WO2018143687A1

WO2018143687A1 - Method and apparatus for performing transformation by using row-column transform

Info

Publication number: WO2018143687A1
Application number: PCT/KR2018/001378
Authority: WO
Inventors: 구문모; 귈레우즈오누르
Original assignee: 엘지전자(주)
Priority date: 2017-02-01
Filing date: 2018-02-01
Publication date: 2018-08-09

Abstract

The present invention provides a method for performing transformation by using a row-column transform, the method comprising the steps of: deriving a row transform set, a column transform set, and first and second permutation matrices on the basis of a given transform matrix (H) and a given error tolerance parameter; acquiring row-column transform (RCT) coefficients on the basis of the row transform set, the column transform set, and the first and second permutation matrices; and performing quantization and entropy-encoding of the RCT coefficients, wherein the RCT coefficients are acquired by applying the first permutation matrix, the row transform set, the column transform set, and the second permutation matrix in that order.

Description

【Specification】

[Name of invention]

Method and apparatus for performing transformation using row-column transformation

Technical Field

The present invention relates to a method and apparatus for encoding / decoding a video signal, and more particularly to a row-column having better characteristics or orthogonality or separabiity to a given target transform. A technique for designing a transform (row-column transform, hereinafter referred to as 'RCT').

Background Art

Compression coding refers to a series of signal processing techniques for transmitting digitized information through a communication line or for storing in a form suitable for a storage medium. Media such as an image, an image, an audio, and the like may be a target of compression encoding. In particular, a technique of performing compression encoding on an image is called video image compression. Next-generation video content will be characterized by high spatial resolution, high frame rate and high dimensionality of scene representation. Processing such content would result in a tremendous increase in terms of memory storage, memory access rate, and processing power.

As a result, new ways to process next-generation video content more efficiently You need to design your coding. In particular, when applying transform, it is necessary to design a transform that is much more efficient in terms of encoding efficiency and complexity.

[Detailed Description of the Invention]

[Technical problem]

The present invention proposes a method of improving coding efficiency through a new transform design.

The present invention seeks to design a transform that provides a low complexity and reasonable coding gain.

The present invention intends to design a row-column transform (RCT) that approximates a target transform well.

An object of the present invention is to provide a method of designing a row-column transform (RCT) having characteristics of orthogonality or separability.

The present invention proposes an encoder / decoder structure to reflect a new transform design.

Technical Solution

The present invention provides a method for improving coding efficiency through a new transform design.

The present invention provides a method for designing a row-column transfum (RCT) that can approximate more important transform basis vectors by applying weights to transform basis vectors. The present invention provides a method of designing all row-column transforms (RCTs) to have orthogonality, respectively.

The present invention provides a method of approximating by multiplying a permutation matrix before a target transform in order to increase an approximation of a row-column transform (RCT).

The present invention provides a method of designing a separable row-column transform (RCT) having only one transform in a row direction and one in a column direction.

The present invention provides a method of applying an absolute value operator when applying a Hungarian method to find a substitution matrix.

【Effects of the Invention】

The present invention can design a much more efficient row-column transformation in terms of encoding efficiency and complexity when applying transform to encode and transmit still images or moving images. As such, the coding efficiency can be improved through the new transform design.

[Brief Description of Drawings]

1 is a schematic block diagram of an encoder in which encoding of a video signal is performed as an embodiment to which the present invention is applied.

2 is a schematic block diagram of a decoder in which decoding of a video signal is performed according to an embodiment to which the present invention is applied.

3 is a diagram illustrating a division structure of a coding unit according to an embodiment to which the present invention is applied. It is a figure for demonstrating.

4 is an embodiment to which the present invention is applied and shows a schematic block diagram of an RCT unit to which an RCT is applied.

5 is an embodiment to which the present invention is applied and is a diagram for explaining a process of applying ROT.

6 is a diagram for describing a process of applying an RCT in which two substitution matrices (P, Q) are used as an embodiment to which the present invention is applied.

7 and 8 illustrate schematic block diagrams of an RCT unit for determining an RCT using two substitution matrices (P, Q) and an inverse RCT unit corresponding thereto according to embodiments to which the present invention is applied.

9 is an embodiment to which the present invention is applied and is a flowchart illustrating a process of obtaining RCT coefficients.

10 is a flowchart illustrating a process of performing decoding based on RCT coefficients according to an embodiment to which the present invention is applied.

[Best form for implementation of the invention]

The present invention relates to a row transform set based on a given transformation matrix (H) and an error tolerance parameter in a method for performing a transformation using a row-column transform. ), Deriving a column transform set and first and second permutation matrices; Obtaining a Row-Column Transform (RCT) coefficient based on the row transform set, the column transform set, and the first and second substitution matrices. step; And performing quantization and entropy encoding on the RCT coefficients, wherein the RCT coefficients are obtained by sequentially applying the first substitution matrix, the row transform set, the column transform set, and the second substitution matrix. It provides a method characterized in that.

In the present invention, the first and second substitution matrices are derived through an optimization process, and the optimization process is determined based on matching between a row-column transform (RCT) matrix and the given transform matrix (H), A row-column transform matrix is derived using the row transform set and the column transform set.

The present invention is characterized in that the weight is applied in the process of inducing RCT. For example, the RCT matrix may be weighted to transform basis vectors.

In the present invention, the type Garlician method is applied, and the type Garlician method is performed by using an input to which the absolute value operator is applied.

In the present invention, each of the transforms in the row transform set and the column transform set is orthogonal.

In the present invention, each of the row transform set and the column transform set is a separable transform having a single transform.

The present invention utilizes a row-column transform to perform an inverse transform. CLAIMS 1. A method, comprising: receiving a video signal; Obtaining coefficients from the video signal through entropy decoding and dequantization; Performing inverse-permutation and inverse-transform on the coefficients; And reconstructing the video signal using an inverse transformed coefficient, wherein the inverse transformed coefficient is applied by a first inverse transform matrix, an inverse-column transform set, an inverse-row transform set, and a second inverse transform matrix in order. It provides a method characterized in that it is obtained by.

In the present invention, performing the inverse transform comprises: applying a first inverse substitution matrix to the coefficients; Performing an inverse-column transform on coefficients to which the first inverse substitution matrix is applied; Performing an inverse-row transform on the inverse-column transformed coefficients; And applying a second inverse substitution matrix to the inverse-row transformed coefficients.

In the present invention, the inverse transform matrix is characterized by being weighted to transform basis vectors.

In the present invention, each transform in the inverse-row transform set and the inverse-column transform set is characterized by being orthogonal.

In the present invention, each of the inverse-row transform set and the inverse-column transform set is a separable transform having a single transform.

