Encoder, decoder, encoding method, and decoding method using bi-directional optical flow with horizontal and vertical gradients for prediction

An encoding method comprising:

• generating a prediction image based on a first parameter and a second 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 is derived based on the following expression:
• Σ[i,j]∈Ωabs(Ix1+Ix0);
• and [Math. 1]
• the second parameter according to the following expression:
• Σ[i,j]∈Ω(−sign(Ix1+Ix0)×(I0−I1), [Math. 2]
• 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 gradient image, and Ix1 indicates a horizontal gradient value at the first pixel position in a second gradient image, the first pixel position being determined based on a relative pixel position [i, j], the first gradient image and the second 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;
• the sign function outputs a sign of an argument;
• and
• each of the relative pixel positions is relative to a position of the current block.