Image coding method and apparatus therefor

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

• deriving residual samples for a target block based on prediction samples for the target block;
• deriving transform coefficients for the target block based on a primary transform on the residual samples;
• deriving modified transform coefficients based on a secondary transform on the transform coefficients;
• and
• encoding image information comprising residual information derived based on the modified transform coefficients,
• wherein the deriving the modified transform coefficients comprises deriving a transform kernel to be applied for the secondary transform,
• wherein based on both of horizontal and vertical lengths of the target block being greater than or equal to 4, and the horizontal or the vertical length being equal to 4, the transform kernel is derived as a 16×16 dimensional matrix,
• wherein based on both of the horizontal and the vertical lengths of the target block being greater than or equal to 8, and the horizontal or the vertical length being equal to 8, the transform kernel is derived as a 16×48 dimensional matrix, and
• wherein the 16×48 dimensional matrix is derived based on the following matrix:
• const int8_t g_lfnst8x8[ 36 ][ 3 ][ 16 ][ 48 ] = {
• { //0
• {
• {111, −23, −25, −1, −4, 0, −2, 0, −38, 24, 4, −2, 1, 0, 0, 0, −28, −1, 11, 0, 1, 0, 1, 0, 3, −3, −1, 1, 0, 0, 0, 0,
• −3, 1, 1, 0, 0, 0, 0, 0, −1, 0, 0, 0, 0, 0, 0, 0 },
• {−16, 44, −4, −8, −2, −2, 0, −1, −95, 1, 35, 1, 4, 0, 2, 0, 39, −39, −7, 8, −1, 1, 0, 1, 22, 7, −12, −1,
• −1, 0, 0, 0, 2, 1, 1, −1, 3, 0, −1, 0, 1, −1, 0, 0, 1, 0, −1, 0 },
• {−18, −98, 37, 18, 5, 3, 2, 1, −42, 17, −10, 4, 2, 0, 0, 0, 37, 26, −15, −10, −2, −1, −1, 0, 6, 2, 1, −2,
• −1, 0, 0, 0, 0, 3, 0, −1, 0, 0, 0, 0, 1, 1, −1, 0, 0, 0, 0, 0 },
• {−44, −10, −3, 8, 4, 1, 1, 0, −14, 62, −1, −17, −1, −3, 0, −1, −66, −16, 47, 1, 0, 1, 1, 0, 35, −36, −14, 12,
• −1, 2, 0, 1, 14, 7, −11, −2, 2, −2, 1, 0, 1, 1, 0, 0, 1, −1, 0, 0 },
• {11, 20, 14, −16, −2, −2, 0, −1, 22, 87, −21, −19, −5, −4, −1, −1, 59, −23, −1, 5, −3, 0, −1, 0, −41,
• −18, 11, 9, 3, 1, 1, 0, −10, −6, 1, 2, −1, −4, 0, 1, 1, −1, −1, 0, −1, −1, 0, 0 },
• {18, 10, 102, −35, −10, −5, −1, −2, 1, −1, −3, 21, −5, 1, −1, 0, −38, −26, −31, 18, 10, 2, 2, 1, 8, −1, −6,
• −6, 2, 0, 0, 0, 5, 5, −4, −1, 0, 1, 0, −1, 0, 0, −2, 0, 0, 0, 0, 0 },
• {3, −41, −18, 8, 6, 3, 1, 1, 39, −2, 23, −8, −7, −1, −1, 0, 12, −75, −3, 36, −1, 3, −1, 1, 14, 32, −48, −7, 7,
• −1, 0, 0, −11, 29, 13, −16, −4, −4, 4, 3, −2, 2, 1, 0, −1, 0, 0, 0 },
• {−10, −11, −15, −13, 9, 1, 2, 0, −26, −20, −83, 20, 14, 3, 2, 1, −12, −54, 23, −1, 1, 3, 0, 1, −34, 24, 32, −7,
• −5, −1, 0, −1, 24, 7, −4, 1, 3, 3, 4, −1, 2, 1, 0, 0, 1, 1, 1, 0 },
• {11, 23, 0, 14, −7, −1, −2, 0, 12, 12, −60, 5, 12, −1, 1, 0, 17, 3, −14, −27, 4, 1, 1, 0, 88, 14, −1, −8, −13, −1,
