Image coding method based on transform, and device for same

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

obtaining residual information from a bitstream;

deriving a position of a last significant coefficient in a current block and transform coefficients for the current block based on the residual information;

determining whether an index of a subblock including the last significant coefficient is 0 and the position of the last significant coefficient in the subblock is greater than 0;

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 the bitstream when it is determined that the position of the last significant coefficient in the subblock having the index 0 is greater than 0 and the significant coefficient does not exist in the second region;

deriving modified transform coefficients by applying an LFNST matrix derived based on the LFNST index to the 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 for the current block,

wherein based on a width and a height of the current block being 4 or more and the width or the height of the current block being less than 8, the first region is a 4×4 area at the top-left of the current block and based on the significant coefficient existing in the second region other than the 4×4 area at the top-left, the LFNST index is not parsed.

2. The image decoding method of claim 1 , further comprising setting first flag information related to whether the position of the last significant coefficient is greater than 0 in the subblock having the index 0 to 1, and

wherein based on the position of the last significant coefficient in the subblock having the index 0 being greater than 0, changing the first flag information to 0 and parsing the LFNST index.

3. The image decoding method of claim 1 , further comprising setting second flag information related to whether a significant coefficient exists in the second region except for the first region to 1, and

wherein when there is no significant coefficient in the second region, maintaining the second flag information as 1 and parsing the LFNST index.

4. The image decoding method of claim 3 , wherein the second flag information is derived as 0 based on the index of the sub-block including the last significant coefficient in the current block being greater than 0 and the width and the height of the current block being 4 or more, and

wherein the LFNST index is not parsed based on the second flag information being 0.

5. The image decoding method of claim 3 , wherein the second flag information is derived as 0 based on a size of the current block being 4×4 or 8×8 and the position of the last significant coefficient being greater than or equal to 8, and

wherein the LFNST index is not parsed based on the second flag information being 0.

6. The image decoding method of claim 1 , wherein the first region is derived based on a size of the current block,

wherein based on the size of the current block being 4×4 or 8×8, the first region is from the top-left of the current block to an 8th sample position in a scan direction, and

wherein based on the size of the current block being not 4×4 or 8×8, the first region is a 4×4 area at the top-left of the current block.

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

wherein based on the height and the width of the current block being greater than or equal to 8, 48 modified transform coefficients are derived, and

wherein based on the width and the height of the current block being 4 or more and the width or the height of the current block being less than 8, 16 modified transform coefficients are derived.

8. The image decoding method of claim 7 , wherein 48 modified transform coefficients are arranged in top-left, top-right, and bottom-left 4×4 areas among a top-left 8×8 area of the current block, and

wherein 16 modified transform coefficients are arranged in the top-left 4×4 area of the current block.

9. 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 the transform coefficients of a first region at a top-left of the current block and a predetermined low-frequency non-separable transform (LFNST) matrix;

zeroing out a second region of the current block in which the modified transform coefficients do not exist;

constructing image information so that an LFNST index related to the LFNST matrix is transmitted when an index of a subblock including a last significant coefficient in the current block is 0, a position of the last significant coefficient in the subblock is greater than 0, and the significant coefficient does not exist in the second region, and

outputting the image information including residual information derived through quantization of the modified transform coefficients and the LFNST index,

wherein based on a width and a height of the current block being 4 or more and the width or the height of the current block being less than 8, the first region is a 4×4 area at the top-left of the current block and based on the significant coefficient existing in the second region other than the 4×4 area at the top-left, the LFNST index is not encoded.

10. The image encoding method of claim 9 , wherein constructing image information comprises:

setting first flag information related to whether the position of the last significant coefficient in the subblock having the index 0 is greater than 0 to 1;

changing the first flag information to 0 based on the position of the last significant coefficient in the subblock having the index 0 being greater than 0; and

encoding the LFNST index.

11. The image encoding method of claim 9 , wherein constructing image information comprises:

setting second flag information related to whether the significant coefficient exists in the second region excluding the first region to 1;

maintaining the second flag information as 1 when there is no significant coefficient in the second region; and

encoding the LFNST index.

12. The image encoding method of claim 11 , wherein the second flag information is changed to 0 based on the index of the sub-block including the last significant coefficient in the current block being greater than 0 and the width and the height of the current block being 4 or more, and

wherein the image information is configured so that the LFNST index is not transmitted based on the second flag information being 0.

13. The image encoding method of claim 11 , wherein the second flag information is changed as 0 based on a size of the current block being 4×4 or 8×8 and the position of the last significant coefficient being greater than or equal to 8, and

wherein the image information is configured so that the LFNST index is not transmitted based on the second flag information being 0.

14. The image encoding method of claim 9 , wherein the first region is derived based on a size of the current block,

wherein based on the height and the width of the current block being greater than or equal to 8, the first region is the top-left, top-right, and bottom-left 4×4 areas within a top-left 8×8 area of the current block, and

wherein based on the width and the height of the current block being 4 or more and the width or the height of the current block being less than 8, the first region is the top-left 4×4 area of the current block.

15. A non-transitory computer-readable digital storage medium that stores a bitstream generated by a method, 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 the transform coefficients of a first region at a top-left of the current block and a predetermined low-frequency non-separable transform (LFNST) matrix;

zeroing out a second region of the current block in which the modified transform coefficients do not exist;

constructing image information so that an LFNST index related to the LFNST matrix is transmitted when an index of a subblock including a last significant coefficient in the current block is 0, a position of the last significant coefficient in the subblock is greater than 0, and the significant coefficient does not exist in the second region, and

outputting the image information including residual information derived through quantization of the modified transform coefficients and the LFNST index to generate the bitstream,

wherein based on a width and a height of the current block being 4 or more and the width or the height of the current block being less than 8, the first region is a 4×4 area at the top-left of the current block and based on the significant coefficient existing in the second region other than the 4×4 area at the top-left, the LFNST index is not encoded.