The present invention utilizes a row-column transform to perform the transformation. In a performing apparatus, a row transform set, a column transform set, and first and second substitution matrices are based on a given transformation matrix H and an error tolerance parameter. a transformation unit for deriving permutation matrices and acquiring " RCT " coefficients based on the row transform set, the column transform set, and the first and second substitution matrices; A quantization unit configured to perform quantization on the quantized RCT coefficients, and an entropy encoding unit performing entropy encoding on the quantized RCT coefficients, wherein the RCT coefficients include the first substitution matrix, the row transform set, the column transform set, and the second transform coefficient. An apparatus is provided which is obtained by applying a substitution matrix in order.

The present invention provides an apparatus for performing inverse transformation using a row-column transform, comprising: a receiver configured to receive a video signal; An entropy decoding unit for entropy decoding the residual signal; An inverse quantizer for inversely quantizing the entropy decoded residual signal to obtain a coefficient; An inverse transform unit performing inverse-permutation and inverse transform on the coefficients; And a reconstruction unit for reconstructing the video signal by using an inverse transform coefficient, wherein the inverse transform coefficient is applied by a first inverse transform matrix, an inverse-column transform set, an inverse-row transform set, and a _second inverse transform matrix in order. It provides an apparatus characterized in that it is obtained by.

[Form for implementation of invention]

Hereinafter, with reference to the accompanying drawings, the configuration and operation of the embodiment of the present invention The configuration and operation of the present invention described with reference to the drawings will be described as one embodiment, and the technical idea and core construction and operation of the present invention are not limited thereto.

In addition, the terminology used in the present invention was selected as a general term widely used as possible now, in a specific case will be described using terms arbitrarily selected by the applicant. In such a case, since the meaning is clearly described in the detailed description of the relevant part, it should not be interpreted simply by the name of the term used in the description of the present invention, and it should be understood that the meaning of the term should be understood and interpreted. .

In addition, terms used in the present invention may be replaced for more appropriate interpretation when there are general terms selected to describe the invention or other terms having similar meanings. For example, signals, data, samples, pictures, frames, blocks, etc. may be appropriately replaced and interpreted in each coding process. In addition, partitioning, decomposition, splitting, and division may be appropriately replaced and interpreted in each coding process. 1 is a schematic block diagram of an encoder in which encoding of a video signal is performed as an embodiment to which the present invention is applied.

1, the encoder 100 includes an image segmentation unit 110, the conversion unit (1 ^20), a quantization unit 130, an inverse quantization unit 140, an inversion unit 150, a filtering unit (ISO) , Decryption It may include a decoded picture buffer (DPB) 170, an inter predictor 180, an intra predictor 185, and an entropy encoder 190. The image divider 110 may divide an input image (or a picture or a frame) input to the encoder 100 into one or more processing units. For example, the processing unit encoding a tree unit may _{be: (Transform Unit Τϋ) (CTU} : Coding Tree Unit), coding units (CU:: Coding Unit), prediction unit (PU Prediction Unit) or a conversion unit.

However, the terms are only used for the convenience of description of the present invention, the present invention is not limited to the definition of the terms. In addition, in the present specification, for convenience of description, the term coding unit is used as a unit used in encoding or decoding a video signal, but the present invention is not limited thereto and may be appropriately interpreted according to the present invention.

The encoder 100 may generate a residual signal by subtracting a prediction signal output from the inter predictor 180 or the intra predictor 185 from the input image signal, and generate the residual signal. Is transmitted to the conversion unit 120>.

The transform unit 120 may generate a transform coefficient by applying a transform technique to the residual signal. The conversion process may be applied to pixel blocks having the same size as the square, or may be applied to blocks of variable size rather than square. The conversion technique described in the present invention

Row-Column Transform (RCT) may be used, which is used herein. Named the RCT department. The RCT unit may be included in or replaced with the conversion unit. In addition, the transform unit may use various transform techniques, and one of them may use RCT.

For example, the present invention provides a method of designing a Row-Column Transform (RCT) that can approximate more important transform basis vectors by applying weights to transform basis vectors.

In addition, the present invention provides a method of designing all row-column transforms (RCTs) to have orthogonality.

The present invention also provides a method of approximating by multiplying a permutation matrix before a target transform in order to increase the approximation of a row-column transform (RCT).

In addition, the present invention provides a method of designing a separable row-column transform (RCT) having only one transform in a row direction and one in a column direction.

In addition, the present invention provides a method of applying an absolute value operator when applying a Hungarian method to find a substitution matrix.

Specific embodiments thereof will be described in more detail herein.

The quantization unit 130 quantizes the transform coefficients to the entropy encoding unit 190. In addition, the entropy encoding unit 190 may entropy-code the quantized signal and output the quantized signal in a bitstream.

The quantized signal output from the quantization unit 130 may be used to generate a prediction signal. For example, the quantized signal may recover the residual signal by applying inverse quantization and inverse transformation through inverse quantization unit 140 and inverse transform unit 150 in a loop. The reconstructed signal may be generated by adding the reconstructed residual signal to a prediction signal output from the inter predictor 180 or the intra predictor 185.

Meanwhile, deterioration of the block boundary may occur due to the quantization error generated in the above compression process. This phenomenon is called blocking artifacts, which is one of the important factors in evaluating image quality. In order to reduce such deterioration, a filtering process may be performed. Through this filtering process, the image quality can be improved by removing the blocking degradation and reducing the error of the current picture.

The filtering unit 160 applies filtering to the reconstruction signal and outputs it to the reproduction apparatus or transmits the decoded picture buffer to the decoded picture buffer 170. The filtered signal transmitted to the decoded picture buffer 170 may be used as the reference picture in the inter predictor 180. As such, by using the filtered picture as a reference picture in the inter prediction mode, not only image quality but also encoding efficiency may be improved.

The decoded picture buffer 170 references the filtered picture in the inter prediction unit 180. You can save it for use as a picture.

The inter prediction unit 180 performs temporal prediction and / or spatial prediction to remove temporal redundancy and / or spatial redundancy with reference to a reconstructed picture. Here, since the reference picture used to perform the prediction is a transformed signal that has been quantized and dequantized in units of blocks at the time of encoding / decoding, a blocking artifact or a ringing artifact may exist. have.

Accordingly, the inter prediction unit 180 may interpolate the signals between pixels in sub-pixel units by applying a lowpass filter in order to solve the performance degradation caused by the block continuity or quantization. Herein, the subpixel refers to a virtual pixel generated by applying an interpolation filter, and the integer pixel refers to an actual pixel existing in the reconstructed picture. As the interpolation method, linear interpolation, bi-linear interpolation, and Wiener filter may be applied.

The interpolation filter may be applied to a reconstructed picture to improve the precision of prediction. For example, the inter prediction unit 180 generates an interpolation pixel by applying an interpolation filter to integer pixels, and uses an interpolated block composed of interpolated pixels as a prediction block. Predictions can be performed.

