating of information indicating an MVR of the current block and a candidate block. Accordingly, information indicating the MVR of the current block and the candidate block may not be included in a bitstream generated by the generator  13 . 
     In an embodiment, when there are two or more candidate MVRs available for a current block, the prediction encoder  11  may generate at least one from among information indicating a candidate block and an MVR of the current block by using a flag or an index. 
     In an embodiment, the prediction encoder  11  may downscale a residual motion vector that is a difference between a motion vector of a current block and a prediction motion vector. 
     For example, when an MVR of the current block is higher than a minimum MVR from among candidate MVRs, the prediction encoder  11  may downscale the residual motion vector based on a difference between the minimum MVR and the MVR of the current block. For example, when the minimum MVR has a ¼ pixel unit and the MVR of the current block has a ½ pixel unit, the prediction encoder  11  may downscale the residual motion vector by ½. 
     In an embodiment, because a residual motion vector is adaptively or selectively downscaled according to an MVR adaptively selected for a current block, a motion vector of the current block may be encoded by using fewer bits. 
       FIG. 2  is a flowchart for describing a motion vector encoding method, according to an embodiment. 
     In operation S 21 , the motion vector encoding apparatus  10  may determine one candidate MVR from among at least one candidate MVR available for a current block as an MVR of the current block, and may determine a candidate block mapped to the selected MVR from among at least one candidate block as a candidate block for a prediction motion vector of the current block. 
     Alternatively, in an embodiment, the motion vector encoding apparatus  10  may select a candidate block to be used as the prediction motion vector from among the at least one candidate block, and may determine a candidate MVR mapped to the selected candidate block as the MVR of the current block. 
     The available at least one candidate MVR may be mapped in a 1:1 manner to the at least one candidate block, and the motion vector encoding apparatus  10  may determine a motion vector of the current block according to each candidate MVR by using each available candidate MVR and a motion vector of a candidate block mapped to the each available candidate MVR. The motion vector encoding apparatus  10  may select a candidate block and one candidate MVR selected based on a cost as the MVR of the current block and the candidate block for the prediction motion vector of the current block. 
     In an embodiment, the motion vector encoding apparatus  10  may determine the number and a type of the at least one candidate MVR in a block unit, a slice unit, or a picture unit, based on at least one from among the current block, a previously encoded block, a current slice, a previously encoded slice, a current picture, and a previously encoded picture. 
     In an embodiment, the motion vector encoding apparatus  10  may determine a position of the at least one candidate block to be respectively mapped to the at least one candidate MVR in the block unit, the slice unit, or the picture unit, based on the information about at least one from among the current block, the previously encoded block, the current slice, the previously encoded slice, the current picture, and the previously encoded picture. 
     In an embodiment, when a motion vector does not exist in a candidate block from among the at least one candidate block respectively mapped to the at least one candidate MVR, the motion vector encoding apparatus  10  may newly map a block other than the at least one candidate block mapped to the candidate MVR to a candidate block, instead of the candidate block not including the motion vector, and may use a motion vector of the newly mapped block as the prediction motion vector of the current block. 
     Also, in an embodiment, when a motion vector does not exist in a candidate block from among the at least one candidate block mapped to the at least one candidate MVR, the motion vector encoding apparatus  10  may use an arbitrary motion vector (e.g., a zero vector) as a motion vector of the candidate block not including the motion vector. 
     Also, in an embodiment, when there are candidate blocks having the same motion vector from among the at least one candidate block respectively mapped to the at least one candidate MVR, the motion vector encoding apparatus  10  may replace some of the candidate blocks having the same motion vector with blocks other than the at least one candidate block mapped to the candidate MVR and may newly map the replaced blocks to the candidate MVR. 
     In operation S 22 , the motion vector encoding apparatus  10  determines a motion vector of the current block in an interpolated reference image, according to the MVR of the current block. 
     The motion vector encoding apparatus  10  may adjust a motion vector of a candidate block by comparing a minimum MVR from among at least one candidate MVR selectable for the current block and the MVR of the current block. The motion vector encoding apparatus  10  may determine a search start position in the reference image according to the adjusted motion vector of the candidate block, may search for an optimal reference block in the reference image, and may determine the motion vector of the current block according to the MVR of the current block. 
     In operation S 23 , the motion vector encoding apparatus  10  obtains a residual motion vector between the motion vector of the current block and the motion vector (or the adjusted motion vector) of the candidate block. 
     In operation S 24 , the motion vector encoding apparatus  10  generates information indicating the residual motion vector, and at least one from among information about the MVR of the current block and information indicating the candidate block used as the prediction motion vector. 
     The information indicating the residual motion vector and at least one from among the information about the MVR of the current block and the information indicating the candidate block used as the prediction motion vector may be included in a bitstream. 
     As described above, the motion vector encoding apparatus  10  may downscale the residual motion vector by comparing the MVR of the current block with the minimum MVR from among the at least one candidate MVR. 
       FIG. 3  is a block diagram illustrating a configuration of the motion vector decoding apparatus  30 , according to an embodiment. The motion vector decoding apparatus  30  of  FIG. 3  may be included in the video decoding apparatus  100 . In detail, an obtainer  31  may be included in a bitstream obtainer  110  of the video decoding apparatus  100 , and a prediction decoder  33  may be included in a decoder  120  of the video decoding apparatus  100 . 
     The motion vector decoding apparatus  30  may determine a motion vector for performing inter prediction of a current block by parsing an obtained bitstream. 
     The obtainer  31  may obtain information indicating a residual motion vector, and at least one from among information about an MVR of the current block and information indicating a candidate block from the bitstream. 
     The information about the MVR of the current block may include an index indicating the MVR of the current block, and the information indicating the candidate block may include an index indicating the candidate block. 
     When the information about the MVR of the current block is obtained by the obtainer  31 , the prediction decoder  33  may determine a candidate block to be used as a prediction motion vector of the current block according to the MVR of the current block. 
     In an embodiment, the obtainer  31  may obtain the information about the MVR for each inter predicted coding unit.  FIG. 10  is a diagram illustrating syntax for obtaining information about an MVR from a bitstream. 
     Referring to  FIG. 10 , when a slice including a current coding unit in a phrase ‘a’ is not an I slice, cu_skip_flag is extracted in a phrase ‘b’. cu_skip_flag indicates whether a skip mode is applied to the current coding unit. When it is checked that the skip mode is applied in a phrase ‘c’, the current coding unit is processed in the skip mode. When it is checked that the skip mode is not applied in a phrase ‘d’, pred_mode_flag is extracted in a phrase ‘e’. pred_mode_flag indicates whether the current coding unit is intra predicted or inter predicted. When the current coding unit is not intra predicted, that is, is inter predicted in a phrase ‘f’, pred_mvr_idx is extracted in a phrase ‘g’. pred_mvr_idx is an index indicating an MVR of the current coding unit, and an MVR corresponding to each index is as shown in Table 1. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
            
               
                   
                 MVR Index 
                 0 
                 1 
                 2 
                 3 
                 4 
               
               
                   
                 Resolution 
                 1/4 
                 1/2 
                 1 
                 2 
                 4 
               
               
                   
                 (R) in pel 
               
               
                   
                   
               
            
           
         
       
     
     In an embodiment, when the information indicating the candidate block to be used as the prediction motion vector of the current block is obtained by the obtainer  31 , the prediction decoder  33  may determine one candidate MVR from among at least one candidate MVR as the MVR of the current block. 
     The prediction decoder  33  may pre-store information about a 1:1 mapping relationship (or a correspondence relationship) between at least one candidate MVR selectable for the current block and at least one candidate block. Accordingly, when the information about the MVR of the current block is obtained by the obtainer  31 , a candidate block of the current block mapped to the obtained information may be selected, or when the information indicating the candidate block is obtained by the obtainer  31 , an MVR of the current block mapped to the obtained information may be selected. 
     In an embodiment, an MVR index shown in Table 1 may be used as an index of the at least one candidate block. A candidate MVR and a candidate block determined according to an index are as shown in Table 2. 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
             
            
               
                 Index 
                 0 
                 1 
                 2 
                 3 
                 4 
               
               
                 Resolution 
                 1/4 
                 1/2 
                 1 
                 2 
                 4 
               
               
                 in pel 
               
               
                 N th  MVP 
                 1 st  MVP 
                 2 nd  MVP 
                 3 rd  MVP 
                 4 th  MVP 
                 5 th  MVP 
               
               
                   
               
            
           
         
       
     
