Encoder, decoder, encoding method, and decoding method
An encoder includes circuitry and memory connected to the circuitry. The circuitry: derives an absolute value of a sum of horizontal gradient values; derives, as a first parameter, the total sum of the absolute values of horizontal gradient values; derives, as a second parameter, the total sum of the absolute values of vertical gradient values; derives a horizontal-related pixel difference value; derives, as a third parameter, the total sum of the absolute values of horizontal-related pixel difference values; derives a vertical-related pixel difference value; derives, as a fourth parameter, the total sum of the absolute values of vertical-related pixel difference values; and generates a prediction image using the first to fourth parameters.
1. An encoding method comprising:
determining whether a bi-directional optical flow (BDOF) process is applied;
generating a prediction image based on a first parameter, a second parameter, a third parameter, and a fourth parameter that are derived in the bi-directional optical flow (BDOF) process; and
encoding a current block using the generated prediction image,
wherein
the first parameter, the second parameter, the third parameter, and the fourth parameter are derived on a subblock-by-subblock basis, the current block being divided into subblocks, and a size of each of the subblocks being 4×4;
the first parameter is derived based on the following expression:
Σ [i,j]∈Ω abs( I x 1 +I x 0 ); [Math. 1]
the second parameter is derived based on the following expression:
Σ [i,j]∈Ω abs( I x 1 +I y 0 ); [Math. 2]
the third parameter is derived based on the following expression:
Σ [i,j]∈Ω (sign( I x 1 +I x 0 )×( I 1 −I 0 )); and [Math. 3]
the fourth parameter is derived based on the following expression:
Σ [i,j]∈Ω (sign( I y 1 +I y 9 )×( I 1 −I 0 )), [Math. 4]
where:
Ω indicates a set of relative pixel positions;
[i, j] indicates a relative pixel position in the set Ω defined by a horizontal position i and a vertical position j;
I x 0 indicates a horizontal gradient value at a first pixel position in a first horizontal gradient image, I x 1 indicates a horizontal gradient value at the first pixel position in a second horizontal gradient image, I y 0 indicates a vertical gradient value at the first pixel position in a first vertical gradient image, and I y 1 indicates a vertical gradient value at the first pixel position in a second vertical gradient image, the first pixel position being determined based on a relative pixel position [i, j], the first horizontal gradient image, the second horizontal gradient image, the first vertical gradient image, and the second vertical gradient image corresponding to the current block;
I 0 indicates a pixel value at the first pixel position in a first interpolated image corresponding to the current block;
I 1 indicates a pixel value at the first pixel position in a second interpolated image corresponding to the current block;
the abs function outputs an absolute value of an argument; and
the sign function outputs a sign of an argument.
2. A decoding method comprising:
determining whether a bi-directional optical flow (BDOF) process is applied;
generating a prediction image based on a first parameter, a second parameter, a third parameter, and a fourth parameter that are derived in the bi-directional optical flow (BDOF) process; and
decoding a current block using the generated prediction image,
wherein
the first parameter, the second parameter, the third parameter, and the fourth parameter are derived on a subblock-by-subblock basis, the current block being divided into subblocks, and a size of each of the subblocks being 4×4;
the first parameter is derived based on the following expression:
Σ [i,j]∈Ω abs( I x 1 +I x 0 ); [Math. 5]
the second parameter is derived based on the following expression:
Σ [i,j]∈Ω abs( I y 1 +I y 0 ); [Math. 6]
the third parameter is derived based on the following expression:
Σ [i,j]∈Ω (sign( I x 1 +I y 0 )×( I 1 −I 0 )); and [Math. 7]
the fourth parameter is derived based on the following expression:
Σ [i,j]∈Ω (sign( I y 1 +I y 0 )×( I 1 −I 0 ), [Math. 8]
where:
Ω indicates a set of relative pixel positions;
[i, j] indicates a relative pixel position in the set Ω defined by a horizontal position i and a vertical position j;
I x 0 indicates a horizontal gradient value at a first pixel position in a first horizontal gradient image, I x 1 indicates a horizontal gradient value at the first pixel position in a second horizontal gradient image, I y 0 indicates a vertical gradient value at the first pixel position in a first vertical gradient image, and I y 1 indicates a vertical gradient value at the first pixel position in a second vertical gradient image, the first pixel position being determined based on a relative pixel position [i, j], the first horizontal gradient image, the second horizontal gradient image, the first vertical gradient image, and the second vertical gradient image corresponding to the current block;
I 0 indicates a pixel value at the first pixel position in a first interpolated image corresponding to the current block;
I 1 indicates a pixel value at the first pixel position in a second interpolated image corresponding to the current block;
the abs function outputs an absolute value of an argument; and
the sign function outputs a sign of an argument.