Meanwhile, the intra predictor 185 may predict the current block by referring to sample poles around the block to which current encoding is to be performed. The intra The prediction unit 185 may perform the following process to perform intra prediction. First, reference samples necessary for generating a prediction signal may be prepared. The prediction signal may be generated using the prepared reference sample. Then, the prediction mode is encoded. In this case, the reference sample may be prepared through reference sample padding and / or reference sample filtering. Since the reference sample has been predicted and reconstructed, there may be a quantization error. Accordingly, the reference sample filtering process may be performed for each prediction mode used for intra prediction to reduce such an error. A prediction signal generated through the inter predictor 180 or the intra predictor 185 may be used to generate a reconstruction signal or to generate a residual signal. 2 is a schematic block diagram of a decoder in which decoding of a video signal is performed as an embodiment to which the present invention is applied.

Referring to FIG. 2, the decoder 200 includes a parser (not shown), an entropy decoder 210, an inverse quantizer 220, an inverse transformer 230, a filter 240, and a decoded picture buffer (DPB). It may include a decoded picture buffer unit) 250, an inter predictor 260, and an intra predictor 265.

The reconstructed video signal output through the decoder 200 may be reproduced through the reproducing apparatus.

The decoder 200 may receive a signal output from the encoder 100 of FIG. 1, and the received signal may be entropy decoded through the entropy decoding unit 210. have.

The inverse quantization unit 220 obtains a transform coefficient from the entropy decoded signal using the quantization stem size information.

The inverse transform unit 230 inversely transforms the transform coefficient to obtain a residual signal. Here, the present invention provides a method of designing a new RCT transform, and the embodiments described herein may be applied. In addition, the processes of the embodiments described in the encoder may be reversely applied.

A reconstructed signal is generated by adding the obtained residual signal to a prediction signal output from the inter predictor 260 or the intra predictor 265.

The filtering unit 240 applies filtering to the reconstructed signal and outputs the filtering to the reproducing apparatus or transmits it to the decoded picture buffer unit 250. The filtered signal transmitted to the decoded picture buffer unit 250 may be used as the reference picture in the inter predictor 260.

In the present specification, the embodiments described in the transform unit 120 and the respective functional units of the encoder 100 may be equally applied to the inverse transform unit 230 and the functional units of the decoder, respectively. 3 is a diagram for describing a division structure of a coding unit according to an embodiment to which the present invention is applied.

The encoder converts one image (or picture) into a rectangular coding tree unit (CTU). Coding Tree Unit) can be divided into units. Then, one CTU is sequentially encoded according to a raster scan order. For example, the size of the CTU may be set to any one of 64x64, 32x32, and 16x16, but the present invention is not limited thereto. The encoder may select and use the size of the CTU according to the resolution of the input video or the characteristics of the input video. The CTU may include a coding tree block (CTB) for luma components and a coding tree block (CTB) for two chroma components.

One CTU may be decomposed into a quadtree (QT) structure. For example, one CTU may be divided into four units having a square shape and each side is reduced by half in length. The decomposition of this QT structure can be done recursively.

Referring to FIG. 3, the root node of the QT may be associated with a CTU. The QT may be split until it reaches a leaf node, where the leaf node may be referred to as a coding unit (CU).

A CU may mean a basic unit of coding in which an input image is processed, for example, intra / inter prediction is performed. The CU may include a coding block (CB) for luma components and a CB for two chroma components. For example, the size of the CU may be determined by any one of 64 × 6 ⁴ , 32 × 32, 16 × 16, and 8 × 8. However, the present invention is not limited thereto, and in the case of a high resolution image, the size of the CU may be larger or more diverse. Referring to FIG. 3, a CTU corresponds to a root node and has a smallest depth (ie, level 0) value. The CTU may not be divided according to the characteristics of the input image. In this case, the CTU corresponds to a CU.

The CTU may be decomposed in QT form, and as a result, lower nodes having a depth of level 1 may be generated. And, a node that is no longer partitioned (ie, a leaf node) in a lower node having a depth of level 1 corresponds to a CU. For example, in FIG. 3 (b), CU (a), CU (b), and CU (j), which perform on nodes a, b, and j, are divided once in the CTU and have a depth of level 1. FIG.

At least one of the nodes having a depth of level 1 may be split into QT again. And, a node that is no longer partitioned (ie, a leaf node) in a lower node having a depth of level 2 corresponds to a CU. For example, in FIG. 3 (b), CU (C), CU (h), CU (i), which complies with nodes c, h and i, are divided twice in the CTU and have a depth of level 2. FIG.

In addition, at least one of the nodes having a depth of 2 may be divided into QTs. And, a node that is no longer partitioned (ie, a leaf node) in a lower node having a depth of level 3 corresponds to a CU. For example, in FIG. 3 (b), CU (d), CU (e), CU (f), and CU (g) for nodes d, e, f, and g are divided three times in the CTU, and level 3 Has a depth of

In the encoder, the maximum size or the minimum size of the CU may be determined according to characteristics (eg, resolution) of the video image or in consideration of encoding efficiency. In addition, information on this or information capable of deriving the information may be included in the bitstream. Can be. A CU having a maximum size may be referred to as a largest coding unit (LCU), and a CU having a minimum size may be referred to as a smallest coding unit (SCU).

In addition, a CU having a tree structure may be hierarchically divided with predetermined maximum depth information (or maximum level information). Each partitioned CU may have depth information. Since the depth information indicates the number and / or degree of division of the CU, the depth information may include information about the size of the CU.

Since the LCU is divided into QT forms, the size of the SCU can be obtained by using the size and maximum depth information of the LCU. Or conversely, using the size of the SCU and the maximum depth information of the tree, the size of the LCU can be obtained.

For one CU, information indicating whether the corresponding CU is split may be delivered to the decoder. For example, the information may be defined as a split pull lag, and may be represented by a syntax element "split_cu_f lag". The division flag may be included in all CUs except the SCU. For example, if the split flag value is '1', the CU is divided into 4 CUs again, and if the split flag value is 0, the CU is no longer divided and the coding process for the CU is not divided. Can be performed.

In the embodiment of FIG. 3, the division process of the OJ has been described as an example, but the QT structure described above may also be applied to the division process of a transform unit (TU), which is a basic unit for performing transformation.

A TU may be hierarchically divided into QT structures from a CU to be coded. example For example, a CU may correspond to a root node of a tree for a transform unit (TU).

Since the TU is divided into QT structures, the TU divided from the CU may be divided into smaller lower TUs. For example, the size of the TU may be determined by any one of 32x32, 16x16, 8x8, and 4x4. However, the present invention is not limited thereto, and in the case of a high resolution image, the size of the TU may be larger or more diverse.

For one TU, information indicating whether the corresponding TU is divided may be delivered to the decoder. For example, the information may be defined as a split transform flag and may be represented by a syntax element "split_transform_flag". The division conversion flag may be included in all TUs except the TU of the minimum size. For example, when the value of the division conversion flag is '1', the corresponding TU is divided into four TUs again. When the value of the division conversion flag is '0', the corresponding TU is no longer divided.