     In Table 2, a 1 st  MVP, a 2 nd  MVP, a 3 rd  MVP, a 4 th  MVP, and a 5 th  MVP indicate different candidate blocks. 
     In an embodiment, the at least one candidate MVR may include at least one from among an MVR of ⅛ pixel unit, an MVR of ¼ pixel unit, an MVR of ½ pixel unit, an MVR of 1 pixel unit, an MVR of 2 pixel unit, an MVR of 4 pixel unit, and an MVR of 8 pixel unit. However, available at least one candidate MVR is not limited to the above example, and MVRs having various values may be included in the candidate MVR. 
     In an embodiment, the at least one candidate block may be selected from among blocks including spatial blocks and temporal blocks associated with the current block. The spatial blocks may include at least one block spatially adjacent to the current block. The temporal blocks may include a block located at the same point as the current block in a reference image having a POC different from a POC of the current block and at least one block spatially adjacent block to the block at the same position. 
     In an embodiment, when the at least one candidate MVR includes an MVR of ¼ pixel unit, an MVR of ½ pixel unit, an MVR of 1 pixel unit, and an MVR of 2 pixel unit and the at least one candidate block includes a left block, an upper block, a left upper block, and an upper left block, a mapping relationship or a correspondence relationship between (the MVR of ¼ pixel unit and the left block), (the MVR of ½ pixel unit and the upper block), (the MVR of 1 pixel unit and the left upper block), and (the MVR of 2 pixel unit and the upper left block) may be set in the motion vector decoding apparatus  30 . Accordingly, when it is checked that the MVR of ¼ pixel unit is the MVR of the current block, the prediction decoder  33  may accordingly use a motion vector of the left block as the prediction motion vector of the current block. Also, when the upper block is checked as the prediction motion vector of the current block, the prediction decoder  33  may accordingly determine the MVR of ½ pixel unit as the MVR of the current block. 
     In an embodiment, the prediction decoder  33  may determine the number and a type of selectable at least one candidate MVR in a block unit, a slice unit, or a picture unit, based on information about at least one from among the current block, a previously decoded block, a current slice, a previously decoded slice, a current picture, and a previously decoded picture. 
     For example, the prediction decoder  33  may differently determine at least one candidate MVR selectable for the current block and at least one candidate MVR selectable for a subsequent block. For example, the MVR of ¼ pixel unit and the MVR of ½ pixel unit may be determined as the at least one candidate MVR selectable for the current block, and the MVR of 1 pixel unit and the MVR of 2 pixel unit may be determined as the at least one candidate MVR selectable for the subsequent block. Alternatively, only one MVR may be included as a candidate MVR for any block. 
     For example, when the at least one candidate MVR is determined in the block unit, the prediction decoder  33  may compare a size of the current block with a pre-determined size, and may cause only one MVR to be included in the candidate MVR or may cause a plurality of MVRs to be included in the candidate MVR. Alternatively, when the at least one candidate MVR is determined in the block unit, the prediction decoder  33  may determine the number and a type of the candidate MVR of the current block, based on an MVR of the previously decoded block. 
     Also, for example, when the selectable at least one candidate MVR is determined in the slice or picture unit, the prediction decoder  33  may determine the number and a type of candidate MVRs available for the current slice or the current picture according to a type of a slice or a picture. Also, for example, when the selected at least one candidate MVR is determined in the slice or picture unit, the prediction decoder  33  may determine the number and a type of candidate MVRs selectable for the current slice or the current picture according to whether the slice or the picture is referred to by another slice or picture. 
     In an embodiment, the prediction decoder  33  may determine a position of the at least one candidate block to be mapped to the at least one candidate MVR in the block unit, the slice unit, or the picture unit, based on the information about at least one from among the current block, the previously decoded block, the current slice, the previously decoded slice, the current picture, and the previously decoded picture. 
     For example, the prediction decoder  33  may determine a position of a candidate block mapped in a 1:1 manner to a candidate MVR selectable for the current block, based on the information about at least one from among the current block, the previously decoded block, the current slice, the previously decoded slice, the current picture, and the previously decoded picture. For example, the prediction decoder  33  may determine a position of each candidate block to be mapped to the candidate MVR selectable for the current block according to information such as a prediction mode (an intra or inter mode), a motion vector, an MVR, a reference image, or existence of bidirectional prediction of the previously decoded block. 
     For example, the prediction decoder  33  may differently determine at least one candidate block selectable for the current block and at least one candidate block selectable for a subsequent block. For example, when a position of the candidate block is determined in the block unit, an upper block and a left block may be respectively mapped to an MVR of 1 pixel unit and an MVR of 2 pixel unit corresponding to a candidate MVR of the current block, and an upper left block and a left lower block may be respectively mapped to an MVR of 1 pixel unit and an MVR of 2 pixel unit corresponding to a candidate MVR of the subsequent block. 
     In an embodiment, an index may be allocated in a unary manner to the each candidate MVR selectable for the current block, and the prediction decoder  33  may select the MVR of the current block according to an index indicating the MVR of the current block obtained by the obtainer  31 . For example, when the available candidate MVR includes an MVR of ¼ pixel unit, an MVR of ½ pixel unit, an MVR of 1 pixel unit, an MVR of 2 pixel unit, an MVR of 4 pixel unit, and an MVR of 8 pixel unit, indices 0, 10, 110, 1110, 11110, and 11111 may be respectively allocated to the MVR of ¼ pixel unit, the MVR of ½ pixel unit, the MVR of 1 pixel unit, the MVR of 2 pixel unit, the MVR of 4 pixel unit, and the MVR of 8 pixel unit. 
     In an embodiment, an index may be allocated in a unary manner to each candidate block mapped to the at least one candidate MVR, and the prediction decoder  33  may select the candidate block used as the prediction motion vector of the current block according to a candidate block index obtained by the obtainer  31 . For example, when the at least one candidate block includes a left block, an upper block, a left upper block, a left lower block, an upper left block, and an upper right block, indices 0, 10, 110, 1110, 11110, and 11111 may be respectively allocated to the left block, the upper block, the left upper block, the left lower block, the upper left block, and the upper right block. 
     In an embodiment, when there is one candidate MVR available for the current block, the obtainer  31  may skip or omit obtaining of the information indicating the candidate block used for the prediction motion vector of the current block and the MVR of the current block. When obtaining of information is skipped, it may mean that the information is not obtained from a bitstream. 
     In an embodiment, when there are two or more candidate MVRs available for the current block, the obtainer  31  may obtain a flag or an index indicating at least one from among the information indicating the MVR of the current block and the information indicating the candidate block used to determine the prediction motion vector of the current block. 
     The prediction decoder  33  according to an embodiment may use directly a motion vector of the candidate block as the prediction motion vector of the current block, or may change the motion vector of the candidate block and may use the changed motion vector as the prediction motion vector of the current block. 
     In an embodiment, when a motion vector does not exist in a candidate block mapped to the MVR of the current block, the prediction decoder  33  may map a block having a motion vector other than candidate blocks respectively mapped to candidate MVRs to the MVR of the current block. The prediction decoder  33  may use a motion vector of the newly mapped block as the prediction motion vector of the current block. When a certain block is intra predicted, the block may be determined to be a block not including a motion vector. 
     For example, when it is assumed that the at least one candidate MVR available for the current block includes the MVR of ¼ pixel unit mapped to the left block, the MVR of ½ pixel unit mapped to the upper block, and the MVR of 1 pixel unit mapped to the upper right block and a motion vector does not exist in the upper right block, the prediction decoder  33  may map the MVR of 1 pixel unit to a block, for example, the upper left block, other than the at least one candidate block. 
     In an embodiment, when a motion vector does not exist in the candidate block mapped to the MVR of the current block, positions and priorities of other blocks to be newly used may be pre-determined. 
     Also, in an embodiment, when a motion vector does not exist in the candidate block mapped to the MVR of the current block, the prediction decoder  33  may use an arbitrary motion vector (e.g., a zero vector) as the prediction motion vector of the current block. 
     Also, in an embodiment, when a motion vector does not exist in the candidate block mapped to an MVR of the current block, a motion vector of a candidate block corresponding to the current block may be derived by using a motion vector of another candidate block. 
     Also, in an embodiment, when candidate blocks having the same motion vector exist from among the at least one candidate block mapped to the at least one candidate MVR available for the current block, the prediction decoder  33  may replace some from among the candidate blocks having the same motion vector with blocks other than the at least one candidate block mapped to each candidate MVR. For example, when a motion vector of the left block mapped to a ¼ pixel unit MVR and a motion vector of the upper block mapped to a ½ pixel unit MVR are the same, the prediction decoder  33  may replace one block (e.g., the upper block) from among the left block and the upper block with another block (e.g., the upper left block) and may map the replaced block to a candidate MVR (e.g., a ½ pixel resolution). 
     When there are a plurality of candidate blocks having the same motion vector, a priority indicating which block from among the plurality of candidate blocks is to be replaced by another block, and types and priorities of blocks to be newly mapped may be pre-determined. 
     In an embodiment, when candidate blocks having the same motion vector exist from among the at least one candidate block mapped to the at least one candidate MVR available for the current block, the prediction decoder  33  may allocate an arbitrary motion vector (e.g., a zero vector) to some from among the candidate blocks having the same motion vector. In this case, priorities of candidate blocks to which the arbitrary motion vector is to be allocated may be pre-determined. 
     In an embodiment, when candidate blocks having the same motion vector exist from among the at least one candidate block mapped to the at least one candidate MVR available for the current block, the prediction decoder  33  may derive a motion vector of any of some from among the candidate blocks having the same motion vector by using a motion vector of another candidate block. 
     In an embodiment, whether motion vectors of two or more candidate blocks are the same may be determined by adjusting motion vectors of the candidate blocks and then comparing the adjusted motion vectors as described below. 
     Also, in an embodiment, the prediction decoder  33  may receive related information from a bitstream, without directly determining whether candidate blocks having the same motion vector exist from among the at least one candidate block. In an embodiment, the obtainer  31  may obtain information indicating that a candidate block is replaced from the bitstream, and the prediction decoder  33  may use a motion vector of the replaced block as the prediction motion vector. When information indicating that a candidate block is replaced is obtained, a type and a priority of a block to be used as the prediction motion vector of the current block according to the MVR of the current block may be pre-determined. 
     In an embodiment, the prediction decoder  33  may upscale a residual motion vector obtained by the obtainer  31 , based on a difference between the MVR of the current block and a minimum MVR from among the at least one candidate MVR. For example, when the MVR of the current block is higher than the minimum MVR, the prediction decoder  33  may upscale the residual motion vector. 
     Also, in an embodiment, the prediction decoder  33  may selectively adjust the motion vector of the candidate block mapped to the MVR of the current block. 
     The prediction decoder  33  may obtain a motion vector of the current block by using the selected adjusted motion vector of the candidate block and the selectively upscaled residual motion vector. 
     Upscaling of the residual motion vector and adjusting of the motion vector of the candidate block will be described in detail. 
     The prediction decoder  33  may search for a prediction block in a reference image by using the motion vector of the current block, and may reconstruct the current block by adding inverse quantized and inverse transformed residual data to the prediction block. 
     In an embodiment, the prediction decoder  33  may search for the prediction block in a reference image that is not interpolated when the MVR of the current block is equal to or greater than a 1 pixel unit, and may search for the prediction block in a reference image that is interpolated when the MVR of the current block is less than a 1 pixel unit. 
       FIG. 4  is a flowchart for describing a motion vector decoding method, according to an embodiment. 
     In operation S 41 , the motion vector decoding apparatus  30  determines an MVR of a current block, and a candidate block used to determine a prediction motion vector of the current block. The MVR of the current block determined by the motion vector decoding apparatus  30  may correspond to one of at least one MVR candidate selectable for the current block, and the candidate block for the prediction motion vector of the current block may correspond to one from among at least one candidate block mapped to each of the at least one MVR candidate. 
     The motion vector decoding apparatus  30  may obtain at least one from among information indicating the MVR of the current block and information indicating the candidate block, and a residual motion vector from a bitstream. 
     When the information indicating the MVR of the current block is obtained from the bitstream, the motion vector decoding apparatus  30  may determine the candidate block to be used as the prediction motion vector based on the obtained information, and when the information indicating the candidate block is obtained from the bitstream, the motion vector decoding apparatus  30  may determine the MVR of the current block based on the obtained information. 
     In operation S 42 , the motion vector decoding apparatus  30  obtains a motion vector of the current block by using a motion vector of the candidate block and the residual motion vector. 
     In an embodiment, the motion vector decoding apparatus  30  may selectively adjust the motion vector of the candidate block according to a difference between the MVR of the current block and a minimum MVR, and may selectively upscale the residual motion vector according to a difference between the minimum MVR and the MVR of the current block. 
       FIG. 5  is a diagram for describing at least one candidate block mapped in a 1:1 manner to at least one candidate MVR. 
     At least one candidate block selected from among spatial blocks and temporal blocks associated with a current block  50  may be mapped to each candidate MVR. 
     For example, the spatial blocks may include a left upper block a, a right upper block b, an upper left block c, an upper right block d, a left top outer block e, a right top outer block f, a left bottom outer block g, a right bottom outer block h, a left lower block I, a right lower block j, a left block k, a right block I, and an upper block m that are adjacent to the current block  50 . The temporal blocks may include a block n that is located at the same position as the current block  50  in a reference image having a POC different from that of the current block  50  and a block o adjacent to the block n at the same position. 
     The at least one candidate block selected from among the spatial blocks and the temporal blocks may be mapped to the each candidate MVR, and as shown in FIG.  6 , an MVR of ⅛ pixel unit may be mapped to the left block k, an MVR of ¼ pixel unit may be mapped to the upper block m, an MVR of ½ pixel unit may be mapped to the left upper block a, an MVR of 1 pixel unit may be mapped to the upper left block c, and an MVR of 2 pixel unit may be mapped to the left lower block i. The illustrated mapping relationship may be an example, and various mapping relationships may be set. 
     According to an embodiment of  FIG. 6 , when an MVR of the current block is determined to be a ⅛ pixel unit, the motion vector encoding apparatus  10  uses a motion vector of the left block as a prediction motion vector of the current block. Also, when a motion vector of the upper block is used as the prediction motion vector of the current block, the motion vector encoding apparatus  10  may determine the MVR of the current block as a ¼ pixel unit. 
     Also, when it is checked that the MVR of the current block is a ⅛ pixel unit, the motion vector decoding apparatus  30  uses a motion vector of the left block as the prediction motion vector of the current block. Also, when it is checked that a motion vector of the upper block is used as the prediction motion vector of the current block, the motion vector decoding apparatus  30  may determine the MVR of the current block as a ¼ pixel unit. 
     In an embodiment, positions of candidate blocks mapped to at least one candidate MVR may be determined in an order of selection as the prediction motion vector when motion vector of blocks in a predetermined number of pictures are determined by using an MVR of arbitrary pixel unit. For example, when the number of available candidate MVRs is 5, each of 5 blocks frequently selected as the prediction motion vector from among blocks including spatial blocks and temporal blocks may be mapped to each candidate MVR. 
     In an embodiment, when candidate MVRs and candidate blocks are mapped in a 1:1 manner, the candidate MVRs may be arranged in an ascending order according to a size of a pixel unit, the candidate blocks may be arranged in a descending order according to the number of times selected as the prediction motion vector, and then candidate MVRs and candidate blocks having orders corresponding to each other may be mapped. 
     As described above, a type and the number of candidate MVRs selectable for the current block may vary according to information about at least one from among the current block, a previously decoded block, a current slice, a previously decoded slice, a current picture, and a previously decoded picture. 
     Also, positions of candidate blocks respectively mapped to the candidate MVRs selectable for the current block may vary according to the information about at least one from among the current block, the previously decoded block, the current slice, the previously decoded slice, the current picture, and the previously decoded picture. 
     The type and the number of the candidate MVRs selectable for the current block and the positions of the candidate blocks respectively mapped to the candidate MVRs selectable for the current block may be determined by using the same criterion by the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30 , and thus although the motion vector encoding apparatus  10  encodes an index indicating the MVR of the current block or an index indicating a candidate block for the current block and transmits the encoded indices to the motion vector decoding apparatus  30 , the motion vector decoding apparatus  30  may determine the MVR or the candidate block corresponding to each index. 
       FIG. 7  is a diagram for describing interpolation for determining a motion vector according to various MVRs. 
     The motion vector encoding apparatus  10  may determine a motion vector of a current block according to at least one candidate MVR to inter predict the current block. Available candidate MVRs may include an MVR of 2k pixel unit (k is an integer). When k is greater than 0, the motion vector may indicate only integer pixels in an interpolated reference image, and when k is less than 0, the motion vector may indicate subpixels and integer pixels. 
     For example, when a minimum MVR has a ¼ pixel unit, the motion vector encoding apparatus  10  may interpolate a reference image so that subpixels of ¼ pixel unit are generated, and may determine the motion vector so that the motion vector indicates a pixel corresponding to each candidate MVR, for example, a ¼ pixel unit MVR, a ½ pixel unit MVR, a 1 pixel unit MVR, or a 2 pixel unit MVR. 
     For example, the motion vector encoding apparatus  10  may generate subpixels (a through l) of ½ pixel unit by performing interpolation on the reference image by using an n-tap finite impulse response (FIR) filter. Upon examining vertical ½ subpixels, the motion vector encoding apparatus  10  may generate the subpixel ‘a’ by performing interpolation by using A1, A2, A3, A4, A5, and A6 of integer pixel unit, and may generate the subpixel ‘b’ by performing interpolation by using B1, B2, B3, B4, B5, and B6 of integer pixel unit. The subpixels ‘c’, ‘d’, ‘e’, and ‘f’ may be generated by using the same method. 
     Pixel values of vertical subpixels may be calculated as follows. For example, pixel values of the subpixels ‘a’ and ‘b’ may be calculated as shown in a=(A1−5×A2+20×A3+20×A4−5×A5+A6)/32 and b=(B1−5×B2+20×B3+20×B4−5×B5+B6)/32. Pixel values of the subpixels ‘c’, ‘d’, ‘e’, and ‘f’ may be calculated by using the same method. 
     The motion vector encoding apparatus  10  may generate horizontal subpixels by performing interpolation by using a 6-tap FIR filter, like vertical subpixels. The subpixel ‘g’ may be generated by using A1, B1, C1, D1, E1, and F1, and the subpixel ‘h’ may be generated by using A2, B2, C2, D2, E2, and F2. 
     Pixel values of the horizontal subpixels are calculated by using the same method as that used to calculate the pixel values of the vertical subpixels. For example, a pixel value of the subpixel ‘g’ may be calculated as shown in g=(A1−5×B1+20×C1+20×D1−5×E1+F1)/32. 
     The subpixel ‘m’ of ½ pixel unit in a diagonal direction may be interpolated by using another ½ pixel unit subpixel. In other words, a pixel value of the subpixel ‘m’ may be calculated as shown in m=(a−5×b+20×c+20×d−5×e+f)/32. 
     When the subpixels of ½ pixel unit are generated, the motion vector encoding apparatus  10  may generate subpixels of ¼ pixel unit by using the subpixels of ½ pixel unit and integer pixels. The motion vector encoding apparatus  10  may generate subpixels of ¼ pixel unit by performing interpolation by using two adjacent pixels. Alternatively, the subpixels of ¼ pixel unit may be generated by directly applying an interpolation filter to pixel values of the integer pixels without using pixel values of the subpixels of ½ pixel unit. 
     Although the interpolation filter is, for example, a 6-tap filter in the above, the motion vector encoding apparatus  10  may interpolate a picture by using a filter having another tap number. Examples of the interpolation filter may include a 4-tap filter, a 7-tap filter, an 8-tap filter, and a 12-tap filter. 
       FIG. 8  illustrates positions of pixels that may be indicated by motion vectors according to a ¼ pixel unit MVR, a ½ pixel unit MVR, a 1 pixel unit MVR, and a 2 pixel unit MVR when an available minimum MVR is the ¼ pixel unit MVR. 
     (a), (b), (c), and (d) of  FIG. 8  respectively illustrate coordinates (marked by black squares) of pixels that may be indicated by motion vectors of the ¼ pixel unit MVR, the ½ pixel unit MVR, the 1 pixel unit MVR, and the 2 pixel unit MVR based on coordinates (0, 0). 
     When a minimum MVR is the ¼ pixel unit MVR, the coordinates of the pixel that may be indicated by the motion vector of the ¼ pixel unit MVR become (a/4, b/4) (a and b are integers), the coordinates of the pixel that may be indicated by the motion vector of the ½ pixel unit MVR become (2c/4, 2d/4) (c and d are integers), the coordinates of the pixel that may be indicated by the motion vector of the 1 pixel unit MVR become (4e/4, 4f/4) (e and f are integers), and the coordinates of the pixel that may be indicated by the motion vector of the 2 pixel unit MVR become (8g/4, 8h/4) (g and h are integers). That is, when a minimum MVR has a 2 m  (m is an integer) pixel unit, coordinates of a pixel that may be indicated by a 2 n  (n is an integer) pixel unit MVR become (2 n-m *i/2 −m , 2 n-m *j/2 −m ) (i and j are integers) Although a motion vector is determined according to a specific MVR, the motion vector is represented by coordinates in an image interpolated according to a ¼ pixel unit. 
     In an embodiment, because the motion vector encoding apparatus  10  determines a motion vector in an image interpolated according to a minimum MVR, in order to represent the motion vector (and a prediction motion vector) by using an integer, the motion vector of an integer unit may be represented by multiplying the motion vector (and the prediction motion vector) by a reciprocal of a pixel unit value of the minimum MVR, for example, 2 −m  when the minimum MVR has a 2 m  (m is an integer) pixel unit. The motion vector of the integer unit multiplied by 2 −m  may be used in the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30 . 
     When the motion vector of the ½ pixel unit MVR starting from the coordinates (0, 0) indicates coordinates ( 2/4, 6/4) and the minimum MVR has a ¼ pixel unit, the motion vector encoding apparatus  10  may determine (2, 6), which is obtained by multiplying the motion vector by an integer 4, as a motion vector. 
     When a size of an MVR is less than a 1 pixel unit, in order to perform motion prediction in a subpixel unit, the motion vector encoding apparatus  10  according to an embodiment may search for a block similar to a current block in a reference image based on the subpixel unit according to a motion vector determined in an integer pixel unit. 
     For example, when an MVR of a current block is the ¼ pixel unit MVR, the motion vector encoding apparatus  10  may determine a motion vector in an integer pixel unit, may interpolate a reference image to generate subpixels of ½ pixel unit, and then may search for a most similar prediction bock in a (−1˜1, −1˜1) range based on the motion vector determined in the integer pixel unit. Next, the motion vector encoding apparatus  10  may interpolate the reference image to generate subpixels of ¼ pixel unit again, and then may search for a most similar prediction block in the (−1˜1, −1˜1) range based on a motion vector determined in a ½ pixel unit, thereby determining a motion vector of the final ¼ pixel unit MVR. 
     For example, when a motion vector of an integer pixel unit is (−4, −3) based on the coordinates (0, 0), a motion vector in the ½ pixel unit MVR becomes (−8, −6) (=(−4*2, −3*2)); and when the motion vector moves by (0, −1), the motion vector of the ½ pixel unit MVR is finally determined to be (−8, −7) (=(−8, −6−1)). When a motion vector in the ¼ pixel unit MVR is changed to (−16, −14) (=(−8*2, −7*2)); and when the motion vector moves by (−1, 0) again, a final motion vector of the ¼ pixel unit MVR may be determined to be (−17, −14) (=(−16−1, −14)). 
     When the MVR of the current block is higher than the 1 pixel unit MVR, in order to perform motion prediction in a large pixel unit, the motion vector encoding apparatus  10  according to an embodiment may search for a block similar to the current block in a reference picture based on a pixel unit larger than a 1 pixel unit according to a motion vector determined in an integer pixel unit. Pixels located in pixel units (e.g., a 2 pixel unit, a 3 pixel unit, or a 4 pixel unit) larger than the 1 pixel unit may be referred to as super pixels. 
     A prediction motion vector adjusting method selectively performed by the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  according to an embodiment will be described with reference to  FIGS. 9A and 9B . 
     When an MVR of the current block is higher than a minimum MVR from among selectable candidate MVRs, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may adjust a motion vector of a candidate block used as a prediction motion vector of the current block. 
     In order to adjust the prediction motion vector represented by coordinates in an image interpolated according to the minimum MVR to the MVR of the current block, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may adjust the prediction motion vector to indicate neighboring pixels instead of a pixel indicated by the prediction motion vector. 
     For example, in order to adjust a prediction motion vector A indicating a pixel  71  of coordinates (19, 27) based on coordinates (0, 0) in  FIG. 9A  to a 1 pixel unit MVR that is the MVR of the current block, the coordinates (19, 27) of the pixel  71  indicated by the prediction motion vector A may be divided by an integer 4 (that is, may be downscaled), and coordinates (19/4, 27/4) obtained as a division result may not indicate an integer pixel unit. 
     The motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may adjust the downscaled prediction motion vector to indicate an integer pixel unit. For example, coordinates of neighboring integer pixels around the coordinates (19/4, 27/4) are (16/4, 28/4), (16/4, 24/4), (20/4, 28/4), and (20/4, 24/4). In this case, after the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may adjust the downscaled prediction motion vector A to indicate the coordinates (20/4, 28/4) located at the right-top instead of the coordinates (19/4, 27/4) and may multiply an integer 4 (that is, upscale) so that a finally adjusted prediction motion vector D indicates a pixel  74  corresponding to coordinates (20, 28). 
     Referring to  FIG. 9A , the prediction motion vector A before adjustment may indicate the pixel  71 , and the finally adjusted prediction motion vector D may indicate the pixel  74  of an integer unit located at the right-top of the pixel  71 . 
     When a prediction motion vector is adjusted according to an MVR of a current block, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  according to an embodiment may cause the adjusted prediction motion vector to indicate a pixel located at the right-top of a pixel indicated by the prediction motion vector before adjustment. The motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  according to another embodiment may cause the adjusted prediction motion vector to indicate a pixel located at the left-top, a pixel located at the left-bottom, or a pixel located at the right-bottom of the pixel indicated by the prediction motion vector before adjustment. 
     In an embodiment, when any one of an x-coordinate value and a y-coordinate value indicated by the downscaled prediction motion vector indicates an integer pixel, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may increase or decrease only the coordinate value not indicating the integer pixel to indicate an integer pixel. That is, when the x-coordinate value indicated by the downscaled prediction motion vector indicates an integer pixel, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may cause the adjusted prediction motion vector to indicate an integer pixel located at the top or the bottom of the pixel indicated by the prediction motion vector before adjustment. Alternatively, when the y-coordinate value indicated by the downscaled prediction motion vector indicates an integer pixel, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may cause the adjusted prediction motion vector to indicate an integer pixel located at the left or the right of the pixel indicated by the prediction motion vector before adjustment. 
     When the prediction motion vector is adjusted, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may different select a point indicated by the adjusted prediction motion vector according to the MVR of the current block. 
     For example, referring to  FIG. 9B , when the MVR of the current block is a ½ pixel unit MVR, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may cause the adjusted prediction motion vector to indicate a pixel  83  at the left-top of a pixel  81  indicated by the prediction motion vector before adjustment; when the MVR of the current block is a 1 pixel unit MVR, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may cause the adjusted prediction motion vector to indicate a pixel  82  at the right-top of the pixel  81  indicated by the prediction motion vector before adjustment; and when the MVR of the current block is a 2 pixel unit MVR, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may cause the adjusted prediction motion vector to indicate a pixel  84  at the right-bottom of the pixel  81  indicated by the prediction motion vector before adjustment. 
     The motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may determine which pixel is to be indicated by the adjusted prediction motion vector, based on at least one from among the MVR of the current block, the prediction motion vector, information of a neighboring block, encoding information, and an arbitrary pattern. 
     When the motion vector of the candidate block is adjusted in consideration of the MVR of the current block and the minimum MVR, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may adjust the motion vector of the candidate block according to Equation 1. 
         pMV ′=(( pMV&gt;&gt;k )+offset)&lt;&lt; k   [Equation 1]
 
