Error surface based sub-pixel accurate refinement method for decoder side motion vector refinement

An encoder apparatus comprising:

• one or more processors;
• and
• a non-transitory computer-readable storage medium coupled to the one or more processors and storing programming for execution by the one or more processors, wherein the programming, when executed by the one or more processors, configures the apparatus to perform operations comprising:
• determining a target integer motion vector displacement by comparing integer distance costs associated with respective candidate integer motion vector displacements with respect to an initial motion vector for a block of a frame in a video;
• determining a sub-pixel motion vector displacement based on the target integer motion vector displacement and the integer distance costs;
• determining a refined motion vector based on the target integer motion vector displacement, the sub-pixel motion vector displacement and the initial motion vector;
• the sub-pixel motion vector displacement is determined as:
• x0=(E(−1,0)−E(1,0))/(2×(E(−1,0)+E(1,0)−2×E(0,0))), and
• y0=(E(0,−1)−E(0,1))/(2×(E(0,−1)+E(0,1)−2×E(0,0))),
• wherein:
• x0 and y0 are coordinates associated with the sub-pixel motion vector displacement relative to a center (0, 0), and
• E(−1, 0), E(1, 0), E(0, 0), E(0, −1) and E(0, 1) are the integer distance costs with respect to the initial motion vector and corresponding to candidate integer motion vector displacements represented by coordinates (−1, 0), (1, 0), (0, 0), (0, −1) and (0, 1), respectively, relative to the center (0,0);
• and
• the center (0,0) represents an integer motion vector displacement among the candidate integer motion vector displacements that has the lowest integer distance cost.

A non-transitory computer-readable medium storing instructions which, when executed by one or more processors of an encoder, perform operations comprising:

• determining a target integer motion vector displacement by comparing integer distance costs associated with respective candidate integer motion vector displacements with respect to an initial motion vector for a block of a frame in a video;
• determining a sub-pixel motion vector displacement based on the target integer motion vector displacement and the integer distance costs;
• determining a refined motion vector based on the target integer motion vector displacement, the sub-pixel motion vector displacement and the initial motion vector;
• wherein the sub-pixel motion vector displacement is determined as:
• x0=(E(−1,0)−E(1,0))/(2×(E(−1,0)+E(1,0)−2×E(0,0))), and
• y0=(E(0,−1)−E(0,1))/(2×(E(0,−1)+E(0,1)−2×E(0,0))),
• wherein:
• x0 and y0 are coordinates associated with the sub-pixel motion vector displacement relative to a center (0, 0), and
• E(−1, 0), E(1, 0), E(0, 0), E(0, −1) and E(0, 1) are the integer distance costs with respect to the initial motion vector and corresponding to candidate integer motion vector displacements represented by coordinates (−1, 0), (1, 0), (0, 0), (0, −1) and (0, 1), respectively, relative to the center (0,0);
• and
• the center (0,0) represents an integer motion vector displacement among the candidate integer motion vector displacements that has the lowest integer distance cost.