As described above, a CU is a basic unit of coding in which intra prediction or inter prediction is performed. It can be divided _into: (Prediction Unit PU) units of the input picture predicting unit CU in order to more efficiently coded.

The PU is a basic unit for generating a prediction block, and may generate different prediction blocks in PU units within one CU. The PU may be divided differently according to whether an intra prediction mode or an inter prediction mode is used as a coding mode of a CU to which the PU belongs. 4 is an embodiment to which the present invention is applied and shows a schematic block diagram of an RCT unit to which an RCT is applied.

The present invention provides an RCT in which transformations that are not two-dimensional separable are defined based on sets of one-dimensional linear transformations and basis ordering permutation.

The invention provides RCT by optimizing the set of one-dimensional .linear transforms applied to the rows and columns of blocks, given non-separable block transforms for the region of interest in the image, and obtaining alignment substitution for the optimal transform coefficients. Can be designed. This allows optimized row-column transforms (RCTs) to be very close to the compression performance of non-separable transforms while maintaining the computational complexity of separable transforms.

Low-Column Transform (RCT) Definition

Considering the transform of NXN block X, let X = vec (X) is a vector obtained by row-major ordering of block X. Then, two sets of one-dimensional linear transformations are ^denoted as R = {R ⁽ⁱ⁾ , ..., R ^<N) } and C = {C ^(j) , ..., C ^(N) }. do. Where R ⁽ⁱ⁾ and C ^(j) (i, j = l, ..., N) represent the (N × N) matrix. rt-L ¹ 1 ¹ 2 ^'''1 Λ ^Γ ''k -i b' ᅳ L ^L 'l * -2' -WJ Slow 'Used to convert the i th row and j th column of the flick. , k, ^ '^ the k-th base vector of the i-th row transformation C _? ^J (χΐ Λ) is the first basis vector _(b a vector _si s) of the j-th row _conversion, it can be expressed by the following matrix shown in Equation (1).

[Equation 1]

0

Using Equation 1, an RCT matrix, G (N ² xN ² ), may be defined as Equation 2 below.

[Equation 2]

If you display it again,

[Equation 3]

G = [B ₁ e ¹ ^ B ₂ C ^ ... B _N C ^ ^]

Therefore, the transformation of the block X can be obtained by applying a substitution matrix after obtaining G ^T x. Row-Column Transform (RCT) Design The optimal row-column (RC) approximation of the desired transform matrix H ¾ ^{(Λ '';<Λ'} ) can be expressed as an optimization problem in .

Equation 4 minimize IIHP Gll

GP ¹

subject to G ：二 row-column transform

P: = permutation matrix where li ^' ᅳ ¹ represents Frobenius norm, G represents an RCT matrix, and P represents a substitution matrix. Equation 4 is due to a P permutation matrix constraint, "is a joint optimization statement. A row-column (RC) constraint for G can be explicitly written as follows.

, Where ^J is the j th column of ^C '^'' . At this time, B _¾ C ⁽³ "'is the same as Equation ₅ .

Equation 5 r

8 _? (: If you replace Mr. ^'in Equation 5 Equation 6 can be derived.

[Equation 6]

Λ (Λ ^Γ ) Γ

C; V where G is N ² xN ² and each N × N block component in Equation 6 above (ie,

For i, j = l, ..., N, ^{1 "J} is the tank-1 matrix. Assuming that the optimal substitution matrix in Equation 4 is P ^* , ^H:二^{Since HP +} , the objective function of Equation 4 may be as shown in Equation 7 below.

[Equation 7]

Here, ^ is the (i, j> th NXN partition of the matrix H and ή can be expressed as Equation (8).

[Equation 8]

Referring to FIG. 4, the RCT unit 400 to which the present invention is applied may largely include an RCT inducing unit 410 and an RCT applying unit 420.

The RCT derivation unit 410 generates a row transform set, a column transform set, and a permutation matrix based on a given transformation matrix ƒ and an error tolerance parameter. ) Can be induced. In this case, the substitution matrix may be derived through an optimization process. The optimization process may be determined by matching a Low-C and n Transform (RCT) matrix with the given transform matrix (H). The RCT matrix may be derived using the row transform set and the column transform set. For example, the row-column transform matrix may mean the matrix G of Equations 2 and 3 above.

The RCT applying unit 420 may obtain a transform coefficient based on the row transform set and the column transform set. For example, the transformation coefficient may be obtained by performing a column transformation after performing a row transformation.

The RCT applying unit 420 may obtain a row-column transform (RCT) coefficient by applying the substitution matrix to the transform coefficient. In the present embodiment, the operation of the RCT unit 400 is divided into the RCT inducing unit 410 and the RCT applying unit 420, but the present invention is not limited thereto, and the process of obtaining the RCT coefficient is It can be understood that the conversion unit 120 is performed.

The RCT unit 400 may be included in, or replaced with, the conversion unit. In addition, the transform unit may use various transformation techniques, and one of them may use RCT. FIG. 5 is a diagram for describing a process in which an RCT and a substitution matrix are applied as an embodiment to which the present invention is applied.

5 (a) to 5 (d), after performing row transformation and column transformation on block X, a series of processes for obtaining a transformation coefficient Y by applying a substitution matrix P can be confirmed. have.

The present invention uses a Row-Column Transform (RCT) as a new method for approximating non-separable transforms. Here, the RCT may be defined as a set of one-dimensional transforms applied to the rows and columns of the signal blocks followed by substitution of coefficients.

Designing or determining the RCT for an xN block consists of (2N + 1) matrices (ie, (N × N) transformation matrices R ^(i> , C ⁽ⁱ⁾ , i = l, ..., N, and It depends on the joint optimization between (N ² × N ² ) substitution matrices P).

The RCT proposed as an embodiment of the present invention is more of a non-separable transform It is advantageous in that it can maintain the complexity of separable transforms while providing good approximations. In particular, in order to transform (NxN) blocks, RCT requires 2N ³ (or multiply-adds of 21 ^ ² 109 ^ in case fast conversion is used, while general non-separable conversion). (non-separable transform) has the computational complexity of.

Hereinafter, various embodiments of designing an RCT will be described in detail. FIG. 6 is a diagram illustrating a process of designing an RCT in which two substitution matrices (P, Q) are used as an embodiment to which the present invention is applied.

The present invention provides various embodiments for designing a Row-Column Transform (RCT) in a new way to better approximate a target transform.

Hereinafter, the method of designing the RCT will be described in detail.

Weighted Row-Column Transform (RCT) Design Algorithm An embodiment of the present invention provides a method of designing a weighted RCT (hereinafter, referred to as a weighted RCT 'or a weighted RCT'). .

Equation 9 may be used to find the weighted RCT.