     In Equation 1, when pMV′ denotes the adjusted prediction motion vector, and k that is a value determined according to a difference between the MVR of the current block and the minimum MVR may be m−n when the MVR of the current block is a 2 m  pixel unit (m is an integer), the minimum MVR is a 2 n  pixel unit (n is an integer), and m&gt;n. 
     In an embodiment, k may be an index of an MVR, and when candidate MVRs include a ¼ pixel unit MVR, a ½ pixel unit MVR, a 1 pixel unit MVR, a 2 pixel unit MVR, and a 4 pixel unit MVR, MVRs corresponding to indices are as shown in Table 1. When an MVR index is received from a bitstream, the motion vector decoding apparatus  30  may adjust the motion vector of the candidate block according to Equation 1 by using the MVR index as k. 
     Also, in Equation 1, &gt;&gt; or &lt;&lt; that is a bit shift operation refers to an operation of reducing or increasing a size of the prediction motion vector. Also, offset denotes a value added or subtracted to indicate an integer pixel when pMV downscaled according to a k value does not indicate an integer pixel. offset may be differently determined according to each of an x-coordinate value and a y-coordinate value of a basic MV. 
     In an embodiment, when the downscaled pMV is changed to indicate an integer pixel, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may change the downscaled pMV according to the same criterion. 
     In an embodiment, when an x-coordinate value and a y-coordinate value of the downscaled pMV do not indicate an integer pixel, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may always increase or decrease the x-coordinate value and the y-coordinate value of the downscaled pMV to indicate an integer pixel. Alternatively, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may round the x-coordinate value and the y-coordinate value of the downscaled pMV to indicate an integer pixel. 
     In an embodiment, when the motion vector of the candidate block is adjusted, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may omit downscaling and upscaling of the motion vector, and may adjust the motion vector in a coordinate plane in a reference image interpolated according to the minimum MVR to indicate a pixel unit corresponding to the MVR of the current block. 
     Also, in an embodiment, when the motion vector of the candidate block is adjusted in consideration of the MVR of the current block and the minimum MVR, the motion vector encoding apparatus  10  and the motion vector decoding apparatus  30  may adjust the motion vector according to Equation 2, instead of Equation 1. 
         pMV ′=(( pMV +offset)&gt;&gt; k )&lt;&lt; k   [Equation 2]
 
     Although Equation 2 is similar to Equation 1, unlike in Equation where offset is applied to the downscaled pMV, offset is applied to original pmV and then is downscaled according to k. 
     The motion vector encoding apparatus  10  finds a motion vector of the current block by using the MVR of the current block, and obtains a difference between the motion vector of the current block and the prediction motion vector that is selectively adjusted as a residual motion vector. 
     The motion vector encoding apparatus  10  may determine and encode the residual motion vector as shown in Equation 3. In Equation 3, MV denotes the motion vector of the current block, pMV′ denotes the adjusted prediction motion vector, and MVD denotes the residual motion vector. 
         MVD=MV−pMV′   [Equation 3]
 
     When the MVR of the current block is higher than the minimum MVR, the motion vector encoding apparatus  10  may downscale the residual motion vector as shown in Equation 4, and may generate a bitstream including information indicating the downscaled residual motion vector. 
         MVD ′=( MVD&gt;&gt;k )  [Equation 4]
 
     In Equation 4, MVD′ denotes the downscaled residual motion vector, and k that is a value determined according to a difference between the minimum MVR and the MVR of the current block is the same as k of Equation 1. 
     In an embodiment, the motion vector encoding apparatus  10  may downscale the motion vector of the current block and the prediction motion vector (or the adjusted prediction motion vector) according to the k value, and then may encode a difference between the two values as the residual motion vector. 
     In an embodiment, the motion vector encoding apparatus  10  may calculate the downscaled residual motion vector according to Equation 5, instead of Equation 3 and Equation 4. 
         MVD ′=( MV−pMV ′)/( R*S )  [Equation 5]
 
     In Equation 5, MVD′ denotes the downscaled residual motion vector, MV denotes the motion vector of the current block, and pMV′ denotes the adjusted prediction motion vector. Also, R denotes a pixel unit value of the MVR of the current block, (e.g., ¼ when the MVR of the current block is a ¼ pixel unit MVR). Also, S denotes a reciprocal of a pixel unit value of the minimum MVR (e.g., 4 when the minimum MVR is a ¼ pixel unit). 
     The motion vector decoding apparatus  30  may reconstruct the motion vector of the current block by using at least one from among information indicating the candidate block and information indicating the MVR of the current block obtained from the bitstream, and the residual motion vector. 
     When the MVR of the current block is higher than the minimum MVR, the motion vector decoding apparatus  30  may adjust the prediction motion vector as shown in Equation 1 or Equation 2. 
     When the MVR of the current block is higher than the minimum MVR, the motion vector decoding apparatus  30  may upscale residual motion data as shown in Equation 6. 
         MVD ″=( MVD′&lt;&lt;k )  [Equation 6]
 
     In Equation 6, MVD′ denotes the residual motion vector downscaled by an encoding apparatus, and MVD″ denotes an upscaled residual motion vector. k that is a value determined according to a difference between the minimum MVR and the MVR of the current block is the same as k of Equation 1. 
     The motion vector decoding apparatus  30  may decode the motion vector of the current block by adding the prediction motion vector that is selectively adjusted according to a size difference between the minimum MVR and the MVR of the current block to the residual motion vector that is selectively upscaled. 
     In an embodiment, the motion vector decoding apparatus  30  may determine the upscaled residual motion vector according to Equation 7, instead of Equation 6. 
         MVD″=MVD ′*( R*S )  [Equation 7]
 