• −2, 0, −35, 15, 17, 1, −8, −10, 7, 3, −5, −2, 1, 1, −1, −1, 1, 0 },
• {5, 15, 17, 102, −26, −6, −8, −2, 1, 5, 8, 1, 19, −6, 0, −1, −13, −30, −24, −36, 14, 8, 3, 2, −28, −5, 2, −3,
• −5, 3, 1, 0, 12, 1, 0, −3, 4, 3, −2, −1, 1, 1, 0, −2, 0, 0, 0, 0 },
• {22, 9, 36, 14, −5, −5, −3, −1, 12, −22, −1, 4, 3, 1, 0, 0, 38, 3, 75, −15, −24, 1, −3, −1, 12, 8, −28, 27, 1,
• −3, 0, 0, 29, 7, −50, −7, −17, 5, 12, −7, −5, −3, 1, 1, −2, 0, 0, 0 },
• {5, −8, −5, −2, −5, 3, 0, 0, −4, −41, −19, −6, 8, 3, 2, 1, 12, −18, −12, 10, 2, 0, 0, 0, −3, −92, −6, 39, 3, 4, 0, 2,
• −39, 30, −9, −11, 14, 16, 6, −8, 3, 4, 1, 0, 1, 3, 1, −1 },
• {4, 3, −28, −7, 4, 2, 2, 1, 9, 14, −6, 29, −5, −5, −1, −1, 14, 9, −45, 5, 18, −3, 0, 0, 15, −30, −11,
• −20, 3, 6, 0, 1, 81, 29, −24, −12, −32, 14, 21, −5, −8, −7, 7, 4, −2, −1, 1, 0 },
• {4, −2, 7, −8, −12, 5, 1, 0, −2, −14, −6, −99, 10, 13, 5, 2, −6, −3, −30, 1, −19, 3, 2, 1, 11, 17, 23, 36, −8, −11,
• −2, −1, 39, 12, 3, 4, −12, 2, 1, 5, −4, −3, 1, 1, −1, 0, 0, 2 },
• {7, 7, 7, 9, 103, −30, −6, −4, 3, 2, 6, 3, 1, 16, −4, 0, −6, −10, −19, −26, −50, 18, 8, 2, 0, −10, −2, 0, −3,
• −7, 2, 1, 1, 1, 2, 8, 0, 3, 0, −1, 1, 1, 0, 0, 0, 0, 0, 0 },
• {−2, 22, 7, 20, 6, −8, −2, −1, −22, 4, −35, −14, 0, 7, 3, 1, −11, 40, −1, 32, −16, −10, 1, −1, −27, 11, −44,
• −6, 43, −6, 1, 0, −3, 17, 25, −58, 5, −14, 27, 14, 3, −6, −5, 5, 2, −1, 1, 0 },
• }.

A transmission method of data for an image, the transmission method comprising:

• obtaining a bitstream for the image, wherein the bitstream is generated by performing deriving residual samples for a target block based on prediction samples for the target block, deriving transform coefficients for the target block based on a primary transform on the residual samples, deriving modified transform coefficients based on a secondary transform on the transform coefficients, and encoding image information comprising residual information derived based on the modified transform coefficients;
• and
• transmitting the data comprising the bitstream,
• wherein the deriving the modified transform coefficients comprises deriving a transform kernel to be applied for the secondary transform,
• wherein based on both of horizontal and vertical lengths of the target block being greater than or equal to 4, and the horizontal or the vertical length being equal to 4, the transform kernel is derived as a 16×16 dimensional matrix,
• wherein based on both of the horizontal and the vertical lengths of the target block being greater than or equal to 8, and the horizontal or the vertical length being equal to 8, the transform kernel is derived as a 16×48 dimensional matrix, and
• wherein the 16×48 dimensional matrix is derived based on the following matrix:
• const int8_t g_lfnst8x8[ 36 ][ 3 ][ 16 ][ 48 ] = {
• { //0
• {
• {111, −23, −25, −1, −4, 0, −2, 0, −38, 24, 4, −2, 1, 0, 0, 0, −28, −1, 11, 0, 1, 0, 1, 0, 3, −3, −1, 1, 0, 0, 0, 0,