[Equation 9] minimize "'H" PG) -d "ia ^ ^■ P ^T w ^J ' Here, G represents an RCT matrix, P represents a substitution matrix, and the weight w is defined by the following equation (10).

[Equation 10]

τ

= WW ≤Ή

The weighting method of Equations 9 and 10 may be applied to the RCT design algorithms Al, A2, and A3 described herein.

Forward transform (forward transform) and inverse transformation (inverse transform) with respect to the embodiments ₂ uses both of the substitution matrix Q and p are the same as PG Q≤f Q ^T ^T ^T GP respectively. Basically, P and Q may be applied to all embodiments, but in the embodiments 1,2 and 4, Q may be regarded as a case of identity matrix I.

G may consist of a ^row, converting the (s row transform) and the heat conversion (column transform). For example, ^ is equal to multiplying 1 ⁽ ^ ^" for each row (i-th row) and then multiplying C ^{(j) 1} ^ for each column (j-th column), where G is each It is equivalent to multiplying C ^(j) for the column (column ^j) and then multiplying R "> for each row (column i).

In Example 4, which will be described below, since a separable row-column transform (RCT) is presented, all R ⁽ "are the same as R and It may mean that all c ^(j> are equal to c. In one embodiment, referring to FIGS. 6 (a) -6 (f), the first substitution matrix Q is applied to block X, and After performing the row transformation and the column transformation, a series of processes for obtaining the transformation coefficient Y can be confirmed by applying the second substitution matrix P. Here, designing or determining the RCT for the NXN block, Between (2N + 2) matrices (ie, (N × N) transformation matrices R ⁽ⁱ⁾ , C ^(j) , i, j = l, ..., N, and two substitution matrices P, Q) 7 and 8 illustrate embodiments to which the present invention may be applied, and schematically illustrate an RCT unit for determining an RCT using two substitution matrices (P, Q) and an inverse RCT unit corresponding thereto. Shows a block diagram.

Referring to FIG. 7, the RCT unit 700 to which the present invention is applied may be divided into a first substitution matrix application unit 710, a row transformation application unit 720, a column transformation application unit 730, and a second substitution matrix application unit. 740 may include.

First, when the pixel data X is input to the RCT unit 700, the first substitution matrix applying unit 710 may apply a first substitution matrix Q to the pixel data X. In addition, the RCT unit 700 may first perform row transformation and column transformation. Here, the row transformation may be performed by the row transformation application unit 720, and the column transformation may be performed by the column transformation application unit 730.

Then, the second substitution matrix applying unit 740 applies the second substitution matrix P by Transformation coefficient Y can be obtained. Referring to FIG. 8, the inverse RCT unit 800 to which the present invention is applied may be divided into a first inverse substitution matrix application unit 810, an inverse-row transformation application unit 820, an inverse-column transformation application unit 830, and the like. A _second inverse substitution matrix application ₈₄₀ . First, the inverse RCT unit 800 obtains the pixel data X by applying an inverse transform to a transform coefficient.

The first inverse-substitution matrix applying unit 810 may apply a first inverse-substitution matrix (∑ ^) to the transform coefficient (k). In addition, the inverse RCT unit 800 may first perform inverse-column conversion and then perform inverse-row transformation. Here, the inverse-column transformation may be performed by the inverse-% conversion application unit 820, and the inverse-row transformation may be performed by the inverse-row transformation application unit 830.

Thereafter, the second inverse substitution matrix applying unit 840 may obtain the transform coefficient 계수 by applying the second substitution matrix. In the present embodiment, it is assumed that both Ρ and Q are applied and that R ″) and c ( ^j ) may be differently applied to each row and column, but the present invention is not limited thereto. For example, when P, Q, _R <i>, and _c (j> are set to be applicable to each embodiment in the present specification, the configuration of FIGS. 6 to 8 may be applied to each embodiment. = I, R ⁽ⁱ⁾ = R for all i, C ^(j) = can be set as C for all j. In another embodiment, in FIGS. 7 and 8, it is assumed that X and Y have a 2D block data type, but the present invention is not limited thereto, and a lexicographical order (eg The conversion matrix can be applied after converting to 1D vector according to, row-first or column-first.

In addition, the block data to which the substitution matrix is applied may be converted back into a 2D block data type in order to apply a row direction or a column direction transformation. In this case, the order may be according to the dictionary order.

(12) Orthogonal Row One Column Transform Design Algorithm

The present invention provides a method for determining a column transform C ⁽ⁱ⁾ when the row transform R ⁽ⁱ⁾ and the substitution matrix P are fixed.

Two sets of one-dimensional linear transformations are given by R = {R ⁽ⁱ⁾ , ..., R ^(N) } and C = {C ⁽ⁱ⁾ , ...,

C ^(N )}. Where ^" ^, ^'二 L ^r l ^Γ 2'''^r; V -i and b -l ^C l ^C 2 ^C NI (i, j = l, ..., _N) represents the (NxN) matrix , To convert the i th row and the j th column of the block, respectively, where r (') (\ Τ y 1

^L k ^ ^A丄 is the k th basis vector of the i th row transformation and l ^{JX l} is the first basis vector of the j th row transformation.

In order to design an orthogonal RCT to which the present invention is applied, Can be used ，

[Equation 11]

H = HP-diag (P ^T wj = H _y Η ₂ Λ HN

Where ^ is a matrix of H divided by the same size and has the dimension of XN. Instead of diag (P ^T w), diag (P ^T z) may be used. diag (x) represents a function that finds the NxN diagonal matrix by placing the Nxl input vector _x on the diagonal line of the NxN matrix and setting the remaining elements to zero.

In the present invention, the following equations (12) to (14) can be used to determine the column transform (C ⁾ .

[Equation 12]

^{) T}

[Equation 13]

[Equation 14]

In Equation 14, C ⁽ⁱ⁾ represents a column transform, which can be calculated by multiplying two orthogonal matrices by V '. And the above V _c ^{ f 'in two orthogonal matrices can be derived by applying Singular Value Decomposition (SVD) to Equation (13). In addition, the present invention provides a column transform C ⁽ⁱ⁾ and substitution. When the matrix (P) is fixed, it provides a way to determine the row transform 1¾.

In the present invention, the following equations (15 to 18) may be used to determine a row transform R ">.

[Equation 15]

[Equation 16]

[Equation 17]

H _{> 2} c, row row row

Equation 18 The matrix H in Equation 16 is equal to H in Equation 11. In Equation 18, 11 represents a row transform, which can be calculated by multiplying two orthogonal matrices by,. And in the two orthogonal matrices,

IT) Jf ^ (2) ... { ^j

L ^/ '°' 2. Singular Value Decomposition to ¹ "> ^ ^L i JI.

Can be derived by applying Decomposition (SVD). In one embodiment, the invention relates to a method of designing an orthogonal RCT.