     In Equation 7, MVD′ denotes the downscaled residual motion vector, and R denotes a pixel unit value of the MVR of the current block (e.g., ¼ when the MVR of the current block is a ¼ pixel unit MVR). Also, S denotes a reciprocal of a pixel unit value of the minimum MVR (e.g., 4 when the minimum MVR is a ¼ pixel unit). 
     In an embodiment, when the MVR of the current block is less than a 1 pixel unit MVR, the motion vector decoding apparatus  30  may interpolate the reference image according to the minimum MVR and then may search for a prediction block according to the motion vector of the current block. Also, when the MVR of the current block is equal to or higher than a 1 pixel unit MVR, the motion vector decoding apparatus  30  may search for the prediction block according to the motion vector of the current block without interpolating the reference image. 
     A video encoding method and apparatus and a video decoding method and apparatus based on coding units and transform units having a tree structure according to an embodiment will be described with reference to  FIGS. 11 through 34 . 
       FIG. 11  is a block diagram of the video decoding apparatus  100  for decoding an image based on at least one from among block shape information and split shape information, according to an embodiment. 
     Referring to  FIG. 11 , according to an embodiment, the video decoding apparatus  100  may include the bitstream obtainer  110  for obtaining predetermined information such as split shape information or block shape information from a bitstream and the decoder  120  for decoding an image by using the obtained information. When the bitstream obtainer  110  of the video decoding apparatus  100  obtains at least one from among the block shape information and the split shape information according to an embodiment, the decoder  120  of the video decoding apparatus  100  may determine at least one coding unit for splitting an image based on the at least one from among the block shape information and the split shape information. 
     According to an embodiment, the decoder  120  of the video decoding apparatus  100  may determine a shape of the coding unit based on the block shape information. For example, the block shape information may include information indicating whether the coding unit has a square shape or a non-square shape. The decoder  120  may determine the shape of the coding unit by using the block shape information. 
     According to an embodiment, the decoder  120  may determine a shape into which a coding unit is to be split based on the split shape information. For example, the split shape information may indicate information about a shape of at least one coding unit included in the coding unit. 
     According to an embodiment, the decoder  120  may determine whether the coding unit is split or not split according to the split shape information. The split shape information may include the information about the at least one coding unit included in the coding unit, and when the split shape information indicates that only one coding unit is included in the coding unit or is not split, the decoder  120  may determine that the coding unit including the split shape information is not split. When the split shape information indicates that the coding unit is split into a plurality of coding units, the decoder  120  may split the coding unit into the plurality of coding units included in the coding unit based on the split shape information. 
     According to an embodiment, the split shape information may indicate the number of coding units into which the coding unit is to be split or a direction in which the coding unit is to be split. For example, the split shape information may indicate that the coding unit is split in at least one direction from among a vertical direction and a horizontal direction or is not split. 
       FIG. 13  illustrates a process in which the video decoding apparatus  100  determines at least one coding unit by splitting a current coding unit according to an embodiment. 
     A block shape may include 4N×4N, 4N×2N, 2N×4N, 4N×N, or N×4N. N may be a positive integer. Block shape information is information indicating at least one from among a ratio or a size of a shape, a direction, a width, and a height of a coding unit. 
     The shape of the coding unit may include a square shape and a non-square shape. When the width and the height of the coding unit are the same (4N×4N), the video decoding apparatus  100  may determine the block shape information of the coding unit as a square shape. The video decoding apparatus  100  may determine the shape of the coding unit as a non-square shape. 
     When the width and the height of the coding unit are different from each other (4N×2N, 2N×4N, 4N×N, or N×4N), the video decoding apparatus  100  may determine the block shape information of the coding unit as a non-square shape. When the shape of the coding unit is a non-square shape, the video decoding apparatus  100  may determine the ratio of the width and the height in the block shape information of the coding unit as at least one from among 1:2, 2:1, 1:4, 4:1, 1:8, and 8:1. Also, the video decoding apparatus  100  may determine whether the coding unit is a horizontal direction or a vertical direction, based on a length of the width and a length of the height of the coding unit. Also, the video decoding apparatus  100  may determine the size of the coding unit, based on at least one from among the length of the width, the length of the height, and an area of the coding unit. 
     According to an embodiment, the video decoding apparatus  100  may determine a shape of the coding unit by using the block shape information, and may determine which shape the coding unit is split into by using information about a split shape mode. That is, a coding unit splitting method indicated by the information about the split shape mode may be determined according to which block shape is indicated by the block shape information used by the video decoding apparatus  100 . 
     The video decoding apparatus  100  may obtain the information about the split shape mode from a bitstream. However, the present disclosure is not limited thereto, and the video decoding apparatus  100  and the video encoding apparatus  200  may obtain the information about the split shape mode that is pre-promised based on the block shape information. The video decoding apparatus  100  may obtain the information about the split shape mode that is pre-promised for a largest coding unit or a smallest coding unit. For example, the video decoding apparatus  100  may determine a size of the largest coding unit to be 256×256. The video decoding apparatus  100  may determine the information about the pre-promised split shape mode by using quad split. The quad split is a split shape mode in which the width and the height of the coding unit are halved. The video decoding apparatus  100  may obtain the coding unit having a size of 128×128 from the largest coding unit having a size of 256×256 based on the information about the split shape mode. Also, the video decoding apparatus  100  may determine a size of the smallest coding unit to be 4×4. The video decoding apparatus  100  may obtain the information about the split shape mode indicating “not to perform splitting” for the smallest coding unit. 
     According to an embodiment, the video decoding apparatus  100  may use the block shape information indicating that the current coding unit has a square shape. For example, the video decoding apparatus  100  may determine whether not to split a square coding unit, whether to vertically split the square coding unit, whether to horizontally split the square coding unit, or whether to split the square coding unit into four coding units, based on the information about the split shape mode. Referring to  FIG. 13 , when the block shape information of a current coding unit  300  indicates a square shape, the decoder  120  may determine that a coding unit  310   a  having the same size as the current coding unit  300  is not split, based on the information about the split shape mode indicating not to perform splitting, or may determine coding units  310   b ,  310   c , or  310   d  split based on the information about the split shape mode indicating a predetermined splitting method. 
     Referring to  FIG. 13 , according to an embodiment, the video decoding apparatus  100  may determine two coding units  310   b  obtained by vertically splitting the current coding unit  300 , based on the information about the split shape mode indicating to vertically perform splitting. The video decoding apparatus  100  may determine two coding units  310   c  obtained by horizontally splitting the current coding unit  300 , based on the information about the split shape mode indicating to horizontally perform splitting. The video decoding apparatus  100  may determine four coding units  310   d  obtained by vertically and horizontally splitting the current coding unit  300 , based on the information about the split shape mode indicating to vertically and horizontally perform splitting. However, splitting methods of the square coding unit are not limited to the above-described methods, and the information about the split shape mode may indicate various methods. Predetermined splitting methods of splitting the square coding unit will be described in detail below in relation to various embodiments. 
       FIG. 14  illustrates a process, performed by the video decoding apparatus  100 , of determining at least one coding unit by splitting a non-square coding unit, according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may use block shape information indicating that a current coding unit has a non-square shape. The video decoding apparatus  100  may determine whether not to split the non-square current coding unit or whether to split the non-square current coding unit by using a predetermined splitting method based on information about a split shape mode. Referring to  FIG. 14 , when the block shape information of a current coding unit  400  or  450  indicates a non-square shape, the video decoding apparatus  100  may determine that a coding unit  410  or  460  having the same size as the current coding unit  400  or  450  is not split, based on the information about the split shape mode indicating not to perform splitting, or determine coding units  420   a  and  420   b ,  430   a  to  430   c ,  470   a  and  470   b , or  480   a  to  480   c  split based on the information about the split shape mode indicating a predetermined splitting method. Predetermined splitting methods of splitting a non-square coding unit will be described in detail below in relation to various embodiments. 
     According to an embodiment, the video decoding apparatus  100  may determine a splitting method of a coding unit by using the information about the split shape mode and, in this case, the split shape information may indicate the number of one or more coding units generated by splitting the coding unit. Referring to  FIG. 14 , when the information about the split shape mode indicates to split the current coding unit  400  or  450  into two coding units, the video decoding apparatus  100  may determine two coding units  420   a  and  420   b , or  470   a  and  470   b  included in the current coding unit  400  or  450 , by splitting the current coding unit  400  or  450  based on the information about the split shape mode. 
     According to an embodiment, when the video decoding apparatus  100  splits the non-square current coding unit  400  or  450  based on the information about the split shape mode, the location of a long side of the non-square current coding unit  400  or  450  may be considered. For example, the video decoding apparatus  100  may determine a plurality of coding units by splitting the long side of the current coding unit  400  or  450 , in consideration of the shape of the current coding unit  400  or  450 . 
     According to an embodiment, when the information about the split shape mode indicates to split a coding unit into an odd number of blocks, the video decoding apparatus  100  may determine an odd number of coding units included in the current coding unit  400  or  450 . For example, when the information about the split shape mode indicates to split the current coding unit  400  or  450  into three coding units, the video decoding apparatus  100  may split the current coding unit  400  or  450  into three coding units  430   a ,  430   b , and  430   c , or  480   a ,  480   b , and  480   c.    
     According to an embodiment, a ratio between a width and a height of the current coding unit  400  or  450  may be 4:1 or 1:4. When the ratio between the width and the height is 4:1, a length of the width is greater than a length of the height, and thus block shape information may be horizontal. When the ratio between the width and the height is 1:4, a length of the width is less than a length of the height, and thus the block shape information may be vertical. The video decoding apparatus  100  may determine to split the current coding unit into an odd number of blocks based on the information about the split shape mode. Also, the video decoding apparatus  100  may determine a split direction of the current coding unit  400  or  450  based on the block shape information of the current coding unit  400  or  450 . For example, when the current coding unit  400  is in a vertical direction, the video decoding apparatus  100  may horizontally split the current coding unit  400  and may determine the coding units  430   a ,  430   b , and  430   c . Also, when the current coding unit  450  is in a horizontal direction, the video decoding apparatus  100  may vertically split the current coding unit  450  and may determine the coding units  480   a ,  480   b , and  480   c.    
     According to an embodiment, the video decoding apparatus  100  may determine an odd number of coding units included in the current coding unit  400  or  450 , and sizes of all of the determined coding units may not be the same. For example, a predetermined coding unit  430   b  or  480   b  from among the determined odd number of coding units  430   a ,  430   b , and  430   c , or  480   a ,  480   b , and  480   c  may have a size different from the size of the other coding units  430   a  and  430   c , or  480   a  and  480   c . That is, coding units which may be determined by splitting the current coding unit  400  or  450  may have multiple sizes and, in some cases, all of the odd number of coding units  430   a ,  430   b , and  430   c , or  480   a ,  480   b , and  480   c  may have different sizes. 
     According to an embodiment, when the information about the split shape mode indicates to split a coding unit into an odd number of blocks, the video decoding apparatus  100  may determine an odd number of coding units included in the current coding unit  400  or  450 , and may put a predetermined restriction on at least one coding unit from among the odd number of coding units generated by splitting the current coding unit  400  or  450 . Referring to  FIG. 4 , the video decoding apparatus  100  may allow a decoding method of the coding unit  430   b  or  480   b  to be different from that of the other coding units  430   a  and  430   c , or  480   a  and  480   c , wherein the coding unit  430   b  or  480   b  is at a center location from among the three coding units  430   a ,  430   b , and  430   c , or  480   a ,  480   b , and  480   c  generated by splitting the current coding unit  400  or  450 . For example, the video decoding apparatus  100  may restrict the coding unit  430   b  or  480   b  at the center location to be no longer split or to be split only a predetermined number of times, unlike the other coding units  430   a  and  430   c , or  480   a  and  480   c.    
       FIG. 15  illustrates a process, performed by the video decoding apparatus  100 , of splitting a coding unit based on at least one from among block shape information and split shape information, according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may determine to split or not to split a square first coding unit  500  into coding units, based on at least one of the block shape information and information about a split shape mode. According to an embodiment, when the information about the split shape mode indicates to split the first coding unit  500  in a horizontal direction, the video decoding apparatus  100  may determine a second coding unit  510  by splitting the first coding unit  500  in a horizontal direction. A first coding unit, a second coding unit, and a third coding unit used according to an embodiment are terms used to understand a relation before and after splitting a coding unit. For example, a second coding unit may be determined by splitting a first coding unit, and a third coding unit may be determined by splitting the second coding unit. It will be understood that a relationship among the first coding unit, the second coding unit, and the third coding unit follows the above descriptions. 
     According to an embodiment, the video decoding apparatus  100  may determine to split or not to split the determined second coding unit  510  into coding units, based on at least one of the block shape information and the information about the split shape mode. Referring to  FIG. 15 , the video decoding apparatus  100  may or may not split the non-square second coding unit  510 , which is determined by splitting the first coding unit  500 , into one or more third coding units  520   a , or  520   b ,  520   c , and  520   d  based on at least one of the block shape information and the information about the split shape mode. The video decoding apparatus  100  may obtain at least one of the block shape information and the information about the split shape mode, and split a plurality of various-shaped second coding units (e.g.,  510 ) by splitting the first coding unit  500 , based on the obtained at least one of the block shape information and the information about the split shape mode, and the second coding unit  510  may be split by using the splitting method of the first coding unit  500 , based on at least one of the block shape information and the information about the split shape mode. According to an embodiment, when the first coding unit  500  is split into the second coding units  510  based on at least one of the block shape information and the information about the split shape mode of the first coding unit  500 , the second coding unit  510  may also be split into the third coding units  520   a , or  520   b ,  520   c , and  520   d  based on at least one of the block shape information and the information about the split shape mode of the second coding unit  510 . That is, a coding unit may be recursively split based on at least one of the block shape information and the information about the split shape mode of each coding unit. Therefore, a square coding unit may be determined by splitting a non-square coding unit, and a non-square coding unit may be determined by recursively splitting the square coding unit. 
     Referring to  FIG. 15 , a predetermined coding unit from among an odd number of third coding units  520   b ,  520   c , and  520   d  determined by splitting the non-square second coding unit  510  (e.g., a coding unit at a center location or a square coding unit) may be recursively split. According to an embodiment, the square third coding unit  520   b  from among the odd number of third coding units  520   b ,  520   c , and  520   d  may be split in a horizontal direction into a plurality of fourth coding units. A non-square fourth coding unit  530   b  or  530   d  from among the plurality of fourth coding units  530   a ,  530   b ,  530   c , and  530   d  may be split into a plurality of coding units. For example, the non-square fourth coding unit  530  or  530   d  may be split into an odd number of coding units again. A method that may be used to recursively split a coding unit will be described below in relation to various embodiments. 
     According to an embodiment, the video decoding apparatus  100  may split each of the third coding units  520   a , or  520   b ,  520   c , and  520   d  into coding units, based on at least one of the block shape information and the information about the split shape mode. Also, the video decoding apparatus  100  may determine not to split the second coding unit  510  based on at least one of the block shape information and the information about the split shape mode. According to an embodiment, the video decoding apparatus  100  may split the non-square second coding unit  510  into the odd number of third coding units  520   b ,  520   c , and  520   d . The video decoding apparatus  100  may put a predetermined restriction on a predetermined third coding unit from among the odd number of third coding units  520   b ,  520   c , and  520   d . For example, the video decoding apparatus  100  may restrict the third coding unit  520   c  at a center location from among the odd number of third coding units  520   b ,  520   c , and  520   d  to be no longer split or to be split a settable number of times. 
     Referring to  FIG. 15 , the video decoding apparatus  100  may restrict the third coding unit  520   c , which is at the center location from among the odd number of third coding units  520   b ,  520   c , and  520   d  included in the non-square second coding unit  510 , to be no longer split, to be split by using a predetermined splitting method (e.g., split into only four coding units or split by using a splitting method of the second coding unit  510 ), or to be split only a predetermined number of times (e.g., split only n times (where n&gt;0)). However, the restrictions on the third coding unit  520   c  at the center location are not limited to the above-described examples, and may include various restrictions for decoding the third coding unit  520   c  at the center location differently from the other third coding units  520   b  and  520   d.    
     According to an embodiment, the video decoding apparatus  100  may obtain at least one of the block shape information and the information about the split shape mode, which is used to split a current coding unit, from a predetermined location in the current coding unit. 
       FIG. 16  illustrates a method, performed by the video decoding apparatus  100 , of determining a predetermined coding unit from among an odd number of coding units, according to an embodiment. 
     Referring to  FIG. 16 , at least one of block shape information and information about a split shape mode of a current coding unit  600  or  650  may be obtained from a sample of a predetermined location from among a plurality of samples included in the current coding unit  600  or  650  (e.g., a sample  640  or  690  of a center location). However, the predetermined location in the current coding unit  600 , from which at least one of the block shape information and the information about the split shape mode may be obtained, is not limited to the center location in  FIG. 16 , and may include various locations included in the current coding unit  600  (e.g., top, bottom, left, right, top left, bottom left, top right, and bottom right locations). The video decoding apparatus  100  may obtain at least one of the block shape information and the information about the split shape mode from the predetermined location and determine to split or not to split the current coding unit into various-shaped and various-sized coding units. 
     According to an embodiment, when the current coding unit is split into a predetermined number of coding units, the video decoding apparatus  100  may select one of the coding units. Various methods may be used to select one of a plurality of coding units, as will be described below in relation to various embodiments. 
     According to an embodiment, the video decoding apparatus  100  may split the current coding unit into a plurality of coding units, and may determine a coding unit at a predetermined location. 
     According to an embodiment, the video decoding apparatus  100  may use information indicating locations of an odd number of coding units to determine a coding unit at a center location from among the odd number of coding units. Referring to  FIG. 16 , the video decoding apparatus  100  may determine an odd number of coding units  620   a ,  620   b , and  620   c  or an odd number of coding units  660   a ,  660   b , and  660   c  by splitting the current coding unit  600  or the current coding unit  650 . The video decoding apparatus  100  may determine the coding unit  620   b  at a center location or the coding unit  660   b  at a center location by using information about locations of the odd number of coding units  620   a ,  620   b , and  620   c  or the odd number of coding units  660   a ,  660   b , and  660   c . For example, the video decoding apparatus  100  may determine the coding unit  620   b  of the center location by determining the locations of the coding units  620   a ,  620   b , and  620   c  based on information indicating locations of predetermined samples included in the coding units  620   a ,  620   b , and  620   c . In detail, the video decoding apparatus  100  may determine the coding unit  620   b  at the center location by determining the locations of the coding units  620   a ,  620   b , and  620   c  based on information indicating locations of top left samples  630   a ,  630   b , and  630   c  of the coding units  620   a ,  620   b , and  620   c.    
     According to an embodiment, the information indicating the locations of the top left samples  630   a ,  630   b , and  630   c , which are included in the coding units  620   a ,  620   b , and  620   c , respectively, may include information about locations or coordinates of the coding units  620   a ,  620   b , and  620   c  in a picture. According to an embodiment, the information indicating the locations of the top left samples  630   a ,  630   b , and  630   c , which are included in the coding units  620   a ,  620   b , and  620   c , respectively, may include information indicating widths or heights of the coding units  620   a ,  620   b , and  620   c  included in the current coding unit  600 , and the widths or heights may correspond to information indicating differences between the coordinates of the coding units  620   a ,  620   b , and  620   c  in the picture. That is, the video decoding apparatus  100  may determine the coding unit  620   b  at the center location by directly using the information about the locations or coordinates of the coding units  620   a ,  620   b , and  620   c  in the picture, or by using the information about the widths or heights of the coding units, which correspond to the difference values between the coordinates. 
     According to an embodiment, information indicating the location of the top left sample  630   a  of the upper coding unit  620   a  may include coordinates (xa, ya), information indicating the location of the top left sample  630   b  of the middle coding unit  620   b  may include coordinates (xb, yb), and information indicating the location of the top left sample  630   c  of the lower coding unit  620   c  may include coordinates (xc, yc). The video decoding apparatus  100  may determine the middle coding unit  620   b  by using the coordinates of the top left samples  630   a ,  630   b , and  630   c  which are included in the coding units  620   a ,  620   b , and  620   c , respectively. For example, when the coordinates of the top left samples  630   a ,  630   b , and  630   c  are sorted in an ascending or descending order, the coding unit  620   b  including the coordinates (xb, yb) of the sample  630   b  at a center location may be determined as a coding unit at a center location from among the coding units  620   a ,  620   b , and  620   c  determined by splitting the current coding unit  600 . However, the coordinates indicating the locations of the top left samples  630   a ,  630   b , and  630   c  may include coordinates indicating absolute locations in the picture, or may use coordinates (dxb, dyb) indicating a relative location of the top left sample  630   b  of the middle coding unit  620   b  and coordinates (dxc, dyc) indicating a relative location of the top left sample  630   c  of the lower coding unit  620   c  with reference to the location of the top left sample  630   a  of the upper coding unit  620   a . Also, a method of determining a coding unit at a predetermined location by using coordinates of a sample included in the coding unit as information indicating a location of the sample is not limited to the above-described method, and may include various arithmetic methods capable of using the coordinates of the sample. 
     According to an embodiment, the video decoding apparatus  100  may split the current coding unit  600  into the plurality of coding units  620   a ,  620   b , and  620   c , and may select one of the coding units  620   a ,  620   b , and  620   c  based on a predetermined criterion. For example, the video decoding apparatus  100  may select the coding unit  620   b , which has a size different from that of the others, from among the coding units  620   a ,  620   b , and  620   c.    