• −3, 1, 1, 0, 0, 0, 0, 0, −1, 0, 0, 0, 0, 0, 0, 0 },
• {−16, 44, −4, −8, −2, −2, 0, −1, −95, 1, 35, 1, 4, 0, 2, 0, 39, −39, −7, 8, −1, 1, 0, 1, 22, 7, −12, −1,
• −1, 0, 0, 0, 2, 1, 1, −1, 3, 0, −1, 0, 1, −1, 0, 0, 1, 0, −1, 0 },
• {−18, −98, 37, 18, 5, 3, 2, 1, −42, 17, −10, 4, 2, 0, 0, 0, 37, 26, −15, −10, −2, −1, −1, 0, 6, 2, 1, −2,
• −1, 0, 0, 0, 0, 3, 0, −1, 0, 0, 0, 0, 1, 1, −1, 0, 0, 0, 0, 0 },
• {−44, −10, −3, 8, 4, 1, 1, 0, −14, 62, −1, −17, −1, −3, 0, −1, −66, −16, 47, 1, 0, 1, 1, 0, 35, −36, −14, 12,
• −1, 2, 0, 1, 14, 7, −11, −2, 2, −2, 1, 0, 1, 1, 0, 0, 1, −1, 0, 0 },
• {11, 20, 14, −16, −2, −2, 0, −1, 22, 87, −21, −19, −5, −4, −1, −1, 59, −23, −1, 5, −3, 0, −1, 0, −41,
• −18, 11, 9, 3, 1, 1, 0, −10, −6, 1, 2, −1, −4, 0, 1, 1, −1, −1, 0, −1, −1, 0, 0 },
• {18, 10, 102, −35, −10, −5, −1, −2, 1, −1, −3, 21, −5, 1, −1, 0, −38, −26, −31, 18, 10, 2, 2, 1, 8, −1, −6,
• −6, 2, 0, 0, 0, 5, 5, −4, −1, 0, 1, 0, −1, 0, 0, −2, 0, 0, 0, 0, 0 },
• {3, −41, −18, 8, 6, 3, 1, 1, 39, −2, 23, −8, −7, −1, −1, 0, 12, −75, −3, 36, −1, 3, −1, 1, 14, 32, −48, −7, 7,
• −1, 0, 0, −11, 29, 13, −16, −4, −4, 4, 3, −2, 2, 1, 0, −1, 0, 0, 0 },
• {−10, −11, −15, −13, 9, 1, 2, 0, −26, −20, −83, 20, 14, 3, 2, 1, −12, −54, 23, −1, 1, 3, 0, 1, −34, 24, 32, −7,
• −5, −1, 0, −1, 24, 7, −4, 1, 3, 3, 4, −1, 2, 1, 0, 0, 1, 1, 1, 0 },
• {11, 23, 0, 14, −7, −1, −2, 0, 12, 12, −60, 5, 12, −1, 1, 0, 17, 3, −14, −27, 4, 1, 1, 0, 88, 14, −1, −8, −13, −1,
• −2, 0, −35, 15, 17, 1, −8, −10, 7, 3, −5, −2, 1, 1, −1, −1, 1, 0 },
• {5, 15, 17, 102, −26, −6, −8, −2, 1, 5, 8, 1, 19, −6, 0, −1, −13, −30, −24, −36, 14, 8, 3, 2, −28, −5, 2, −3,
• −5, 3, 1, 0, 12, 1, 0, −3, 4, 3, −2, −1, 1, 1, 0, −2, 0, 0, 0, 0 },
• {22, 9, 36, 14, −5, −5, −3, −1, 12, −22, −1, 4, 3, 1, 0, 0, 38, 3, 75, −15, −24, 1, −3, −1, 12, 8, −28, 27, 1,
• −3, 0, 0, 29, 7, −50, −7, −17, 5, 12, −7, −5, −3, 1, 1, −2, 0, 0, 0 },
• {5, −8, −5, −2, −5, 3, 0, 0, −4, −41, −19, −6, 8, 3, 2, 1, 12, −18, −12, 10, 2, 0, 0, 0, −3, −92, −6, 39, 3, 4, 0, 2,
• −39, 30, −9, −11, 14, 16, 6, −8, 3, 4, 1, 0, 1, 3, 1, −1 },
• {4, 3, −28, −7, 4, 2, 2, 1, 9, 14, −6, 29, −5, −5, −1, −1, 14, 9, −45, 5, 18, −3, 0, 0, 15, −30, −11,
• −20, 3, 6, 0, 1, 81, 29, −24, −12, −32, 14, 21, −5, −8, −7, 7, 4, −2, −1, 1, 0 },
• {4, −2, 7, −8, −12, 5, 1, 0, −2, −14, −6, −99, 10, 13, 5, 2, −6, −3, −30, 1, −19, 3, 2, 1, 11, 17, 23, 36, −8, −11,
• −2, −1, 39, 12, 3, 4, −12, 2, 1, 5, −4, −3, 1, 1, −1, 0, 0, 2 },
• {7, 7, 7, 9, 103, −30, −6, −4, 3, 2, 6, 3, 1, 16, −4, 0, −6, −10, −19, −26, −50, 18, 8, 2, 0, −10, −2, 0, −3,
• −7, 2, 1, 1, 1, 2, 8, 0, 3, 0, −1, 1, 1, 0, 0, 0, 0, 0, 0 },
• {−2, 22, 7, 20, 6, −8, −2, −1, −22, 4, −35, −14, 0, 7, 3, 1, −11, 40, −1, 32, −16, −10, 1, −1, −27, 11, −44,
• −6, 43, −6, 1, 0, −3, 17, 25, −58, 5, −14, 27, 14, 3, −6, −5, 5, 2, −1, 1, 0 },
• }.