An algorithm is provided, which is shown in Table 1 below.

Table 1 (Algorithm A1)

Require: Transform matm: H, weight matrix W, and error tolerance parameter ε * ^-1

Initialize k —0 'G (0) ― I, P (0) ― J, R ⁱ⁾ <-ΐξ ^, C ⁽ ― C suffer for all 2, and c ^ while c> ε do ^

k ^ k + \ and HP (kl) -diag (p (l -l) ^T w) or HP (k-\)-diag (p (k-) ^T z) ^ for ί = 1, ... N do »

B ^ H ^ U ^ V ^-apply SVD to Β ^ Η, '

^ = ^ Γ _'' apply

11: end forv

12: G build amatnx through (6) with R ⁽ⁱ⁾ and

13: P (k) «— solve (13) given G and HWW (Hunganan method) ^

14: G (k) ―

15: c-J (HP (k-1)-G (Jt-1)) diag (p (k -l) ^T w)-\\ (HP (k)-or

I {HP (k-1)-G (k-1)) diag {p (k-1) ^r 2) ᅳ-1 | {HP (k) -G (h))-diag (p (k) ^r ζ).

16: end whiles

17: Return G * ᅳ G (k), P 'ᅳ P (k) ^

The algorithm Al represents a flow to which the scheme described in Equations 11 to 18 is applied.

First, in step 1, the encoder is k k0, G (0), P (0)

I, R ^U) — CC ⁽ −C ;, for all /, c—∞) may be initialized, wherein steps 4 to 7 correspond to Equations 11 to 14, which are row transforms. ) The process of determining the column transform C ⁽ⁱ⁾ when R ⁽ⁱ⁾ and the substitution matrix (P) are fixed.

Steps 8 to 11 are based on Equations 15 to IS, and include column transform C ⁽ⁱ⁾ and a substitution matrix. When (P) is fixed, the row A process of determining a row transform R ″ ⁾ is shown.

The column transforms C ⁽ⁱ⁾ obtained from the above steps 4 to 7 are input to the above steps 8 to 11, and the row transforms obtained from the current while-loop iteration R ⁽ⁱ⁾ column transforms transform) C ⁽ⁱ⁾ can be used in the next while-loop iteration.

The while-loop is repeated until the amount of change in the error value obtained in step 15 becomes small enough to converge. When calculating the difference between HP and G in step 15, the weight is also reflected (for example, diag (P ^T w) or diag (P ^T _Z )), and when the change amount (c) of the difference is hardly changed. Exit the while-loop. When the substitution matrix P is obtained in step 13, G and 服 W ^T are input to a Hungarian method algorithm, which can be confirmed by Equation 19 below. Here, P (k) represents a P matrix value in the k-th iteration, and G (k) can be interpreted in the same manner.

[Equation 19]

P * = argmin (HP-G) -W ', where W = diag (P ^T w)

= argmin Tr {w ^T. (HP-G) ^T (HP-G)

e

= argmin Tr ((p ^T H ^T HP-2G ^T HP + G ^T G) -WW ^t \

= argmax Tr (G ^T HPWW ^T )

= argmax 7r (G ^r HiW ^r )

3) New substitution for RCT (Row-Column Transform) design Method The present invention provides a new substitution method for RCT design. The approximation quality of the RCT matrix G may be improved through pre-multiplication of the substitution matrix Q as shown in Equation 20 below. Equation 20

| 2

minimize QHP― Q IF

a, r, Q where G represents an RCT matrix and P, Q represents a substitution matrix. In Equation 20, an optimal substitution matrix P may be obtained by Equation 21 below, and an optimal substitution matrix Q may be obtained by Equation 22 below. Equation 21

Tr (G ^T QHP)

p Here, Tr ( ') denotes a trace _(trace), p represents the substitution matrix.

Equation 22

Q * G) ^T (QHP ᅳ G, O ， T,

-f-

= argmin Ί> (Η ^Τ ΗΡΡ ^τ )-TrilHPG ¹ Q)

Q

argmax ΤΓ (Η ^Ί GO) where Η = Ρ Η and G = G

Equation 22 can be solved by finding an optimal assignment between H and G column vectors, and the type Garian method can be applied. Through this, an optimal substitution matrix Q can be obtained.

Only one substitution matrix of P and Q in Equation 21 may be used for the optimization process. In this case, the remaining substitution matrix should be set as an identity matrix. In one embodiment, the present invention provides an overall algorithm for a new substitution method for RCT design, as shown in Table 2 below.

Table ² (Algorithm A ² )

Require: Transform matrix H and error tolerance parameter

1: Initialize c —Q, G (0)

I, P (0)-I, Q (0)-I

2: while c> ε do * ¹

3: k ^ k + I and H Q (k- V) HP k-1) ^

4: for J = 1, ..N do ^ ¹

5: for j = 1, ... N do '

6: (α ^, ΐ ^., Ν) —apply SVD to in (8) ^

7: <— cr ^ iiyV ^, using (6) and (10) *-·

8: endfoiv

9: end for- ¹

10: G build a matrix through (6) with R ^(l) and C ⁽ , i = 1, .N- 11: P (k) ^ solve (13) given Q (k-\) ^T G and H ( Hungarian method), — ^!

12: Q (k) solve (E10) given P (k) ^T H ^T and G ^T (Hungarian tnethod>

13: G (k) ―

14 ： c-

15: end whiles

Algorithm A2 represents an exemplary flow for the method of Equations 20-22. For example, steps 11 to 12 first find P (k), and then Q (k) is determined as the new P (k). Steps 11 to 12 may be performed in reverse. For example, first Q (k) is determined and then Q (k) can be used to determine P (k). The substitution matrix Q of Equation 20 may be used for the RCT design in the algorithms Ά1, A2, and A3.

Algorithm A2 solves Equations ₂₀ and ₂₂ to find transform matrix G 'and substitution matrix P', Q ^* (step 16). For example, the encoder transforms a given A row transform set, a column transform set and a permutation matrix can be derived based on the matrix H and the error tolerance parameter. Here, the substitution matrix may mean a matrix obtained by replacing a row of an identity matrix. The encoder can perform initialization such as k — 0, G (0) — I, P (0) — I, Q (0) —] :, c — ∞ (step 1). If C> ε, k _{λ / f N}

( ^Σ ύ ^' ' ύ ' ^ν ύ ^' ) can be obtained (steps 3 to 6). In this case, singular value decomposition with respect to Equation (16)

SVD) may be applied. T

The encoder may acquire or derive ^G ij ^ ^σ υ ^ιιί ^ν using Equation 18 (step 7). When obtaining ^ρ in step 11, using ρ (−ι) ^Γ σ instead of G can be described by the following equation (23). [Equation 23]

Here, P (k) and Q (k) mean P and Q substitution matrices in the k-th while-loop iteration, and P (k) obtained in step 11 may be used to obtain Q in step 12. Can be. In step 14, the amount of difference between QHP and G is calculated. If the amount of change of the difference is small enough, the while-loop is terminated.