     According to an embodiment, the video decoding apparatus  100  may determine the widths or heights of the coding units  620   a ,  620   b , and  620   c  by using the coordinates (xa, ya) indicating the location of the top left sample  630   a  of the upper coding unit  620   a , the coordinates (xb, yb) indicating the location of the top left sample  630   b  of the middle coding unit  620   b , and the coordinates (xc, yc) indicating the location of the top left sample  630   c  of the lower coding unit  620   c . The video decoding apparatus  100  may determine the respective sizes of the coding units  620   a ,  620   b , and  620   c  by using the coordinates (xa, ya), (xb, yb), and (xc, yc) indicating the locations of the coding units  620   a ,  620   b , and  620   c . According to an embodiment, the video decoding apparatus  100  may determine the width of the upper coding unit  620   a  to be a width of the current coding unit  600 . The video decoding apparatus  100  may determine the height of the upper coding unit  620   a  to be yb-ya. According to an embodiment, the video decoding apparatus  100  may determine the width of the middle coding unit  620   b  to be a width of the current coding unit  600 . The video decoding apparatus  100  may determine the height of the middle coding unit  620   b  to be yc-yb. According to an embodiment, the video decoding apparatus  100  may determine the width or height of the lower coding unit  620   c  by using the width or height of the current coding unit  600  or the widths or heights of the upper and middle coding units  620   a  and  620   b . The video decoding apparatus  100  may determine a coding unit, which has a size different from that of the others, based on the determined widths and heights of the coding units  620   a  to  620   c . Referring to  FIG. 16 , the video decoding apparatus  100  may determine the middle coding unit  620   b , which has a size different from the size of the upper and lower coding units  620   a  and  620   c , as the coding unit of the predetermined location. However, the above-described method, performed by the video decoding apparatus  100 , of determining a coding unit having a size different from the size of the other coding units merely corresponds to an example of determining a coding unit at a predetermined location by using the sizes of coding units, which are determined based on coordinates of samples, and thus various methods of determining a coding unit at a predetermined location by comparing the sizes of coding units, which are determined based on coordinates of predetermined samples, may be used. 
     The video decoding apparatus  100  may determine a width or a height of each of the coding units  660   a ,  660   b , and  660   c  by using coordinates (xd, yd) that are information indicating a location of a top left sample  670   a  of the left coding unit  660   a , coordinates (xe, ye) that are information indicating a location of a top left sample  670   b  of the middle coding unit  660   b , and coordinates (xf, yf) that are information indicating a location of a top left sample  670   c  of the right coding unit  660   c . The video decoding apparatus  100  may determine sizes of the coding units  660   a ,  660   b , and  660   c  by using the coordinates (xd, yd), (xe, ye), and (xf, yf) indicating locations of the coding units  660   a ,  660   b , and  660   c.    
     According to an embodiment, the video decoding apparatus  100  may determine the width of the left coding unit  660   a  to be xe-xd. The video decoding apparatus  100  may determine the height of the left coding unit  660   a  as the height of the current coding unit  650 . According to an embodiment, the video decoding apparatus  100  may determine the width of the middle coding unit  660   b  to be xf-xe. The video decoding apparatus  100  may determine the height of the middle coding unit  660   b  to be the height of the current coding unit  600 . According to an embodiment, the video decoding apparatus  100  may determine the width or the height of the right coding unit  660   c  by using the width or the height of the current coding unit  650  and the width and the height of the left coding unit  660   a  and the middle coding unit  660   b . The video decoding apparatus  100  may determine a coding unit, which has a size different from that of the others, based on the determined widths and heights of the coding units  660   a ,  660   b , and  660   c . Referring to  FIG. 16 , the video decoding apparatus  100  may determine the middle coding unit  660   b , which has a size different from the size of the left coding unit  660   a  and the right coding unit  660   c , as the coding unit of the predetermined location. However, the above-described method, performed by the video decoding apparatus  100 , of determining a coding unit having a size different from the size of the other coding units merely corresponds to an example of determining a coding unit at a predetermined location by using the sizes of coding units, which are determined based on coordinates of samples, and thus various methods of determining a coding unit at a predetermined location by comparing the sizes of coding units, which are determined based on coordinates of predetermined samples, may be used. 
     However, locations of samples considered to determine locations of coding units are not limited to the above-described top left locations, and information about arbitrary locations of samples included in the coding units may be used. 
     According to an embodiment, the video decoding apparatus  100  may select a coding unit at a predetermined location from among an odd number of coding units determined by splitting the current coding unit, considering the shape of the current coding unit. For example, when the current coding unit has a non-square shape, a width of which is longer than a height, the video decoding apparatus  100  may determine the coding unit at the predetermined location in a horizontal direction. That is, the video decoding apparatus  100  may determine one of coding units at different locations in a horizontal direction and may put a restriction on the coding unit. When the current coding unit has a non-square shape, a height of which is longer than a width, the video decoding apparatus  100  may determine the coding unit at the predetermined location in a vertical direction. That is, the video decoding apparatus  100  may determine one of coding units at different locations in a vertical direction and may put a restriction on the coding unit. 
     According to an embodiment, the video decoding apparatus  100  may use information indicating respective locations of an even number of coding units, to determine the coding unit at the predetermined location from among the even number of coding units. The video decoding apparatus  100  may determine an even number of coding units by splitting the current coding unit, and may determine the coding unit at the predetermined location by using the information about the locations of the even number of coding units. An operation related thereto may correspond to the operation of determining a coding unit at a predetermined location (e.g., a center location) from among an odd number of coding units, which has been described in detail above in relation to  FIG. 16 , and thus detailed descriptions thereof are not provided here. 
     According to an embodiment, when a non-square current coding unit is split into a plurality of coding units, predetermined information about a coding unit at a predetermined location may be used in a splitting operation to determine the coding unit at the predetermined location from among the plurality of coding units. For example, the video decoding apparatus  100  may use at least one of block shape information and information about a split shape mode, which is stored in a sample included in a coding unit at a center location, in a splitting operation to determine the coding unit at the center location from among the plurality of coding units determined by splitting the current coding unit. 
     Referring to  FIG. 16 , the video decoding apparatus  100  may split the current coding unit  600  into the plurality of coding units  620   a ,  620   b , and  620   c  based on at least one of the block shape information and the information about the split shape mode, and may determine the coding unit  620   b  at a center location from among the plurality of the coding units  620   a ,  620   b , and  620   c . Furthermore, the video decoding apparatus  100  may determine the coding unit  620   b  at the center location, in consideration of a location from which at least one of the block shape information and the information about the split shape mode is obtained. That is, at least one of the block shape information and the information about the split shape mode of the current coding unit  600  may be obtained from the sample  640  at a center location of the current coding unit  600  and, when the current coding unit  600  is split into the plurality of coding units  620   a ,  620   b , and  620   c  based on at least one of the block shape information and the information about the split shape mode, the coding unit  620   b  including the sample  640  may be determined as the coding unit at the center location. However, information used to determine the coding unit at the center location is not limited to at least one of the block shape information and the information about the split shape mode, and various kinds of information may be used to determine the coding unit at the center location. 
     According to an embodiment, predetermined information for identifying the coding unit at the predetermined location may be obtained from a predetermined sample included in a coding unit to be determined. Referring to  FIG. 16 , the video decoding apparatus  100  may use at least one of the block shape information and the information about the split shape mode, which is obtained from a sample at a predetermined location in the current coding unit  600  (e.g., a sample at a center location of the current coding unit  600 ) to determine a coding unit at a predetermined location from among the plurality of the coding units  620   a ,  620   b , and  620   c  determined by splitting the current coding unit  600  (e.g., a coding unit at a center location from among a plurality of split coding units). That is, the video decoding apparatus  100  may determine the sample at the predetermined location by considering a block shape of the current coding unit  600 , determine the coding unit  620   b  including a sample, from which predetermined information (e.g., at least one of the block shape information and the information about the split shape mode) may be obtained, from among the plurality of coding units  620   a ,  620   b , and  620   c  determined by splitting the current coding unit  600 , and may put a predetermined restriction on the coding unit  620   b . Referring to  FIG. 16 , according to an embodiment, the video decoding apparatus  100  may determine the sample  640  at the center location of the current coding unit  600  as the sample from which the predetermined information may be obtained, and may put a predetermined restriction on the coding unit  620   b  including the sample  640 , in a decoding operation. However, the location of the sample from which the predetermined information may be obtained is not limited to the above-described location, and may include arbitrary locations of samples included in the coding unit  620   b  to be determined for a restriction. 
     According to an embodiment, the location of the sample from which the predetermined information may be obtained may be determined based on the shape of the current coding unit  600 . According to an embodiment, the block shape information may indicate whether the current coding unit has a square or non-square shape, and the location of the sample from which the predetermined information may be obtained may be determined based on the shape. For example, the video decoding apparatus  100  may determine a sample located on a boundary for dividing at least one of a width and height of the current coding unit in half, as the sample from which the predetermined information may be obtained, by using at least one of information about the width of the current coding unit and information about the height of the current coding unit. As another example, when the block shape information of the current coding unit indicates a non-square shape, the video decoding apparatus  100  may determine one of samples adjacent to a boundary for dividing a long side of the current coding unit in half, as the sample from which the predetermined information may be obtained. 
     According to an embodiment, when the current coding unit is split into a plurality of coding units, the video decoding apparatus  100  may use at least one of the block shape information and the information about the split shape mode to determine a coding unit at a predetermined location from among the plurality of coding units. According to an embodiment, the video decoding apparatus  100  may obtain at least one of the block shape information and the information about the split shape mode from a sample at a predetermined location in a coding unit, and may split the plurality of coding units, which are generated by splitting the current coding unit, by using at least one of the block shape information and the information about the split shape mode, which is obtained from the sample of the predetermined location in each of the plurality of coding units. That is, a coding unit may be recursively split based on at least one of the block shape information and the information about the split shape mode, which is obtained from the sample at the predetermined location in each coding unit. An operation of recursively splitting a coding unit has been described above in relation to  FIG. 15 , and thus detailed descriptions thereof will not be provided here. 
     According to an embodiment, the video decoding apparatus  100  may determine one or more coding units by splitting the current coding unit, and may determine an order of decoding the one or more coding units, based on a predetermined block (e.g., the current coding unit). 
       FIG. 17  illustrates an order of processing a plurality of coding units when the video decoding apparatus  100  determines the plurality of coding units by splitting a current coding unit, according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may determine second coding units  710   a  and  710   b  by splitting a first coding unit  700  in a vertical direction, determine second coding units  730   a  and  730   b  by splitting the first coding unit  700  in a horizontal direction, or determine second coding units  750   a  to  750   d  by splitting the first coding unit  700  in vertical and horizontal directions, based on block shape information and information about a split shape mode. 
     Referring to  FIG. 17 , the video decoding apparatus  100  may determine to process the second coding units  710   a  and  710   b , which are determined by splitting the first coding unit  700  in a vertical direction, in a horizontal direction order  710   c . The video decoding apparatus  100  may determine to process the second coding units  730   a  and  730   b , which are determined by splitting the first coding unit  1400  in a horizontal direction, in a vertical direction order  730   c . The video decoding apparatus  100  may determine to process the second coding units  750   a  to  750   d , which are determined by splitting the first coding unit  700  in vertical and horizontal directions, in a predetermined order for processing coding units in a row and then processing coding units in a next row (e.g., in a raster scan order or Z-scan order  750   e ). 
     According to an embodiment, the video decoding apparatus  100  may recursively split coding units. Referring to  FIG. 17 , the video decoding apparatus  100  may determine the plurality of coding units  710   a ,  710   b ,  730   a ,  730   b ,  750   a ,  750   b ,  750   c , and  750   d  by splitting the first coding unit  700 , and may recursively split each of the determined plurality of coding units  710   a ,  710   b ,  730   a ,  730   b ,  750   a ,  750   b ,  750   c , and  750   d . A splitting method of the plurality of coding units  710   a ,  710   b ,  730   a ,  730   b ,  750   a ,  750   b ,  750   c , and  750   d  may correspond to a splitting method of the first coding unit  700 . As such, each of the plurality of coding units  710   a ,  710   b ,  730   a ,  730   b ,  750   a ,  750   b ,  750   c , and  750   d  may be independently split into a plurality of coding units. Referring to  FIG. 17 , the video decoding apparatus  100  may determine the second coding units  710   a  and  710   b  by splitting the first coding unit  700  in a vertical direction, and may determine to independently split or not to split each of the second coding units  710   a  and  710   b.    
     According to an embodiment, the video decoding apparatus  100  may determine third coding units  720   a  and  720   b  by splitting the left second coding unit  710   a  in a horizontal direction, and may not split the right second coding unit  710   b.    
     According to an embodiment, a processing order of coding units may be determined based on an operation of splitting a coding unit. In other words, a processing order of split coding units may be determined based on a processing order of coding units immediately before being split. The video decoding apparatus  100  may determine a processing order of the third coding units  720   a  and  720   b  determined by splitting the left second coding unit  710   a , independently of the right second coding unit  710   b . Because the third coding units  720   a  and  720   b  are determined by splitting the left second coding unit  710   a  in a horizontal direction, the third coding units  720   a  and  720   b  may be processed in a vertical direction order  720   c . Because the left and right second coding units  710   a  and  710   b  are processed in the horizontal direction order  710   c , the right second coding unit  710   b  may be processed after the third coding units  720   a  and  720   b  included in the left second coding unit  710   a  are processed in the vertical direction order  720   c . An operation of determining a processing order of coding units based on a coding unit before being split is not limited to the above-described example, and various methods may be used to independently process coding units, which are split and determined to various shapes, in a predetermined order. 
       FIG. 18  illustrates a process, performed by the video decoding apparatus  100 , of determining that a current coding unit is to be split into an odd number of coding units, when the coding units are not processable in a predetermined order, according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may determine whether the current coding unit is split into an odd number of coding units, based on obtained block shape information and information about a split shape mode. Referring to  FIG. 18 , a square first coding unit  800  may be split into non-square second coding units  810   a  and  810   b , and the second coding units  810   a  and  810   b  may be independently split into third coding units  820   a  and  820   b , and  820   c  to  820   e . According to an embodiment, the video decoding apparatus  100  may determine the plurality of third coding units  820   a  and  820   b  by splitting the left second coding unit  810   a  in a horizontal direction, and may split the right second coding unit  810   b  into an odd number of third coding units  820   c  to  820   e.    
     According to an embodiment, the video decoding apparatus  100  may determine whether any coding unit is split into an odd number of coding units, by determining whether the third coding units  820   a  and  820   b , and  820   c  to  820   e  are processable in a predetermined order. Referring to  FIG. 18 , the video decoding apparatus  100  may determine the third coding units  820   a  and  820   b , and  820   c  to  820   e  by recursively splitting the first coding unit  800 . The video decoding apparatus  100  may determine whether any of the first coding unit  800 , the second coding units  810   a  and  810   b , and the third coding units  820   a  and  820   b , and  820   c ,  820   d , and  820   e  are split into an odd number of coding units, based on at least one of the block shape information and the information about the split shape mode. For example, the right second coding unit  810   b  may be split into an odd number of third coding units  820   c ,  820   d , and  820   e . A processing order of a plurality of coding units included in the first coding unit  800  may be a predetermined order (e.g., a Z-scan order  830 ), and the video decoding apparatus  100  may decide whether the third coding units  820   c ,  820   d , and  820   e , which are determined by splitting the right second coding unit  810   b  into an odd number of coding units, satisfy a condition for processing in the predetermined order. 
     According to an embodiment, the video decoding apparatus  100  may determine whether the third coding units  820   a  and  820   b , and  820   c ,  820   d , and  820   e  included in the first coding unit  800  satisfy the condition for processing in the predetermined order, and the condition relates to whether at least one of a width and height of the second coding units  810   a  and  810   b  is divided in half along a boundary of the third coding units  820   a  and  820   b , and  820   c ,  820   d , and  820   e . For example, the third coding units  820   a  and  820   b  determined by dividing the height of the non-square left second coding unit  810   a  in half satisfy the condition. However, because boundaries of the third coding units  820   c ,  820   d , and  820   e  determined by splitting the right second coding unit  810   b  into three coding units do not divide the width or height of the right second coding unit  810   b  in half, it may be determined that the third coding units  820   c ,  820   d , and  820   e  do not satisfy the condition. When the condition is not satisfied as described above, the video decoding apparatus  100  may decide disconnection of a scan order, and determine that the right second coding unit  810   b  is split into an odd number of coding units, based on a result of the decision. According to an embodiment, when a coding unit is split into an odd number of coding units, the video decoding apparatus  100  may put a predetermined restriction on a coding unit at a predetermined location among the split coding units, and the restriction or the predetermined location has been described above in relation to various embodiments and thus detailed descriptions thereof will not be provided here. 
       FIG. 19  illustrates a process, performed by the video decoding apparatus  100 , of determining at least one coding unit by splitting a first coding unit  900 , according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may split the first coding unit  900 , based on at least one of block shape information and information about a split shape mode, which is obtained by the bitstream obtainer  110 . The square first coding unit  900  may be split into four square coding units, or may be split into a plurality of non-square coding units. For example, referring to  FIG. 19 , when the block shape information indicates that the first coding unit  900  has a square shape and the information about the split shape mode indicates to split the first coding unit  900  into non-square coding units, the video decoding apparatus  100  may split the first coding unit  900  into a plurality of non-square coding units. In detail, when the information about the split shape mode indicates to determine an odd number of coding units by splitting the first coding unit  900  in a horizontal direction or a vertical direction, the video decoding apparatus  100  may split the square first coding unit  900  into an odd number of coding units, e.g., second coding units  910   a ,  910   b , and  910   c  determined by splitting the square first coding unit  900  in a vertical direction or second coding units  920   a ,  920   b , and  920   c  determined by splitting the square first coding unit  900  in a horizontal direction. 
     According to an embodiment, the video decoding apparatus  100  may determine whether the second coding units  910   a ,  910   b ,  910   c ,  920   a ,  920   b , and  920   c  included in the first coding unit  900  satisfy a condition for processing in a predetermined order, and the condition relates to whether at least one of a width and height of the first coding unit  900  is divided in half along a boundary of the second coding units  910   a ,  910   b ,  910   c ,  920   a ,  920   b , and  920   c . Referring to  FIG. 19 , because boundaries of the second coding units  910   a ,  910   b , and  910   c  determined by splitting the square first coding unit  900  in a vertical direction do not divide the width of the first coding unit  900  in half, it may be determined that the first coding unit  900  does not satisfy the condition for processing in the predetermined order. In addition, because boundaries of the second coding units  920   a ,  920   b , and  920   c  determined by splitting the square first coding unit  900  in a horizontal direction do not divide the width of the first coding unit  900  in half, it may be determined that the first coding unit  900  does not satisfy the condition for processing in the predetermined order. When the condition is not satisfied as described above, the video decoding apparatus  100  may decide disconnection of a scan order, and may determine that the first coding unit  900  is split into an odd number of coding units, based on a result of the decision. According to an embodiment, when a coding unit is split into an odd number of coding units, the video decoding apparatus  100  may put a predetermined restriction on a coding unit at a predetermined location from among the split coding units, and the restriction or the predetermined location has been described above in relation to various embodiments and thus detailed descriptions thereof will not be provided herein. 
     According to an embodiment, the video decoding apparatus  100  may determine various-shaped coding units by splitting a first coding unit. 
     Referring to  FIG. 19 , the video decoding apparatus  100  may split the square first coding unit  900  or a non-square first coding unit  930  or  950  into various-shaped coding units. 
       FIG. 20  illustrates that a shape into which a second coding unit is splittable by the video decoding apparatus  100  is restricted when the second coding unit having a non-square shape, which is determined by splitting a first coding unit  1000 , satisfies a predetermined condition, according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may determine to split the square first coding unit  1000  into non-square second coding units  1010   a ,  1010   b ,  1020   a , and  1020   b , based on at least one of block shape information and information about a split shape mode, which is obtained by the bitstream obtainer  110 . The second coding units  1010   a ,  1010   b ,  1020   a , and  1020   b  may be independently split. As such, the video decoding apparatus  100  may determine to split or not to split the first coding unit  1000  into a plurality of coding units, based on at least one of the block shape information and the information about the split shape mode of each of the second coding units  1010   a ,  1010   b ,  1020   a , and  1020   b . According to an embodiment, the video decoding apparatus  100  may determine third coding units  1012   a  and  1012   b  by splitting the non-square left second coding unit  1010   a , which is determined by splitting the first coding unit  1000  in a vertical direction, in a horizontal direction. However, when the left second coding unit  1010   a  is split in a horizontal direction, the video decoding apparatus  100  may restrict the right second coding unit  1010   b  to not be split in a horizontal direction in which the left second coding unit  1010   a  is split. When third coding units  1014   a  and  1014   b  are determined by splitting the right second coding unit  1010   b  in a same direction, because the left and right second coding units  1010   a  and  1010   b  are independently split in a horizontal direction, the third coding units  1012   a ,  1012   b ,  1014   a , and  1014   b  may be determined. However, this case serves equally as a case in which the video decoding apparatus  100  splits the first coding unit  1000  into four square second coding units  1030   a ,  1030   b ,  1030   c , and  1030   d , based on at least one of the block shape information and the information about the split shape mode, and may be inefficient in terms of image decoding. 
