Method and apparatus for coding image on basis of transform

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

obtaining residual information from a bitstream;

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

determining whether a Low Frequency Non-Separable Transform (LFNST) index is parsed;

parsing the LFNST index based on the determination that the LFNST index is parsed;

deriving modified transform coefficients by applying an LFNST matrix derived based on the LFNST index to the transform coefficients in a first region at a top-left of the current block;

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 determining whether the LFNST index is parsed comprising:

deriving a first variable related to whether a significant coefficient exists in a region excluding a Direct-Current (DC) region of the current block; and

deriving a second variable related to whether the significant coefficient exists in a second region other than the first region in the current block;

wherein the first variable is derived as 0 based on an index of a subblock including a last significant coefficient in the current block being 0 and a position of the last significant coefficient in the subblock being greater than 0, and

wherein the LFNST index is parsed based on the first variable being 0 and the second variable being related to that the significant coefficient does not exist in the second region.

2. 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 not being 4×4 and 8×8, the first region is a 4×4 area at the top-left of the current block.

3. 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 a height and a width of the current block being greater than or equal to 8, 48 modified transform coefficients are derived, and

wherein based on one of the width or the height of the current block being greater than or equal to 4 and the other of the width or the height of the current block is less than 8, 16 modified transform coefficients are derived.

4. An image encoding method performed by an image encoding apparatus, 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;

constructing image information so that an LFNST index related to the LFNST matrix is signaled based on a significant coefficient existing in a region excluding a Direct-Current (DC) region of the current block and the significant coefficient not existing in a second region other than the first region in the current block; and

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

wherein based on an index of a subblock including a last significant coefficient in the current block being 0 and a position of the last significant coefficient in the subblock being greater than 0, it is determined that the significant coefficient exists in the region excluding the DC region, and the image information is configured such that the LFNST index is signaled.

5. The image encoding method of claim 4 , wherein the first region is derived based on a size of the current block,

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

wherein based on one of the width or the height of the current block being greater than or equal to 4 and the other of 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.

6. The image encoding method of claim 4 , wherein a predetermined number of the modified transform coefficients are derived based on a size of the current block,

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

wherein based on the size of the current block not being 4×4 and 8×8, 16 modified transform coefficients are derived.

7. A non-transitory computer-readable storage medium storing a bitstream generated by the image encoding method of claim 4 .

8. A transmission method of data for an image, comprising:

obtaining a bitstream for the image, wherein the bitstream is generated based on 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, constructing image information so that an LFNST index related to the LFNST matrix is signaled based on a significant coefficient existing in a region excluding a Direct-Current (DC) region of the current block and the significant coefficient not existing in a second region other than the first region in the current block, and encoding the image information including residual information derived through quantization of the modified transform coefficients and the LFNST index; and

transmitting the data comprising the bitstream,

wherein based on an index of a subblock including a last significant coefficient in the current block being 0 and a position of the last significant coefficient in the subblock being greater than 0, it is determined that the significant coefficient exists in the region excluding the DC region, and the image information is configured such that the LFNST index is signaled.