Encoder, decoder, encoding method, and decoding method

A decoder which decodes a video from a bitstream using a predicted image, the decoder comprising:

• circuitry;
• and
• memory,
• wherein, using the memory, the circuitry:
• derives a maximum number based on a partition shape of a first partition in the video, the maximum number being a first number when the partition shape is a square or a rectangle, and the maximum number being a second number different from the first number when the partition shape is a non-square and a non-rectangle;
• generates a motion vector candidate list including a plurality of candidates equal to the derived maximum number, the plurality of candidates being for a first motion vector for the first partition;
• decodes an index indicating the first motion vector among the plurality of candidates in the motion vector candidate list from the bitstream based on the maximum number;
• selects the first motion vector from the plurality of candidates in the motion vector candidate list using the index;
• and
• generates the predicted image for the first partition using the first motion vector,
• wherein the shape of the non-square and the non-rectangle includes a triangle.

A decoding method of decoding a video from a bitstream using a predicted image, the decoding method comprising:

• deriving a maximum number based on a partition shape of a first partition in the video, the maximum number being a first number when the partition shape is a square or a rectangle, and the maximum number being a second number different from the first number when the partition shape is a non-square and a non-rectangle;
• generating a motion vector candidate list including a plurality of candidates equal to the derived maximum number, the plurality of candidates being for a first motion vector for the first partition;
• decoding an index indicating the first motion vector among the plurality of candidates in the motion vector candidate list from the bitstream based on the maximum number;
• selecting the first motion vector from the plurality of candidates in the motion vector candidate list using the index;
• and
• generating the predicted image for the first partition using the first motion vector,
• wherein the shape of the non-square and the non-rectangle includes a triangle.

A non-transitory computer readable medium storing a bitstream, the bitstream including syntax information according to which a computer performs a decoding process of decoding a video from the bitstream using a predicted image, the decoding process comprising:

• deriving a maximum number based on a partition shape of a first partition in the video, the maximum number being a first number when the partition shape is a square or a rectangle, and the maximum number being a second number different from the first number when the partition shape is a non-square and a non-rectangle;
• generating a motion vector candidate list including a plurality of candidates equal to the derived maximum number, the plurality of candidates being for a first motion vector for the first partition;
• decoding an index indicating the first motion vector among the plurality of candidates in the motion vector candidate list from the bitstream based on the maximum number;
• selecting the first motion vector from the plurality of candidates in the motion vector candidate list using the index;
• and
• generating the predicted image for the first partition using the first motion vector,
• wherein the shape of the non-square and the non-rectangle includes a triangle.

An encoder which encodes a video into a bitstream using a predicted image, the encoder comprising:

• circuitry;
• and
• memory,
• wherein, using the memory, the circuitry:
• derives a maximum number based on a partition shape of a first partition in the video, the maximum number being a first number when the partition shape is a square or a rectangle, and the maximum number being a second number different from the first number when the partition shape is a non-square and a non-rectangle;
• generates a motion vector candidate list including a plurality of candidates equal to the derived maximum number, the plurality of candidates being for a first motion vector for the first partition;
• selects the first motion vector from the plurality of candidates included in the motion vector candidate list;
• encodes an index indicating the first motion vector among the plurality of candidates in the motion vector candidate list into the bitstream based on the maximum number;
• and
• generates the predicted image for the first partition using the first motion vector,
• wherein the shape of the non-square and the non-rectangle includes a triangle.

An encoding method of encoding a video into a bitstream using a predicted image, the encoding method comprising:

• deriving a maximum number based on a partition shape of a first partition in the video, the maximum number being a first number when the partition shape is a square or a rectangle, and the maximum number being a second number different from the first number when the partition shape is a non-square and a non-rectangle;
• generating a motion vector candidate list including a plurality of candidates equal to the derived maximum number, the plurality of candidates being for a first motion vector for the first partition;
• selecting the first motion vector from the plurality of candidates in the motion vector candidate list;
• encoding an index indicating the first motion vector among the plurality of candidates in the motion vector candidate list into the bitstream based on the maximum number;
• and
• generating the predicted image for the first partition using the first motion vector,
• wherein the shape of the non-square and the non-rectangle includes a triangle.