Example 4 Separable Row-Column Transform (RCT) Design Method

The present invention provides a method of designing a separable RCT with only unique transformations for row and column directions. Here, the separable RCT may mean that a single transform exists in the row and column directions, respectively.

In one embodiment, the method of determining one row direction transformation is represented by Equation 24 below.

[Equation 24]

where H = HP and W = where R stands for row direction transformation and ^ ⁼ [ ^{Γΐ Γ?} It can be expressed as ^"' .

When in the above formula ₂₄ can be used for diag (P ^T z) in place of diag (P ^T w), using the diag ^(T P z) there is a f ^^ ^^ diag). The present invention proposes the following two methods for determining one row direction transformation.

1) non-orthogonal transform

[Equation 25]

Where r _s represents a non-orthogonal row-directional transform. And, C ¹ =

... consists of j 1 and C stands for the transformation matrix that is commonly applied to all columns. Here, C ¹ ᅳ means a forward transform. W _j is the above equation

It represents the j-th block diagonal matrix divided by the same size in ^ given from 24 and has the dimension NxN. For example, the following equation (26) is obtained.

[Equation 26]

Equation ₂ 5 is a transformation commonly used in the row direction The formula for finding the j th column. Ie 2

Satisfy the relationship.

2) orthogonal transform

[Equation 27]

s = u rrooww∑ πnm "·· I

R = U row V 'T

'r ^1' ow

Here, singular value decomposition can be applied to the matrix s,

Two orthogonal matrices U, 1 are computed to derive one. And,

These can be multiplied to determine R. The present invention proposes the following two methods for determining one thermal direction conversion.

1) non-orthogonal transform

(28) 一 ― t _{1 2} c _v J, where c _{ 5,

Where c stands for non—orthogonal row-directional transform. Equation ₂₈ is an i-th column vector of the forward transform c ^T applied to all columns.

It is to ask. Denotes the j-th block diagonal matrix divided by the same size in ^ as shown in Equation 26, and has an NxN dimension.

And r, is the j th column of the transformation matrix R commonly used in the row direction

r

Points to a vector, i.e. satisfies the relationship of N.

2) orthogonal transform

Equation 29

S = b _{(; ol} ∑ _/ where singular value decomposition can be applied to the matrix s, where

Calculated to derive two orthogonal matrices V _rnl , U. Then, they can be multiplied to determine the column direction transformation C.

Table 3 (Algorithm A3:

Require: Transform matrix H, weight matrix W, and error tolerance parameter ε-

1: Initialize k — 0, G (0) ― I, F (0) ᅳ I, RC ― C _ini! andc ^ oo

4: R * ~ Find an orthogonal or non-orthogonal row transform using (El 2) or (E15) ' ¹

5: C <— Find an orthogonal or non- orthogonal column transform using (E17) or (E19)

6: G «— build a matnx through (6) with R and C where = r) ²⁾ = A = ^{ή ΚΓ)} = r ^,, c < _{^ c = A = c} ^ _{= c} . _i knee "

7: P k) «— solve (13) given G and HWW (Hungarian method) ''

8: G k)-G, '

9: c-J (HP (k-1)-G (k-l))-diag (p (k-l) ^r -1 | {HP (k)-G (k))-diag {p (k ) ^r w) or

I {HP (k-1)-G (k-1)) diag (p (k-1) ^r z) || {HP (k) ―

,

10: end while *

11: Return G ^* G (k), P * <-P (k) The algorithm A3 represents the overall flow for designing a detachable RCT.

When deriving R (C) in step 4 (step 5), it is assumed that C (R) is given and fixed. Steps 4 and 5 may be switched.

Also, matrices such as unit matrix, discrete cosine transform (DCT), karhunen—loeve transform (KLT), and sparse orthonormal transform (SOT), such as R, _ml , and C _ma may be starting points. In step 4, it is assumed that C is fixed using Equations 25 and 27, and R is obtained. In step 5, C is obtained using Equations 28 and 29 using R obtained from step 4. do .

In step 9, the difference between HP and G is calculated, and if there is little change, the algorithm is considered to have converged and the while-loop Will end.

Example 5 A method of using an absolute value operator when applying a Hungarian method to find a substitution matrix

The present invention proposes a method of applying an absolute operator when applying a Hungarian method to find a substitution matrix.

For example, when applying the Hungarian method to find the optimal allocation between the column vectors of G and H, the input J of the Hungarian method can be understood and defined in the following equation (30).

Equation 30

J = G ^T H

However, the present invention is not limited thereto, and the input J may be modified according to the Hungarian algorithm.

The present invention proposes a method of using J calculated by the following equation (31) as an input to a type Garian algorithm.

Equation 31

Where | · | Denotes an absolute value operator for each element. If the G ^r H matrix is input directly to the Hungarian algorithm (where the cost matrix can be-G ^T H o \), the elements of the matrix are negative. It may have a sign. If there is an element with a large absolute value and a negative sign in the G ^T H matrix, the absolute value of the dot product is excluded except that the corresponding base vector pairs (the base vector of G and the base vector of H) are in opposite directions. Although the matching is good because the value is large, the phenomenon may be excluded from the matching by considering the corresponding cost value large. Therefore, by taking an absolute value on the input of the Hungarian method as shown in Equation 31, the above solution can be solved and the optimal solution can be found by considering the case where the direction of the base vector pair is reversed. Through this, the convergence speed of the _RCT design algorithm described above can be increased, and an RCT closer to the target transform can be designed in terms of encoding / decoding. Therefore, when the matrix J of Equation 31 is used, the problem of finding an optimal allocation may be summarized as in Equation 32 below.

[Equation 32] = argmax

9 is an embodiment to which the present invention is applied and is a flowchart illustrating a process of obtaining RCT coefficients. The encoder may derive the row transform set, the column transform set, and the first and second substitution matrices based on the given transformation matrix) and the error tolerance parameter (S910). Here, the first and second substitution matrices are derived through an optimization process, and the optimization process is performed by using a low-column transform (RCT) matrix with the given transform matrix (H). It can be determined based on the match.

In one embodiment, the row-column transform matrix may be derived using the row transform set and the column transform set, wherein the RCT matrix is weighted to transform basis vectors. It features.

In one embodiment, the type Garlician method is applied, the type Garlician method may be performed by using an input to which the absolute value operator is applied. In one embodiment, each of the transforms in the row transform set and the column transform set is orthogonal.

In an embodiment, each of the row transform set and the column transform set is a separable transform having a single transform. The encoder may obtain a Row-Column Transform (RCT) coefficient based on the row transform set, the column transform set, and the first and second substitution matrices (S920). Here, the first substitution matrix, the row transformation set, the column transformation set, and the nearly b substitution matrix may be sequentially applied.

