Encoder, decoder, encoding method, and decoding method

An encoding method comprising:

• generating a prediction image based on a first parameter, a second parameter, a third parameter, and a fourth parameter that are derived in a 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]∈Ωabs(Ix1+Ix0);
• [Math. 1]
• the second parameter is derived based on the following expression:
• Σ[i,j]∈Ωabs(Iy1+Iy0);
• [Math. 2]
• the third parameter is derived based on the following expression:
• Σ[i,j]∈Ω(sign(Ix1+Ix0)×(I1−I0));
• and [Math. 3]
• the fourth parameter is derived based on the following expression:
• Σ[i,j]∈Ω(sign(Iy1+Iy0)×(I1−I0)), [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;
• Ix0 indicates a horizontal gradient value at a first pixel position in a first horizontal gradient image, Ix1 indicates a horizontal gradient value at the first pixel position in a second horizontal gradient image, Iy0 indicates a vertical gradient value at the first pixel position in a first vertical gradient image, and Iy1 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;
• I0 indicates a pixel value at the first pixel position in a first interpolated image corresponding to the current block;
• I1 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.