     According to an embodiment, the video decoding apparatus  100  may determine third coding units  1022   a ,  1022   b ,  1024   a , and  1024   b  by splitting the non-square second coding unit  1020   a  or  1020   b , which is determined by splitting the first coding unit  1000  in a horizontal direction, in a vertical direction. However, when a second coding unit (e.g., the upper second coding unit  1020   a ) is split in a vertical direction, for the above-described reason, the video decoding apparatus  100  may restrict the other second coding unit (e.g., the lower second coding unit  1020   b ) to not be split in a vertical direction in which the upper second coding unit  1020   a  is split. 
       FIG. 21  illustrates a process, performed by the video decoding apparatus  100 , of splitting a square coding unit when information about a split shape mode indicates that the square coding unit is not to be split into four square coding units, according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may determine second coding units  1110   a ,  1110   b ,  1120   a ,  1120   b , etc. by splitting a first coding unit  1100 , based on at least one of block shape information and information about a split shape mode. The information about the split shape mode may include information about various methods of splitting a coding unit but, the information about various splitting methods may not include information for splitting a coding unit into four square coding units. According to such information about a split shape mode, the video decoding apparatus  100  may not split the first square coding unit  1100  into four square second coding units  1130   a ,  1130   b ,  1130   c , and  1130   d . The video decoding apparatus  100  may determine the non-square second coding units  1110   a ,  1110   b ,  1120   a ,  1120   b , etc., based on the information about the split shape mode. 
     According to an embodiment, the video decoding apparatus  100  may independently split the non-square second coding units  1110   a ,  1110   b ,  1120   a ,  1120   b , etc. Each of the second coding units  1110   a ,  1110   b ,  1120   a ,  1120   b , etc. may be recursively split in a predetermined order, and this splitting method may correspond to a method of splitting the first coding unit  1100 , based on at least one of the block shape information and the information about the split shape mode. 
     For example, the video decoding apparatus  100  may determine square third coding units  1112   a  and  1112   b  by splitting the left second coding unit  1110   a  in a horizontal direction, and may determine square third coding units  1114   a  and  1114   b  by splitting the right second coding unit  1110   b  in a horizontal direction. Furthermore, the video decoding apparatus  100  may determine square third coding units  1116   a ,  1116   b ,  1116   c , and  1116   d  by splitting both of the left and right second coding units  1110   a  and  1110   b  in a horizontal direction. In this case, coding units having the same shape as the four square second coding units  1130   a ,  1130   b ,  1130   c , and  1130   d  split from the first coding unit  1100  may be determined. 
     As another example, the video decoding apparatus  100  may determine square third coding units  1122   a  and  1122   b  by splitting the upper second coding unit  1120   a  in a vertical direction, and may determine square third coding units  1124   a  and  1124   b  by splitting the lower second coding unit  1120   b  in a vertical direction. Furthermore, the video decoding apparatus  100  may determine square third coding units  1126   a ,  1126   b ,  1126   c , and  1126   d  by splitting both of the upper and lower second coding units  1120   a  and  1120   b  in a vertical direction. In this case, coding units having the same shape as the four square second coding units  1130   a ,  1130   b ,  1130   c , and  1130   d  split from the first coding unit  1100  may be determined. 
       FIG. 22  illustrates that a processing order between a plurality of coding units may be changed depending on a process of splitting a coding unit, according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may split a first coding unit  1200 , based on block shape information and information about a split shape mode. When the block shape information indicates a square shape and the information about the split shape mode indicates to split the first coding unit  1200  in at least one of horizontal and vertical directions, the video decoding apparatus  100  may determine second coding units  1210   a ,  1210   b ,  1220   a , and  1220   b , by splitting the first coding unit  1200 . Referring to  FIG. 22 , the non-square second coding units  1210   a ,  1210   b ,  1220   a , and  1220   b  determined by splitting the first coding unit  1200  in only a horizontal direction or vertical direction may be independently split based on the block shape information and the information about the split shape mode of each coding unit. For example, the video decoding apparatus  100  may determine third coding units  1216   a ,  1216   b ,  1216   c , and  1216   d  by splitting the second coding units  1210   a  and  1210   b , which are generated by splitting the first coding unit  1200  in a vertical direction, in a horizontal direction, and may determine third coding units  1226   a ,  1226   b ,  1226   c , and  1226   d  by splitting the second coding units  1220   a  and  1220   b , which are generated by splitting the first coding unit  1200  in a horizontal direction, in a horizontal direction. An operation of splitting the second coding units  1210   a ,  1210   b ,  1220   a , and  1220   b  has been described above in relation to  FIG. 21 , and thus detailed descriptions thereof will not be provided herein. 
     According to an embodiment, the video decoding apparatus  100  may process coding units in a predetermined order. An operation of processing coding units in a predetermined order has been described above in relation to  FIG. 17 , and thus detailed descriptions thereof will not be provided herein. Referring to  FIG. 22 , the video decoding apparatus  100  may determine four square third coding units  1216   a ,  1216   b ,  1216   c , and  1216   d , and  1226   a ,  1226   b ,  1226   c , and  1226   d  by splitting the square first coding unit  1200 . According to an embodiment, the video decoding apparatus  100  may determine processing orders of the third coding units  1216   a ,  1216   b ,  1216   c , and  1216   d , and  1226   a ,  1226   b ,  1226   c , and  1226   d  based on a splitting method of the first coding unit  1200 . 
     According to an embodiment, the video decoding apparatus  100  may determine the third coding units  1216   a ,  1216   b ,  1216   c , and  1216   d  by splitting the second coding units  1210   a  and  1210   b  generated by splitting the first coding unit  1200  in a vertical direction, in a horizontal direction, and may process the third coding units  1216   a ,  1216   b ,  1216   c , and  1216   d  in a processing order  1217  for initially processing the third coding units  1216   a  and  1216   c , which are included in the left second coding unit  1210   a , in a vertical direction and then processing the third coding unit  1216   b  and  1216   d , which are included in the right second coding unit  1210   b , in a vertical direction. 
     According to an embodiment, the video decoding apparatus  100  may determine the third coding units  1226   a ,  1226   b ,  1226   c , and  1226   d  by splitting the second coding units  1220   a  and  1220   b  generated by splitting the first coding unit  1200  in a horizontal direction, in a vertical direction, and may process the third coding units  1226   a ,  1226   b ,  1226   c , and  1226   d  in a processing order  1227  for initially processing the third coding units  1226   a  and  1226   b , which are included in the upper second coding unit  1220   a , in a horizontal direction and then processing the third coding unit  1226   c  and  1226   d , which are included in the lower second coding unit  1220   b , in a horizontal direction. 
     Referring to  FIG. 22 , the square third coding units  1216   a ,  1216   b ,  1216   c , and  1216   d , and  1226   a ,  1226   b ,  1226   c , and  1226   d  may be determined by splitting the second coding units  1210   a ,  1210   b ,  1220   a , and  1220   b , respectively. Although the second coding units  1210   a  and  1210   b  are determined by splitting the first coding unit  1200  in a vertical direction differently from the second coding units  1220   a  and  1220   b  which are determined by splitting the first coding unit  1200  in a horizontal direction, the third coding units  1216   a ,  1216   b ,  1216   c , and  1216   d , and  1226   a ,  1226   b ,  1226   c , and  1226   d  split therefrom eventually show same-shaped coding units split from the first coding unit  1200 . As such, by recursively splitting a coding unit in different manners based on at least one of the block shape information the information about the split shape mode, the video decoding apparatus  100  may process a plurality of coding units in different orders even when the coding units are eventually determined to be the same shape. 
       FIG. 23  illustrates a process of determining a depth of a coding unit as a shape and size of the coding unit change, when the coding unit is recursively split such that a plurality of coding units are determined, according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may determine the depth of the coding unit, based on a predetermined criterion. For example, the predetermined criterion may be the length of a long side of the coding unit. When the length of a long side of a coding unit before being split is 2n times (n&gt;0) the length of a long side of a split current coding unit, the video decoding apparatus  100  may determine that a depth of the current coding unit is increased from a depth of the coding unit before being split, by n. In the following description, a coding unit having an increased depth is expressed as a coding unit of a deeper depth. 
     Referring to  FIG. 23 , according to an embodiment, the video decoding apparatus  100  may determine a second coding unit  1302  and a third coding unit  1304  of deeper depths by splitting a square first coding unit  1300  based on block shape information indicating a square shape (for example, the block shape information may be expressed as ‘0: SQUARE’). Assuming that the size of the square first coding unit  1300  is 2N×2N, the second coding unit  1302  determined by dividing a width and height of the first coding unit  1300  to ½ may have a size of N×N. Furthermore, the third coding unit  1304  determined by dividing a width and height of the second coding unit  1302  to ½ may have a size of N/2×N/2. In this case, a width and height of the third coding unit  1304  are ¼ times those of the first coding unit  1300 . When a depth of the first coding unit  1300  is D, a depth of the second coding unit  1302 , the width and height of which are ½ times those of the first coding unit  1300 , may be D+1, and a depth of the third coding unit  1304 , the width and height of which are ¼ times those of the first coding unit  1300 , may be D+2. 
     According to an embodiment, the video decoding apparatus  100  may determine a second coding unit  1312  or  1322  and a third coding unit  1314  or  1324  of deeper depths by splitting a non-square first coding unit  1310  or  1320  based on block shape information indicating a non-square shape (for example, the block shape information may be expressed as ‘1: NS_VER’ indicating a non-square shape, a height of which is longer than a width, or as ‘2: NS_HOR’ indicating a non-square shape, a width of which is longer than a height). 
     The video decoding apparatus  100  may determine the second coding unit  1302 ,  1312 , or  1322  by dividing at least one of a width and height of the first coding unit  1310  having a size of N×2N. That is, the video decoding apparatus  100  may determine the second coding unit  1302  having a size of N×N or the second coding unit  1322  having a size of N×N/2 by splitting the first coding unit  1310  in a horizontal direction, or may determine the second coding unit  1312  having a size of N/2×N by splitting the first coding unit  1310  in horizontal and vertical directions. 
     According to an embodiment, the video decoding apparatus  100  may determine the second coding unit  1302 ,  1312 , or  1322  by dividing at least one of a width and height of the first coding unit  1320  having a size of 2N×N. That is, the video decoding apparatus  100  may determine the second coding unit  1302  having a size of N×N or the second coding unit  1312  having a size of N/2×N by splitting the first coding unit  1320  in a vertical direction, or may determine the second coding unit  1322  having a size of N×N/2 by splitting the first coding unit  1320  in horizontal and vertical directions. 
     According to an embodiment, the video decoding apparatus  100  may determine the third coding unit  1304 ,  1314 , or  1324  by dividing at least one of a width and height of the second coding unit  1302  having a size of N×N. That is, the video decoding apparatus  100  may determine the third coding unit  1304  having a size of N/2×N/2, the third coding unit  1314  having a size of N/4×N/2, or the third coding unit  1324  having a size of N/2×N/4 by splitting the second coding unit  1302  in vertical and horizontal directions. 
     According to an embodiment, the video decoding apparatus  100  may determine the third coding unit  1304 ,  1314 , or  1324  by dividing at least one of a width and height of the second coding unit  1312  having a size of N/2×N. That is, the video decoding apparatus  100  may determine the third coding unit  1304  having a size of N/2×N/2 or the third coding unit  1324  having a size of N/2×N/4 by splitting the second coding unit  1312  in a horizontal direction, or may determine the third coding unit  1314  having a size of N/4×N/2 by splitting the second coding unit  1312  in vertical and horizontal directions. 
     According to an embodiment, the video decoding apparatus  100  may determine the third coding unit  1304 ,  1314 , or  1324  by dividing at least one of a width and height of the second coding unit  1322  having a size of N×N/2. That is, the video decoding apparatus  100  may determine the third coding unit  1304  having a size of N/2×N/2 or the third coding unit  1314  having a size of N/4×N/2 by splitting the second coding unit  1322  in a vertical direction, or may determine the third coding unit  1324  having a size of N/2×N/4 by splitting the second coding unit  1322  in vertical and horizontal directions. 
     According to an embodiment, the video decoding apparatus  100  may split the square coding unit  1300 ,  1302 , or  1304  in a horizontal or vertical direction. For example, the video decoding apparatus  100  may determine the first coding unit  1310  having a size of N×2N by splitting the first coding unit  1300  having a size of 2N×2N in a vertical direction, or may determine the first coding unit  1320  having a size of 2N×N by splitting the first coding unit  1300  in a horizontal direction. According to an embodiment, when a depth is determined based on the length of the longest side of a coding unit, a depth of a coding unit determined by splitting the first coding unit  1300  having a size of 2N×2N in a horizontal or vertical direction may be the same as the depth of the first coding unit  1300 . 
     According to an embodiment, a width and height of the third coding unit  1314  or  1324  may be ¼ times those of the first coding unit  1310  or  1320 . When a depth of the first coding unit  1310  or  1320  is D, a depth of the second coding unit  1312  or  1322 , the width and height of which are ½ times those of the first coding unit  1310  or  1320 , may be D+1, and a depth of the third coding unit  1314  or  1324 , the width and height of which are ¼ times those of the first coding unit  1310  or  1320 , may be D+2. 
       FIG. 24  illustrates depths that are determinable based on shapes and sizes of coding units, and part indexes (PIDs) that are for distinguishing the coding units, according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may determine various-shape second coding units by splitting a square first coding unit  1400 . Referring to  FIG. 14 , the video decoding apparatus  100  may determine second coding units  1402   a  and  1402   b ,  1404   a  and  1404   b , and  1406   a ,  1406   b ,  1406   c , and  1406   d  by splitting the first coding unit  1400  in at least one of vertical and horizontal directions based on information about a split shape mode. That is, the video decoding apparatus  100  may determine the second coding units  1402   a  and  1402   b ,  1404   a  and  1404   b , and  1406   a ,  1406   b ,  1406   c , and  1406   d , based on the information about the split shape mode of the first coding unit  1400 . 
     According to an embodiment, a depth of the second coding units  1402   a  and  1402   b ,  1404   a  and  1404   b , and  1406   a ,  1406   b ,  1406   c , and  1406   d , which are determined based on the information about the split shape mode of the square first coding unit  1400 , may be determined based on the length of a long side thereof. For example, because the length of a side of the square first coding unit  1400  equals the length of a long side of the non-square second coding units  1402   a  and  1402   b , and  1404   a  and  1404   b , the first coding unit  1400  and the non-square second coding units  1402   a  and  1402   b , and  1404   a  and  1404   b  may have the same depth, e.g., D. However, when the video decoding apparatus  100  splits the first coding unit  1400  into the four square second coding units  1406   a ,  1406   b ,  1406   c , and  1406   d  based on the information about the split shape mode, because the length of a side of the square second coding units  1406   a ,  1406   b ,  1406   c , and  1406   d  is ½ times the length of a side of the first coding unit  1400 , a depth of the second coding units  1406   a ,  1406   b ,  1406   c , and  1406   d  may be D+1 which is deeper than the depth D of the first coding unit  1400  by  1 . 
     According to an embodiment, the video decoding apparatus  100  may determine a plurality of second coding units  1412   a  and  1412   b , and  1414   a ,  1414   b , and  1414   c  by splitting a first coding unit  1410 , a height of which is longer than a width, in a horizontal direction based on the information about the split shape mode. According to an embodiment, the video decoding apparatus  100  may determine a plurality of second coding units  1422   a  and  1422   b , and  1424   a ,  1424   b , and  1424   c  by splitting a first coding unit  1420 , a width of which is longer than a height, in a vertical direction based on the information about the split shape mode. 
     According to an embodiment, a depth of the second coding units  1412   a  and  1412   b ,  1414   a ,  1414   b , and  1414   c ,  1422   a  and  1422   b , and  1424   a ,  1424   b , and  1424   c , which are determined based on the information about the split shape mode of the non-square first coding unit  1410  or  1420 , may be determined based on the length of a long side thereof. For example, because the length of a side of the square second coding units  1412   a  and  1412   b  is ½ times the length of a long side of the first coding unit  1410  having a non-square shape, a height of which is longer than a width, a depth of the square second coding units  1412   a  and  1412   b  is D+1 which is deeper than the depth D of the non-square first coding unit  1410  by  1 . 
     Furthermore, the video decoding apparatus  100  may split the non-square first coding unit  1410  into an odd number of second coding units  1414   a ,  1414   b , and  1414   c  based on the information about the split shape mode. The odd number of second coding units  1414   a ,  1414   b , and  1414   c  may include the non-square second coding units  1414   a  and  1414   c  and the square second coding unit  1414   b . In this case, because the length of a long side of the non-square second coding units  1414   a  and  1414   c  and the length of a side of the square second coding unit  1414   b  are ½ times the length of a long side of the first coding unit  1410 , a depth of the second coding units  1414   a ,  1414   b , and  1414   c  may be D+1 which is deeper than the depth D of the non-square first coding unit  1410  by  1 . The video decoding apparatus  100  may determine depths of coding units split from the first coding unit  1420  having a non-square shape, a width of which is longer than a height, by using the above-described method of determining depths of coding units split from the first coding unit  1410 . 
     According to an embodiment, the video decoding apparatus  100  may determine PIDs for identifying split coding units, based on a size ratio between the coding units when an odd number of split coding units do not have equal sizes. Referring to  FIG. 24 , a coding unit  1414   b  of a center location among an odd number of split coding units  1414   a ,  1414   b , and  1414   c  may have a width equal to that of the other coding units  1414   a  and  1414   c  and a height which is two times that of the other coding units  1414   a  and  1414   c . That is, in this case, the coding unit  1414   b  at the center location may include two of the other coding unit  1414   a  or  1414   c . Therefore, when a PID of the coding unit  1414   b  at the center location is 1 based on a scan order, a PID of the coding unit  1414   c  located next to the coding unit  1414   b  may be increased by 2 and thus may be 3. That is, discontinuity in PID values may be present. According to an embodiment, the video decoding apparatus  100  may determine whether an odd number of split coding units do not have equal sizes, based on whether discontinuity is present in PIDs for identifying the split coding units. 
     According to an embodiment, the video decoding apparatus  100  may determine whether to use a specific splitting method, based on PID values for identifying a plurality of coding units determined by splitting a current coding unit. Referring to  FIG. 24 , the video decoding apparatus  100  may determine an even number of coding units  1412   a  and  1412   b  or an odd number of coding units  1414   a ,  1414   b , and  1414   c  by splitting the first coding unit  1410  having a rectangular shape, a height of which is longer than a width. The video decoding apparatus  100  may use PIDs to identify respective coding units. According to an embodiment, the PID may be obtained from a sample of a predetermined location of each coding unit (e.g., a top left sample). 
     According to an embodiment, the video decoding apparatus  100  may determine a coding unit at a predetermined location from among the split coding units, by using the PIDs for distinguishing the coding units. According to an embodiment, when the information about the split shape mode of the first coding unit  1410  having a rectangular shape, a height of which is longer than a width, indicates to split a coding unit into three coding units, the video decoding apparatus  100  may split the first coding unit  1410  into three coding units  1414   a ,  1414   b , and  1414   c . The video decoding apparatus  100  may assign a PID to each of the three coding units  1414   a ,  1414   b , and  1414   c . The video decoding apparatus  100  may compare PIDs of an odd number of split coding units to determine a coding unit at a center location from among the coding units. The video decoding apparatus  100  may determine the coding unit  1414   b  having a PID corresponding to a middle value among the PIDs of the coding units, as the coding unit at the center location from among the coding units determined by splitting the first coding unit  1410 . According to an embodiment, the video decoding apparatus  100  may determine PIDs for distinguishing split coding units, based on a size ratio between the coding units when the split coding units do not have equal sizes. Referring to  FIG. 24 , the coding unit  1414   b  generated by splitting the first coding unit  1410  may have a width equal to that of the other coding units  1414   a  and  1414   c  and a height which is two times that of the other coding units  1414   a  and  1414   c . In this case, when the PID of the coding unit  1414   b  at the center location is 1, the PID of the coding unit  1414   c  located next to the coding unit  1414   b  may be increased by 2 and thus may be 3. When the PID is not uniformly increased as described above, the video decoding apparatus  100  may determine that a coding unit is split into a plurality of coding units including a coding unit having a size different from that of the other coding units. According to an embodiment, when the information about the split shape mode indicates to split a coding unit into an odd number of coding units, the video decoding apparatus  100  may split a current coding unit in such a manner that a coding unit of a predetermined location among an odd number of coding units (e.g., a coding unit of a centre location) has a size different from that of the other coding units. In this case, the video decoding apparatus  100  may determine the coding unit of the centre location, which has a different size, by using PIDs of the coding units. However, the PIDs and the size or location of the coding unit of the predetermined location are not limited to the above-described examples, and various PIDs and various locations and sizes of coding units may be used. 
     According to an embodiment, the video decoding apparatus  100  may use a predetermined data unit where a coding unit starts to be recursively split. 
       FIG. 25  illustrates that a plurality of coding units are determined based on a plurality of predetermined data units included in a picture, according to an embodiment. 
     According to an embodiment, a predetermined data unit may be defined as a data unit where a coding unit starts to be recursively split by using at least one of block shape information and information about a split shape mode. That is, the predetermined data unit may correspond to a coding unit of an uppermost depth, which is used to determine a plurality of coding units split from a current picture. In the following descriptions, for convenience of explanation, the predetermined data unit is referred to as a reference data unit. 
     According to an embodiment, the reference data unit may have a predetermined size and a predetermined size shape. According to an embodiment, the reference data unit may include M×N samples. Herein, M and N may be equal to each other, and may be integers expressed as multipliers of 2. That is, the reference data unit may have a square or non-square shape, and may be split into an integer number of coding units. 
     According to an embodiment, the video decoding apparatus  100  may split the current picture into a plurality of reference data units. According to an embodiment, the video decoding apparatus  100  may split the plurality of reference data units, which are split from the current picture, by using information about a split shape mode for each reference data unit. The operation of splitting the reference data unit may correspond to a splitting operation using a quadtree structure. 
     According to an embodiment, the video decoding apparatus  100  may previously determine the minimum size allowed for the reference data units included in the current picture. Accordingly, the video decoding apparatus  100  may determine various reference data units having sizes equal to or greater than the minimum size, and may determine one or more coding units by using the block shape information and the information about the split shape mode with reference to the determined reference data unit. 
     Referring to  FIG. 25 , the video decoding apparatus  100  may use a square reference coding unit  1500  or a non-square reference coding unit  1502 . According to an embodiment, the shape and size of reference coding units may be determined based on various data units capable of including one or more reference coding units (e.g., sequences, pictures, slices, slice segments, largest coding units, or the like). 
