Transform-based image coding method and device therefor

1. An image decoding method performed by a decoding apparatus, the method comprising:

deriving transform coefficients for a current block based on residual information;

determining whether a significant coefficient exists in a second region other than a first region at a top-left of the current block;

parsing a Low Frequency Non-Separable Transform (LFNST) index from a bitstream based on the determination that the significant coefficient does not exist in the second region;

deriving prediction samples for the current block;

deriving modified transform coefficients by applying an LFNST matrix derived based on the LFNST index to transform coefficients in the first region;

deriving residual samples for the current block based on an inverse primary transform for the modified transform coefficients; and

generating a reconstructed picture based on the residual samples and the prediction samples for the current block,

wherein based on a size of the current block being 4×4, the first region to which the LFNST matrix is applied is from the top-left of the current block to an 8th sample position in a scan order,

wherein based on the size of the current block being 8×8, the first region to which the LFNST matrix is applied is from the top-left of the current block to the 8th sample position in the scan order, and

wherein based on one of the width or height of the current block being greater than 4 and the other of the width or height of the current block being 4, the first region to which the LFNST matrix is applied is a top-left 4×4 area of the current block.

2. The image decoding method of claim 1 , wherein the scan order is a diagonal scan order.

3. The image decoding method of claim 1 , wherein a predetermined number of the modified transform coefficients are derived based on the size of the current block, and

wherein based on the one of the width or height of the current block being greater than or equal to 4 and the other of the width or height of the current block being equal to 4, 16 modified transform coefficients are derived.

4. The image decoding method of claim 3 , wherein the 16 modified transform coefficients are arranged in the top-left 4×4 area of the current block.

5. The image decoding method of claim 3 , wherein the 16 modified transform coefficients are arranged in a vertical or horizontal order according to an intra prediction mode of the current block.

6. An image encoding method performed by an image encoding apparatus, the method comprising:

deriving prediction samples for a current block;

deriving residual samples for the current block based on the prediction samples;

deriving transform coefficients for the current block based on a primary transform for the residual samples;

deriving modified transform coefficients for the current block based on transform coefficients of a first region at a top-left of the current block and a predetermined Low Frequency Non-Separable Transform (LFNST) matrix; and

encoding residual information related to the modified transform coefficients and an LFNST index indicating the LFNST matrix,

wherein based on a size of the current block being 4×4, the first region to which the LFNST matrix is applied is a top-left 4×4 area of the current block,

wherein based on the size of the current block being 8×8, the first region to which the LFNST matrix is applied is top-left, top-right, and bottom-left 4×4 areas of the current block, and

wherein based on one of a width or height of the current block being greater than 4 and the other of the width or height of the current block being 4, the first region to which the LFNST matrix is applied is a top-left 4×4 area of the current block.

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

8. The image encoding method of claim 6 , wherein a predetermined number of the modified transform coefficients are derived based on the size of the current block,

wherein based on the size of the current block being 4×4, 8 modified transform coefficients are derived, and

wherein based on the one of the width or height of the current block being greater than 4 and the other of the width or height of the current block being 4, 16 modified transform coefficients are derived.

9. The image encoding method of claim 8 , wherein the modified transform coefficients are arranged in a diagonal scan order at the top-left of the current block.

10. The image encoding method of claim 9 , wherein based on the size of the current block being 4×4, the modified transform coefficients are arranged from the top-left of the current block to the 8th sample position in the diagonal scan order, and

wherein based on the one of the width or height of the current block being greater than 4 and the other of the width or height of the current block being 4, the modified transform coefficients are arranged in the top-left 4×4 area of the current block in the diagonal scan order.

11. A non-transitory computer-readable digital storage medium that stores a bitstream generated by an image encoding method, the image encoding method comprising:

deriving prediction samples for a current block;

deriving residual samples for the current block based on the prediction samples;

deriving transform coefficients for the current block based on a primary transform for the residual samples;

deriving modified transform coefficients for the current block based on transform coefficients of a first region at a top-left of the current block and a predetermined Low Frequency Non-Separable Transform (LFNST) matrix; and

encoding residual information related to the modified transform coefficients and an LFNST index indicating the LFNST matrix to generate the bitstream,

wherein based on a size of the current block being 4×4, the first region to which the LFNST matrix is applied is a top-left 4×4 area of the current block,

wherein based on the size of the current block being 8×8, the first region to which the LFNST matrix is applied is top-left, top-right, and bottom-left 4×4 areas of the current block, and

wherein based on one of a width or height of the current block being greater than 4 and the other of the width or height of the current block being 4, the first region to which the LFNST matrix is applied is a top-left 4×4 area of the current block.

12. A transmission method, comprising:

obtaining a bitstream, wherein the bitstream is generated by: deriving prediction samples for a current block, deriving residual samples for the current block based on the prediction samples, deriving transform coefficients for the current block based on a primary transform for the residual samples, deriving modified transform coefficients for the current block based on transform coefficients of a first region at a top-left of the current block and a predetermined Low Frequency Non-Separable Transform (LFNST) matrix, and encoding residual information related to the modified transform coefficients and an LFNST index indicating the LFNST matrix; and

transmitting the bitstream,

wherein based on a size of the current block being 4×4, the first region to which the LFNST matrix is applied is a top-left 4×4 area of the current block,

wherein based on the size of the current block being 8×8, the first region to which the LFNST matrix is applied is top-left, top-right, and bottom-left 4×4 areas of the current block, and

wherein based on one of a width or height of the current block being greater than 4 and the other of the width or height of the current block being 4, the first region to which the LFNST matrix is applied is a top-left 4×4 area of the current block.