The encoder may perform quantization and entropy encoding on the RCT coefficients (S930). 10 is a flowchart illustrating a process of performing decoding based on RCT coefficients according to an embodiment to which the present invention is applied.

The decoder to which the present invention is applied may receive a video signal. The decoder may obtain transform coefficients from the video signal through entropy decoding and inverse quantization. Here, the transform coefficient may refer to a Row-Column Transform (RCT) coefficient to which the present invention is applied, and the RCT coefficient may mean that the embodiments described herein are applied.

The decoder comprises: a first station for the substitution matrix transform coefficients - can be applied to ^{(1 st inverse permutation matrix) (} S1010).

The decoder may perform an inverse-column transform on coefficients to which the first inverse substitution matrix is applied (S1020).

The decoder may perform an inverse-row transform on the inverse-column transformed coefficient (S1030).

The decoder, it is possible to apply the second reverse substitution matrix (2 ^nd inverse- permutation matrix) for an inverse transform coefficients (S1040).

In an embodiment, the inverse transform matrix used in the inverse transform process may be weighted to transform basis vectors.

In one embodiment, each transform in the inverse-row transform set and the inverse-column transform set is all orthogonal.

In one embodiment, each of the inverse-row transform set and the inverse-column transform set is a separable transform having a single transform.

The decoder may reconstruct the video signal using the pixel data (S1050). As described above, the embodiments described herein may be implemented and performed on a processor, microprocessor, controller, or chip. For example, the functional units illustrated in FIGS. 1, 2, 4, and 7 to 8 may be implemented by a computer, a processor, a microprocessor, a controller, or a chip.

In addition, the decoder and encoder to which the present invention is applied include a multimedia broadcasting transmitting and receiving device, a mobile communication terminal, a home cinema video device, a digital cinema video device, a surveillance camera, a video chat device, a real time communication device such as video communication, a mobile streaming device, Storage media, camcorders, video on demand (VoD) service providing devices, internet streaming service providing devices, three-dimensional (3D) video devices, video telephony video devices, and medical video devices, and the like, for processing video signals and data signals Can be used for.

In addition, the processing method to which the present invention is applied can be produced in the form of a program executed by a computer, and can be stored in a computer-readable recording medium. Multimedia data having a data structure according to the present invention can also be stored in a computer-readable recording medium. The computer readable recording medium includes all kinds of storage devices for storing computer readable data. The computer-readable recording medium may include, for example, a Blu-ray disc (BD), a universal serial bus (USB), a ROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, and an optical data storage device. Can be. Also, the Computer-readable recording media include media embodied in the form of carrier waves (eg, transmission over the Internet). In addition, the bit stream generated by the encoding method may be stored in a computer-readable recording medium or transmitted through a wired or wireless communication network.

Industrial Applicability

As mentioned above, preferred embodiments of the present invention are disclosed for purposes of illustration, and those skilled in the art can improve and change various other embodiments within the spirit and technical scope of the present invention disclosed in the appended claims below. , Replacement or addition would be possible.

Claims

[Range of claims] [claim 1]

[Claim 1]

In a method of performing a transform using a row—column transform,

Derive a row transform set, a column transform set and the first and second permutation matrices based on a given transformation matrix (H) and an error tolerance parameter Doing;

Obtaining a Row-Column Transform (RCT) coefficient based on the row transform set, the column transform set, and the first and second substitution matrices; And

Performing quantization and entropy encoding on the RCT coefficients,

Wherein the RCT coefficients are obtained by sequentially applying the first substitution matrix, the row transformation set, the column transformation set, and the second substitution matrix.

[Claim 2]

The method of claim 1,

The first and second substitution matrices are derived through an optimization process, and the optimization process is determined based on matching between a row-column transform (RCT) matrix and the given transform matrix (H), The row-column transform (RCT) matrix is derived using the row transform set and the column transform set.

[Claim 3]

The method of claim 2,

And wherein the RCT matrix is weighted to transform basis vectors.

[Claim 4]

The method of claim 2,

And the optimization process is performed by using a type-Garian method, and the type-Garian method is performed by using an input to which an absolute value operator is applied.

[Claim 5]

The method of claim 1,

Wherein each transform in the row transform set and the column transform set is all orthogormal.

[Claim 6]

The method of claim 1,

Wherein each of the row transform set and the column transform set is a separable transform having a single transform.

[Claim 7]

In the method for performing inverse transformation using a row-column transform, Receiving a video signal;

Obtaining coefficients from the video signal through entropy decoding and dequantization;

Performing inverse -permutation and inverse transform on the coefficients; And

Reconstructing the video signal using an inverse transformed coefficient

Including but

Wherein the inverse transformed coefficients are obtained by applying a first inverse substitution matrix, an inverse-column transformation set, an inverse-row transformation set, and a second inverse substitution matrix in sequence.

[Claim 8]

The method of claim 10, wherein performing the inverse transform comprises:

Applying a first inverse substitution matrix to the coefficients;

Performing an inverse-column transform on coefficients to which the first inverse substitution matrix is applied;

Performing an inverse-row transform on the inverse-column transformed coefficients; And

Applying a second inverse substitution matrix to the inverse-row transformed coefficients

Method comprising a.

[Claim 9]

G)

The inverse transformation matrix is applied to the transform basis vectors. Weighted to the method.

[Claim 10]

The method of claim 7, wherein

Wherein each transform in the inverse-row transform set and the inverse-column transform set is all orthogormal.

[Claim 11]

The method of claim 7, wherein

Wherein each of said inverse-row transform set and said inverse-column transform set is a separable transform having a single transform.

[Claim 12]

In a device that performs a transformation using a row-column transform,

Based on the given transformation matrix (H) and error tolerance parameter 1 row transform set, column transform ^λ (column transform set) and first, crab 2 permutation matrices A transform unit for deriving and obtaining RCT coefficients based on the row transform set, the column transform set, and the first and second substitution matrices;

A quantization unit performing quantization on the RCT coefficients; And

An entropy encoding unit that performs entropy encoding on the quantized RCT coefficients Including but

Wherein the RCT coefficient is obtained by applying the first substitution matrix, the row transformation set, the column transformation set, and the second substitution matrix in order.

[Claim 13]

In the apparatus for performing the inverse transformation using a row-column transformation,

A receiver for receiving a video signal;

An entropy decoding unit for entropy decoding the residual signal;

An inverse quantization unit for inversely quantizing the entropy decoded residual signal to obtain a coefficient;

入 o ^{1 "} inverse transform unit for performing inverse-permutation and inverse (transverse) on the coefficient; and

A reconstruction unit for reconstructing the video signal using an inverse transformed coefficient

Including but

And the inverse transformed coefficients are obtained by applying a first inverse substitution matrix, an inverse-column transformation set, an inverse-row transformation set, and a second inverse substitution matrix in sequence.