     According to an embodiment, the bitstream obtainer  110  of the video decoding apparatus  100  may obtain, from a bitstream, at least one of reference coding unit shape information and reference coding unit size information with respect to each of the various data units. An operation of splitting the square reference coding unit  1500  into one or more coding units has been described above in relation to the operation of splitting the current coding unit  300  of  FIG. 13 , and an operation of splitting the non-square reference coding unit  1502  into one or more coding units has been described above in relation to the operation of splitting the current coding unit  400  or  450  of  FIG. 14 , and thus, detailed descriptions thereof will not be provided herein. 
     According to an embodiment, the video decoding apparatus  100  may use a PID for identifying the size and shape of reference coding units, to determine the size and shape of reference coding units according to some data units previously determined based on a predetermined condition. That is, the bitstream obtainer  110  may obtain, from the bitstream, only the PID for identifying the size and shape of reference coding units with respect to each slice, slice segment, or largest coding unit which is a data unit satisfying a predetermined condition (e.g., a data unit having a size equal to or smaller than a slice) among the various data units (e.g., sequences, pictures, slices, slice segments, largest coding units, or the like). The video decoding apparatus  100  may determine the size and shape of reference data units with respect to each data unit, which satisfies the predetermined condition, by using the PID. When the reference coding unit shape information and the reference coding unit size information are obtained and used from the bitstream according to each data unit having a relatively small size, efficiency of using the bitstream may not be high, and therefore, only the PID may be obtained and used instead of directly obtaining the reference coding unit shape information and the reference coding unit size information. In this case, at least one of the size and shape of reference coding units corresponding to the PID for identifying the size and shape of reference coding units may be previously determined. That is, the video decoding apparatus  100  may determine at least one of the size and shape of reference coding units included in a data unit serving as a unit for obtaining the PID, by selecting the previously determined at least one of the size and shape of reference coding units based on the PID. 
     According to an embodiment, the video decoding apparatus  100  may use one or more reference coding units included in a largest coding unit. That is, a largest coding unit split from a picture may include one or more reference coding units, and coding units may be determined by recursively splitting each reference coding unit. According to an embodiment, at least one of a width and height of the largest coding unit may be integer times at least one of the width and height of the reference coding units. According to an embodiment, the size of reference coding units may be obtained by splitting the largest coding unit n times based on a quadtree structure. That is, the video decoding apparatus  100  may determine the reference coding units by splitting the largest coding unit n times based on a quadtree structure, and may split the reference coding unit based on at least one of the block shape information and the information about the split shape mode according to various embodiments. 
       FIG. 26  illustrates a processing block serving as a unit for determining a determination order of reference coding units included in a picture  1600 , according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may determine one or more processing blocks split from a picture. The processing block is a data unit including one or more reference coding units split from a picture, and the one or more reference coding units included in the processing block may be determined according to a specific order. That is, a determination order of one or more reference coding units determined in each processing block may correspond to one of various types of orders for determining reference coding units, and may vary depending on the processing block. The determination order of reference coding units, which is determined with respect to each processing block, may be one of various orders, e.g., raster scan order, Z-scan, N-scan, up-right diagonal scan, horizontal scan, and vertical scan, but is not limited to the above-mentioned scan orders. 
     According to an embodiment, the video decoding apparatus  100  may obtain processing block size information and may determine the size of one or more processing blocks included in the picture. The video decoding apparatus  100  may obtain the processing block size information from a bitstream and may determine the size of one or more processing blocks included in the picture. The size of processing blocks may be a predetermined size of data units, which is indicated by the processing block size information. 
     According to an embodiment, the bitstream obtainer  110  of the video decoding apparatus  100  may obtain the processing block size information from the bitstream according to each specific data unit. For example, the processing block size information may be obtained from the bitstream in a data unit such as an image, sequence, picture, slice, or slice segment. That is, the bitstream obtainer  110  may obtain the processing block size information from the bitstream according to each of the various data units, the video decoding apparatus  100  may determine the size of one or more processing blocks, which are split from the picture, by using the obtained processing block size information, and the size of the processing blocks may be integer times that of the reference coding units. 
     According to an embodiment, the video decoding apparatus  100  may determine the size of processing blocks  1602  and  1612  included in the picture  1600 . For example, the video decoding apparatus  100  may determine the size of processing blocks based on the processing block size information obtained from the bitstream. Referring to  FIG. 26 , according to an embodiment, the video decoding apparatus  100  may determine a width of the processing blocks  1602  and  1612  to be four times the width of the reference coding units, and may determine a height of the processing blocks  1602  and  1612  to be four times the height of the reference coding units. The video decoding apparatus  100  may determine a determination order of one or more reference coding units in one or more processing blocks. 
     According to an embodiment, the video decoding apparatus  100  may determine the processing blocks  1602  and  1612 , which are included in the picture  1600 , based on the size of processing blocks, and may determine a determination order of one or more reference coding units included in the processing blocks  1602  and  1612 . According to an embodiment, determination of reference coding units may include determination of the size of the reference coding units. 
     According to an embodiment, the video decoding apparatus  100  may obtain, from the bitstream, determination order information of one or more reference coding units included in one or more processing blocks, and may determine a determination order with respect to one or more reference coding units based on the obtained determination order information. The determination order information may be defined as an order or direction for determining the reference coding units in the processing block. That is, the determination order of reference coding units may be independently determined with respect to each processing block. 
     According to an embodiment, the video decoding apparatus  100  may obtain, from the bitstream, the determination order information of reference coding units according to each specific data unit. For example, the bitstream obtainer  110  may obtain the determination order information of reference coding units from the bitstream according to each data unit such as an image, sequence, picture, slice, slice segment, or processing block. Because the determination order information of reference coding units indicates an order for determining reference coding units in a processing block, the determination order information may be obtained with respect to each specific data unit including an integer number of processing blocks. 
     According to an embodiment, the video decoding apparatus  100  may determine one or more reference coding units based on the determined determination order. 
     According to an embodiment, the bitstream obtainer  110  may obtain the determination order information of reference coding units from the bitstream as information related to the processing blocks  1602  and  1612 , and the video decoding apparatus  100  may determine a determination order of one or more reference coding units included in the processing blocks  1602  and  1612  and determine one or more reference coding units, which are included in the picture  1600 , based on the determination order. Referring to  FIG. 26 , the video decoding apparatus  100  may determine determination orders  1604  and  1614  of one or more reference coding units in the processing blocks  1602  and  1612 , respectively. For example, when the determination order information of reference coding units is obtained with respect to each processing block, different kinds of the determination order information of reference coding units may be obtained for the processing blocks  1602  and  1612 . When the determination order  1604  of reference coding units in the processing block  1602  is a raster scan order, reference coding units included in the processing block  1602  may be determined according to a raster scan order. On the contrary, when the determination order  1614  of reference coding units in the other processing block  1612  is a backward raster scan order, reference coding units included in the processing block  1612  may be determined according to the backward raster scan order. 
     According to an embodiment, the video decoding apparatus  100  may decode the determined one or more reference coding units. The video decoding apparatus  100  may decode an image, based on the reference coding units determined as described above. A method of decoding the reference coding units may include various image decoding methods. 
     According to an embodiment, the video decoding apparatus  100  may obtain block shape information indicating the shape of a current coding unit or information about a split shape mode indicating a splitting method of the current coding unit, from the bitstream, and may use the obtained information. The block shape information or the information about the split shape mode may be included in the bitstream related to various data units. For example, the video decoding apparatus  100  may use the block shape information or the information about the split shape mode included in a sequence parameter set, a picture parameter set, a video parameter set, a slice header, or a slice segment header. Furthermore, the video decoding apparatus  100  may obtain, from the bitstream, a syntax element corresponding to the block shape information or the information about the split shape mode according to each largest coding unit, each reference coding unit, or each processing block, and may use the obtained syntax element. 
       FIG. 27  illustrates coding units determinable per picture when a combination of shapes into which a coding unit is splittable is different per picture, according to an embodiment. 
     Referring to  FIG. 27 , the video decoding apparatus  100  may differently determine, per picture, a combination of shapes into which a coding unit is splittable. For example, the video decoding apparatus  100  may decode an image by using a picture that is splittable into 4 coding units, a picture  1710  that is splittable into 2 or 4 coding units, and a picture  1720  that is splittable into 2, 3, or 4 coding units, from among at least one picture included in the image. In order to split the picture  1700  into a plurality of coding units, the video decoding apparatus  100  may use only split shape information indicating that the picture  1700  is split into 4 square coding units. In order to split the picture  1710 , the video decoding apparatus  100  may use only split shape information indicating that the picture  1710  is split into 2 or 4 coding units. In order to split the picture  1720 , the video decoding apparatus  100  may use only split shape information indicating that the picture  1720  is divided into 2, 3, or 4 coding units. Because such a combination of split shapes is only an embodiment for describing operations of the video decoding apparatus  100 , the combination of split shapes should not be interpreted as being limited to the embodiment and various combinations of split shapes may be used according to predetermined data units. 
     According to an embodiment, the bitstream obtainer  110  of the video decoding apparatus  100  may obtain a bitstream including an index indicating a combination of split shape information according to predetermined data unit units (e.g., sequences, pictures, or slices). For example, the bitstream obtainer  110  may obtain an index indicating a combination of split shape information from a sequence parameter set, a picture parameter set, or a slice header. The video decoding apparatus  100  may determine a combination of split shapes into which a coding unit is splittable according to predetermined data units by using the obtained index, and thus different combinations of split shapes may be used according to predetermined data units. 
       FIG. 28  illustrates various shapes of a coding unit determinable based on split shape information representable as a binary code, according to an embodiment. 
     According to an embodiment, the video decoding apparatus  100  may split a coding unit into various shapes by using block shape information and split shape information obtained by the bitstream obtainer  110 . Shapes into which a coding unit is splittable may correspond to various shapes including the shapes described through the above embodiments. 
     Referring to  FIG. 28 , the video decoding apparatus  100  may split a coding unit having a square shape into at least one direction from among a horizontal direction and a vertical direction and may split a coding unit having a non-square shape in a horizontal direction or a vertical direction, based on split shape information. 
     According to an embodiment, when the video decoding apparatus  100  is able to split a coding unit having a square shape in a horizontal direction and a vertical direction to obtain four square coding units, the number of split shapes that may be indicated by split shape information about the coding unit having the square shape may be 4. According to an embodiment, split shape information may be represented as a 2-digit binary code, and a binary code may be allocated to each split shape. For example, when a coding unit is not split, split shape information may be represented as (00)b; when a coding unit is split in a horizontal direction and a vertical direction, split shape information may be represented as (01)b; when a coding unit is split in a horizontal direction, split shape information may be represented as (10)b; and when a coding unit is spilt in a vertical direction, split shape information may be represented as (11)b. 
     According to an embodiment, when the video decoding apparatus  100  splits a coding unit having a non-square shape in a horizontal direction or a vertical direction, types of split shapes that may be indicated by split shape information may be determined according to the number of coding units into which a coding unit is split. Referring to  FIG. 28 , the video decoding apparatus  100  may split a coding unit having a non-square shape into 3 coding units according to an embodiment. The video decoding apparatus  100  may split a coding unit into two coding units, and in this case, split shape information may be represented as (10)b. The video decoding apparatus  100  may split a coding unit into three coding units, and in this case, split shape information may be represented as (11)b. The video decoding apparatus  100  may determine not to split a coding unit, and in this case, split shape information may be represented as (0)b. That is, in order to use a binary code indicating split shape information, the video decoding apparatus  100  may use variable length coding (VLC), instead of fixed length coding (FLC). 
     According to an embodiment, referring to  FIG. 28 , a binary code of split shape information indicating that a coding unit is not split may be represented as (0)b. When a binary code of split shape information indicating that a coding unit is not split is set to (00)b, all 2-bit binary codes of split shape information have to be used despite that there is no split shape information set to (01)b. However, as shown in  FIG. 28 , when 3 split shapes are used for a coding unit having a non-square shape, the video decoding apparatus  100  may determine not to split a coding unit even by using a 1-bit binary code (0)b as split shape information, thereby efficiently using a bitstream. However, split shapes of a coding unit having a non-square shape, which are indicated by split shape information, should not be interpreted as being limited to 3 shapes shown in  FIG. 28  and should be interpreted as being various shapes including the above embodiments. 
       FIG. 29  illustrates other shapes of a coding unit determinable based on split shape information representable as a binary code, according to an embodiment. 
     Referring to  FIG. 29 , the video decoding apparatus  100  may split a coding unit having a square shape in a horizontal direction or a vertical direction and may split a coding unit having a non-square shape in a horizontal direction or a vertical direction, based on split shape information. That is, split shape information may indicate that a coding unit having a square shape is split in one direction. In this case, a binary code of split shape information indicating that a coding unit having a square shape is not split may be represented as (0)b. When a binary code of split shape information indicating that a coding unit is not split is set to (00)b, all 2-bit binary codes of split shape information have to be used despite that there is no split shape information set to (01)b. However, as shown in  FIG. 29 , when 3 split shapes are used for a coding unit having a square shape, the video decoding apparatus  100  may determine not to split a coding unit even by using a 1-bit binary code (0)b as split shape information, thereby efficiently using a bitstream. However, split shapes of a coding unit having a square shape, which are indicated by split shape information, should not be interpreted as being limited to 3 shapes shown in  FIG. 29  and should be interpreted as being various shapes including the above embodiments. 
     According to an embodiment, block shape information or split shape information may be represented by using a binary code, and such information may be immediately generated as a bitstream. Alternatively, block shape information or split shape information representable as a binary code may not be immediately generated in a bitstream and may be used as a binary code input during context adaptive binary arithmetic coding (CABAC). 
     According to an embodiment, a process, performed by the video decoding apparatus  100 , of obtaining syntax about block shape information or split shape information through CABAC will be described. A bitstream including a binary code for the syntax may be obtained by the bitstream obtainer  110 . The video decoding apparatus  100  may detect a syntax element indicating the block shape information or the split shape information by de-binarizing a bin string included in the obtained bitstream. According to an embodiment, the video decoding apparatus  100  may obtain a set of binary bin strings corresponding to the syntax element to be decoded and may decode each bin by using probability information, and the video decoding apparatus  100  may repeatedly perform this process until a bin string including such decoded bins is the same as one of pre-obtained bin strings. The video decoding apparatus  100  may determine the syntax element by de-binarizing the bin string. 
     According to an embodiment, the video decoding apparatus  100  may determine syntax about a bin string by performing a decoding process of adaptive binary arithmetic coding, and may update a probability model for bins obtained by the bitstream obtainer  110 . Referring to  FIG. 28 , the bitstream obtainer  110  of the video decoding apparatus  100  may obtain a bitstream indicating a binary code indicating split shape information according to an embodiment. The video decoding apparatus  100  may determine syntax about the split shape information by using the obtained binary code having a size of 1 bit or 2 bits. In order to determine the syntax about the split shape information, the video decoding apparatus  100  may update a probability of each bit from among the 2 bits of the binary code. That is, the video decoding apparatus  100  may update a probability that may have a value of 0 or 1 when decoding a next bin according to whether a value of a first bin in the 2-bits of the binary code is 0 or 1. 
     According to an embodiment, while determining the syntax, the video decoding apparatus  100  may update a probability of the bins used in a process of decoding the bins of the bin string for the syntax, and the video decoding apparatus  100  may determine that a specific bit in the bin string has the same probability without updating the probability. 
     Referring to  FIG. 28 , while determining syntax by using a bin string indicating split shape information about a coding unit having a non-square shape, the video decoding apparatus  100  may determine the syntax about the split shape information by using one bin having a value of 0 when the coding unit having a non-square shape is not split. That is, when block shape information indicates that a current coding unit has a non-square shape, a first bin of a bin string for the split shape information may be 0 when the coding unit having a non-square shape is not split and may be 1 when the coding unit having a non-square shape is split into two or three coding units. Accordingly, a probability that a first bin of a bin string of split shape information about a coding unit having a non-square shape is 0 may be ⅓, and a probability that the first bin of the bin string of the split shape information about the coding unit having a non-square shape is 1 may be ⅔. As described above, because split shape information indicating that a coding unit having a non-square shape is not split may represent only a bin string of 1 bit having a value of 0, the video decoding apparatus  100  may determine syntax about the split shape information by determining whether a second bin is 0 or 1 only when the first bin of the split shape information is 1. According to an embodiment, when the first bin for the split shape information is 1, the video decoding apparatus  100  may decode a bin by determining that probabilities that the second bin is 0 and 1 are the same. 
     According to an embodiment, the video decoding apparatus  100  may use various probabilities for each bin while determining a bin of a bin string for split shape information. According to an embodiment, the video decoding apparatus  100  may differently determine probabilities of bins for split shape information according to a direction of a non-square block. According to an embodiment, the video decoding apparatus  100  may differently determine probabilities of bins for split shape information according to an area or a length of a long side of a current coding unit. According to an embodiment, the video decoding apparatus  100  may differently determine probabilities of bins for split shape information according to at least one from among a shape and a length of a long side of a current coding unit. 
     According to an embodiment, the video decoding apparatus  100  may determine that probabilities of bins for split shape information are the same with respect to coding units having a predetermined size or more. For example, the video decoding apparatus  100  may determine that probabilities of bins for split shape information are the same with respect to coding units having a size equal to or greater than 64 samples based on a length of a long side of each coding unit. 
     According to an embodiment, the video decoding apparatus  100  may determine an initial probability of bins constituting a bin string of split shape information based on a slice type (e.g., an I-slice, a P-slice, a B-slice, or the like). 
       FIG. 30  is a block diagram of an image encoding and decoding system  2000  for performing loop filtering. 
     An encoding end  2010  of the image encoding and decoding system  2000  transmits an encoded bitstream of an image, and a decoding end  2050  receives and decodes the bitstream and outputs a reconstruction image. The encoding end  2010  may have a configuration similar to that of a video encoding apparatus  200  which will be described below, and the decoding end  2050  may have a configuration similar to that of the video decoding apparatus  100 . 
     In the encoding end  2010 , a prediction encoder  2015  outputs a reference image through inter prediction and intra prediction, and a transformer and quantizer  2020  quantizes residual data between the reference image and a current input image into a quantized transform coefficient and outputs the quantized transform coefficient. An entropy encoder  2025  encodes and transforms the quantized transform coefficient into a bitstream and outputs the bitstream. The quantized transform coefficient is reconstructed as data in a spatial domain by a de-quantizer and inverse converter  2030 , and the reconstructed data in the spatial domain is output as a reconstruction image through a deblocking filter  2035  and a loop filter  2040 . The reconstruction image may be used as a reference image of a next input image through the prediction encoder  2015 . 
     Encoded image data from among the bitstream received by the decoding end  2050  is reconstructed as residual data in a spatial domain through an entropy decoder  2055  and a de-quantizer and inverse converter  2060 . Image data in a spatial domain is formed as the residual data and a reference image output from a prediction decoder  2075  are combined, and a deblocking filter  2065  and a loop filter  2070  may filter the image data in the spatial domain and may output a reconstruction image for a current original image. The reconstruction image may be used as a reference image for a next original image by the prediction decoder  2075 . 
     The loop filter  2040  of the encoding end  2010  performs loop filtering by using filter information input according to a user input or a system setting. The filter information used by the loop filter  2040  is output to the entropy encoder  2025 , and is transmitted along with the encoded image data to the decoding end  2050 . The loop filter  2070  of the decoding end  2050  may perform loop filtering based on the filter information input from the decoding end  2050 . 
       FIG. 31  illustrates an example of filtering units included in a largest coding unit and filtering performance information of a filtering unit, according to an embodiment. 
     When filtering units of the loop filter  2040  of the encoding end  2010  and the loop filter  2070  of the decoding end  2050  include data units similar to coding units according to an embodiment described with reference to  FIGS. 13 through 15 , filter information may include block shape information and split shape information of a data unit for indicating a filtering unit, and loop filtering performance information indicating whether loop filtering is performed on the filtering unit. 
     Filtering units included in a largest coding unit  2100  according to an embodiment may have the same block shape and split shape as coding units included in the largest coding unit  2100 . Also, the filtering units included in the largest coding unit  2100  according to an embodiment may be split based on sizes of the coding units included in the maximum coding units  2100 . Referring to  FIG. 31 , for example, the filtering units may include a filtering unit  2140  having a square shape and a depth of D, filtering units  2132  and  2134  having a non-square shape and a depth of D, filtering units  2112 ,  2114 ,  2116 ,  2152 ,  2154 , and  2164  having a square shape and a depth of D+1, filtering units  2162  and  2166  having a non-square shape and a depth of D+1, and filtering units  2122 ,  2124 ,  2126 , and  2128  having a square shape and a depth of D+2. 
     The block shape information, the split shape information (depth), and the loop filtering performance information of the filtering units included in the largest coding unit  2100  may be encoded as shown in Table 3. 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                   
                 Block Shape 
                   
               
               
                 Depth 
                 Information 
                 Loop Filtering Performing Information 
               
               
                   
               
             
            
               
                 D 
                 0: SQUARE 
                 0(2140) 
               
               
                   
                 1: NS_VER 
                 0(2132), 1(2134) 
               
               
                   
                 2: NS_HOR 
               
               
                 D + 1 
                 0: SQUARE 
                 1(2112), 1(2114), 0(2116), 1(2152), 0(2154), 
               
               
                   
                   
                 1(2164) 
               
               
                   
                 1: NS_VER 
               
               
                   
                 2: NS_HOR 
                 0(2162), 1(2166) 
               
               
                 D + 2 
                 0: SQUARE 
                 1(2122), 0(2124), 0(2126), 0(2128) 
               
               
                   
                 1: NS_VER 
               
               
                   
                 2: NS_HOR 
               
               
                   
               
            
           
         
       
     
     A process of determining a plurality of coding units by recursively splitting a coding unit according to block shape information and block split information according to an embodiment is the same as that described with reference to  FIG. 23 . Loop filtering performance information of filtering units according to an embodiment indicates that loop filtering is performed on the filtering units when a flag value is 1, and indicates that loop filtering is not performed on the filtering units when a flag value is 0. Referring to Table 1, information of data units for determining filtering units to be filtered by the loop filters  2040  and  2070  may all be encoded and transmitted as filter information. 
     Because coding units configured according to an embodiment are coding units configured to minimize an error with an original image, it is expected to have a high spatial correlation in the coding units. Accordingly, because a filtering unit is determined based on a coding unit according to an embodiment, an operation of determining a filtering unit, separate from determining of a coding unit, may be omitted. Also, accordingly, because a filtering unit is determined based on a coding unit according to an embodiment and thus information for determining a split shape of the filtering unit may be omitted, a transfer bit rate of filter information may be saved. 
     Although it is described in the above embodiments that a filtering unit is determined based on a coding unit according to an embodiment, a filtering unit may be split based on a coding unit until an arbitrary depth, and thus a shape of the filtering unit may be determined up to only the arbitrary depth. 
     The determining of a filtering unit described in the above embodiments may be applied not only to loop filtering but also to various embodiments such as deblocking filtering and adaptive loop filtering. 
     According to an embodiment, the video decoding apparatus  100  may split a current coding unit by using at least one of block shape information and split shape information, and the block shape information may be pre-determined to indicate using only a square shape and the split shape information may be pre-determined to indicate that the current coding unit is not split or split into 4 square coding units. That is, coding units of the current coding unit may always have a square shape according to the block shape information and the current coding unit may not be split or split into 4 square coding units based on the split shape information. The video decoding apparatus  100  may obtain, by using the bitstream obtainer  110 , a bitstream generated by using a predetermined encoding method that is pre-determined to only use such block shapes and split shapes, and the video decoding apparatus  100  may use only the pre-determined block shapes and split shapes. In this case, because the video decoding apparatus  100  may solve a compatibility problem with the predetermined encoding method by using a predetermined decoding method similar to the predetermined encoding method. According to an embodiment, when the video decoding apparatus  100  uses the predetermined decoding method using only the pre-determined block shapes and split shapes from among various shapes that may be indicated by the block shape information and the split shape information, the block shape information only indicates a square shape, and thus the video decoding apparatus  100  may not perform a process of obtaining the block shape information from the bitstream. Syntax indicating whether to use the predetermined decoding method may be used, and such syntax may be obtained from the bitstream according to data units having various shapes that may include a plurality of coding units such as sequences, pictures, slice units, and largest coding units. That is, the bitstream obtainer  110  may determine whether syntax indicating the block shape information is to be obtained from the bitstream based on syntax indicating whether the predetermined decoding method is used. 
       FIG. 33  illustrates an index according to a Z-scan order of a coding unit according to an embodiment. 
     The video decoding apparatus  100  according to an embodiment may scan lower data units included in an upper data unit according to a Z-scan order. Also, the video decoding apparatus  100  according to an embodiment may sequentially access data according to a Z-scan index in a coding unit included in a processing block or a largest coding unit. 
     The video decoding apparatus  100  according to an embodiment may split a reference coding unit into at least one coding unit as described with reference to  FIGS. 13 and 14 . In this case, coding units having a square shape and coding units having a non-square shape may co-exist in the reference coding unit. The video decoding apparatus  100  according to an embodiment may access data according to a Z-scan index included in each coding unit in the reference coding unit. In this case, a method of applying a Z-scan index may vary according to whether a coding unit having a non-square shape exists in the reference coding unit. 
     According to an embodiment, when a coding unit having a non-square shape does not exist in the reference coding unit, coding units of a lower depth in the reference coding unit may have continuous Z-scan indices. For example, according to an embodiment, a coding unit of an upper depth may include four coding units of a lower depth. Boundaries of the four coding units of the lower depth may be continuous, and the coding units of the lower depth may be scanned in a Z-scan order according to indices indicating the Z-scan order. The indices indicating the Z-scan order according to an embodiment may be set to numbers that increase according to the Z-scan order for the coding units. In this case, deeper coding units of the same depth may be scanned according to the Z-scan order. 
     According to an embodiment, when at least one coding unit having a non-square shape exists in the reference coding unit, the video decoding apparatus  100  may split each of the coding units in the reference coding unit into sub-blocks, and may scan the split sub-blocks according to the Z-scan order. For example, when a coding unit having a non-square shape in a vertical direction or a horizontal direction exists in the reference coding unit, Z-scan may be performed by using split sub-blocks. Also, for example, when the reference coding unit is split into an odd number of coding units, Z-scan may be performed by using sub-blocks. A sub-block is a coding unit that is no longer split or a coding unit obtained by splitting an arbitrary coding unit, and may have a square shape. For example, four sub-blocks having a square shape may be split from a coding unit having a square shape. Also, for example, two sub-blocks having a square shape may be split from a coding unit having a non-square shape. 
     Referring to  FIG. 33 , for example, the video decoding apparatus  100  according to an embodiment may scan coding units  2302 ,  2304 ,  2306 ,  2308 , and  2310  of a lower depth in a coding unit  2300  according to a Z-scan order. The coding unit  2300  and the coding units  2302 ,  2304 ,  2306 ,  2308 , and  2310  are respectively an upper coding unit and lower coding units. The coding unit  2300  includes the coding units  2306  and  2310  having a non-square shape in a horizontal direction. The coding units  2306  and  2310  having a non-square shape have discontinuous boundaries with the coding units  2302  and  2304  that are adjacent to each other and have a square shape. Also, the coding unit  2308  has a square shape, and is a coding unit at the center when a coding unit having a non-square shape is split into an odd number of coding units. Like the coding units  2306  and  2310  having a non-square shape, the coding unit  2308  has discontinuous boundaries with the coding units  2302  and  2304  that are adjacent to each other and have a square shape. When the coding unit  2300  includes the coding units  2306  and  2310  having a non-square shape or the coding unit  2308  located at the center when a coding unit having a non-square shape is split into an odd number of coding units, because adjacent boundaries between coding units are discontinuous, continuous Z-scan indices may not be set. Accordingly, the video decoding apparatus  100  may continuously set Z-scan indices by splitting coding units into sub-blocks. Also, the video decoding apparatus  100  may perform continuous Z-scan on the coding units  2306  and  2310  having a non-square shape or the coding unit  2308  located at the center of an odd number of coding units having a non-square shape. 
     A coding unit  2320  of  FIG. 33  is obtained by splitting the coding units  2302 ,  2304 ,  2306 ,  2308 , and  2310  in the coding unit  2300  into sub-blocks. Because a Z-scan index may be set for each of the sub-blocks and adjacent boundaries between the sub-blocks are continuous, the sub-blocks may be scanned according to a Z-scan order. For example, in a decoding apparatus according to an embodiment, the coding unit  2308  may be split into sub-blocks  2322 ,  2324 ,  2326  and  2328 . In this case, the sub-blocks  2322  and  2324  may be scanned after data processing is performed on a sub-block  2330 , and the sub-blocks  2326  and  2328  may be scanned after data processing is performed on a sub-block  2332 . Also, the sub-blocks may be scanned according to the Z-scan order. 
     In the above embodiments, data units are scanned according to a Z-scan order for data storage, data loading, and data accessing. 
     Also, in the above embodiments, although data units may be scanned according to a Z-scan order, a scan order of data units may be one of various orders such as a raster scan order, an N-scan order, an up-right diagonal scan order, a horizontal scan order, and a vertical scan order, and should not be limited to the Z-scan order. 
     Also, in the above embodiments, although coding units in a reference coding unit are scanned, the present disclosure is not limited thereto and a target to be scanned may be an arbitrary block in a processing block or a largest coding unit. 
     Also, in the above embodiments, although a block is split into sub-blocks and scanning is performed according to a Z-scan order only when at least one block having a non-square shape exists, a block may be split into sub-blocks and scanning may be performed according to a Z-scan order even when a block having a non-square shape does not exist for a simplified embodiment. 
     The video decoding apparatus  100  according to an embodiment may generate prediction data by performing inter prediction or intra prediction on a coding unit, may generate residual data by performing inverse transformation on a transform unit included in a current coding unit, and may reconstruct the current coding unit by using the generated prediction data and the residual data. 
     A prediction mode of a coding unit according to an embodiment may be at least one of an intra mode, an inter mode, and a skip mode. According to an embodiment, a prediction mode may be independently selected according to coding units. 
     When a coding unit having a 2N×2N shape is split into two coding units having a 2N×N shape or a N×2N shape according to an embodiment, inter mode prediction and intra mode prediction may be separately performed on each coding unit. Also, a skip mode may be applied to the coding units having the 2N×N or N×2N shape according to an embodiment. 
     The video decoding apparatus  100  according to an embodiment may allow performing bi-prediction in a skip mode of a coding unit having a 8×4 or 4×8 shape. Because only skip mode information about a coding unit is received in a skip mode, the use of residual data for the coding unit is omitted. Accordingly, in this case, an overhead of de-quantization and inverse transformation may be reduced. Instead, the video decoding apparatus  100  according to an embodiment may allow performing bi-prediction on a coding unit to which a skip mode is applied, thereby improving decoding efficiency. Also, the video decoding apparatus  100  according to an embodiment may set an interpolation tap number to a relatively small value during motion compensation while allowing performing bi-prediction on a coding unit having a 8×4 or 4×8 shape, thereby efficiently using a memory bandwidth. For example, an interpolation filter having a tap number less than 8 (e.g., a 2-tap interpolation filter), instead of an 8-tap interpolation filter, may be used. 
     Also, the video decoding apparatus  100  according to an embodiment may signal intra or inter prediction information about each region included in a current coding unit by splitting the region into a pre-set shape (e.g., diagonal-based split). 
     The video decoding apparatus  100  according to an embodiment may obtain a prediction sample of a current coding unit using an intra mode by using adjacent samples of the current coding unit. In this case, intra prediction is performed by using adjacent samples that are pre-reconstructed, and the samples are referred to as reference samples. 
       FIG. 34  is a diagram of a reference sample for intra prediction of a coding unit, according to an embodiment. Referring to  FIG. 34 , for a coding unit  2400  where a block shape is a non-square shape, a length in a horizontal direction is w, and a length in a vertical length is h, w+h upper reference samples  2402 , w+h left reference samples  2404 , and one upper left reference sample  2406  are required, that is, the total number of 2(w+h)+1 reference samples are required. In order to prepare a reference sample, padding may be performed on a part where the reference sample does not exist, and a reference sample filtering process may be performed for each prediction mode to reduce a quantization error included in a reconstructed reference sample. 
     Although the number of reference samples when a block shape of a current coding unit is a non-square shape has been described in the above embodiments, the number of reference samples is equally applied even when a current coding unit is a rectangular shape. 
     The above various embodiments describe an operation related to an image decoding method performed by the video decoding apparatus  100 . An operation of the video encoding apparatus  200  for performing an image encoding method corresponding to a reverse order process of the image decoding method will be described through various embodiments. 
       FIG. 12  is a block diagram of the video encoding apparatus  200  for encoding an image based on at least one from among block shape information and split shape information, according to an embodiment. 
     The video encoding apparatus  200  may include an encoder  220  and a bitstream generator  210 . The encoder  220  may receive an input image and may encode the input image. The encoder  220  may encode the input image and may obtain at least one syntax element. The syntax element may include at least one from among skip flag, prediction mode, motion vector difference, motion vector prediction method (or index), transform quantized coefficient, coded block pattern, coded block flag, intra prediction mode, direct flag, merge flag, delta QP, reference index, prediction direction, and transform index. The encoder  220  may determine a context model based on block shape information including at least one from among a ratio or a size of a shape, a direction, a width, and a height of a coding unit. 
     The bitstream generator  210  may generate a bitstream based on the encoded input image. For example, the bitstream generator  210  may generate the bitstream by entropy encoding the syntax element based on the context model. Also, the video encoding apparatus  200  may transmit the bitstream to the video decoding apparatus  100 . 
     According to an embodiment, the encoder  220  of the video encoding apparatus  200  may determine a shape of a coding unit. For example, the coding unit may have a square shape or a non-square shape, and information indicating the shape may be included in the block shape information. 
     According to an embodiment, the encoder  220  may determine which shape the coding unit is to be split into. The encoder  220  may determine a shape of at least one coding unit included in the coding unit, and the bitstream generator  210  may generate the bitstream including split shape information including information about the shape of the coding unit. 
     According to an embodiment, the encoder  220  may determine whether the coding unit is split or not split. When the encoder determines that only one coding unit is included in the coding unit or the coding unit is not split, the bitstream generator  210  may generate the bitstream including the split shape information indicating that the coding unit is not split. Also, the encoder  220  may split the coding unit into a plurality of coding units, and the bitstream generator  210  may generate the bitstream including the split shape information indicating that the coding unit is split into the plurality of coding units. 
     According to an embodiment, information indicating the number of coding units into which the coding unit is to be split or a direction in which the coding unit is to be split may be included in the split shape information. For example, the split shape information may indicate that the coding unit is split in at least one direction from among a vertical direction and a horizontal direction or is not split. 
     The video encoding apparatus  200  determines information about a split shape mode based on the split shape mode of the coding unit. The video encoding apparatus  200  determines the context model based on at least one from among the ratio or the size of the shape, the direction, the width, and the height of the coding unit. The video encoding apparatus  200  generates the information about the split shape mode for splitting the coding unit based on the context model as the bitstream. 
     In order to determine the context model, the video encoding apparatus  200  may obtain an arrangement for corresponding at least one from among the ratio or the size of the shape, the direction, the width, and the height of the coding unit to an index for the context model. The video encoding apparatus  200  may obtain the index for the context model based on at least one from among the ratio or the size of the shape, the direction, the width, and the height of the coding unit in the arrangement. The video encoding apparatus  200  may determine the context model based on the index for the context model. 
     In order to determine the context model, the video encoding apparatus  200  may determine the context model further based on block shape information including at least one from among a ratio or a size of a shape, a direction, a width, and a height of a neighboring coding unit adjacent to the coding unit. Also, the neighboring coding unit may include at least one from among coding units located at a left lower side, a left side, a left upper side, an upper side, a right upper side, a right side, or a right lower side of the coding unit. 
     Also, in order to determine the context model, the video encoding apparatus  200  may compare a length of a width of an upper neighboring coding unit with a length of the width of the coding unit. Also, the video encoding apparatus  200  may compare a length of a height of left and right neighboring coding units with a length of the height of the coding unit. Also, the video encoding apparatus  200  may determine the context model based on comparison results. 
     An operation of the video encoding apparatus  200  is similar to an operation of the video decoding apparatus  100  described with reference to  FIGS. 13 through 34 , and thus a detailed explanation thereof is not provided here. 
     The embodiments may be implemented as a computer-executable program, and the program may be stored in a medium. 
     The medium may continuously store the computer-executable program, or may temporarily store the computer-executable program to execute or download the computer-executable program. Also, the medium may be any of various recording means or storage means including a single hardware or a combination of a plurality of hardware, and may be distributed in a network without being limited to a medium directly connected to a computer system. The medium may be configured to store program instructions, and examples of the medium may include a magnetic medium such as a hard disk, a floppy disk, or a magnetic tape, an optical recording medium such as a compact disc read-only memory (CD-ROM) or a digital versatile disc (DVD), a magneto-optical medium such as a floptical disk, a ROM, a random-access memory (RAM), and a flash memory. Also, other examples of the medium may include a recording medium and a storage medium managed by an application store that distributes applications or a site or a server that supplies or distributes various other software. 
     While the disclosure has been particularly shown and described with reference to embodiments thereof, it will be understood by one of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope of the disclosure as defined by the appended claims.