Encoder, decoder, encoding method, and decoding method

A decoder, comprising:

• circuitry;
• and
• memory, wherein
• using the memory, the circuitry:
• derives a one-dimensional array of a plurality of reference samples for intra prediction by projecting a value of at least one first decoded pixel located on a first line onto a second line to derive the one-dimensional array of the plurality of reference samples, the second line being perpendicular to the first line and including values of a plurality of second decoded pixels, and the plurality of reference samples of the one-dimensional array being located on the second line and including the value of the at least one first decoded pixel projected on the second line and the values of the plurality of second decoded pixels;
• after deriving the one-dimensional array of the plurality of reference samples, performs smoothing on the derived one-dimensional array of the plurality of reference samples;
• and
• after performing smoothing on the derived one-dimensional array of the plurality of reference samples, generates a prediction image using the plurality of reference samples upon which the smoothing has been performed,
• wherein the circuitry performs the smoothing on the derived one-dimensional array of the plurality of reference samples according to the following:
• smoothed_ref[x]=(ref[x−1]+2*ref[x]+ref[x+1])>>2,
• where ref[x] is a reference sample at index x from among the derived one-dimensional array of the plurality of reference samples not including the minimum value of the indexes of the derived one-dimensional array of the plurality of reference samples and the maximum value of the indexes of the derived one-dimensional array of the plurality of reference samples, and
• where smoothed_ref[x] is a smoothed reference sample at index x from among the plurality of reference samples upon which the smoothing has been performed.

An encoding method for encoding a video, the encoding method comprising:

• deriving a one-dimensional array of a plurality of reference samples for intra prediction by projecting a value of at least one first decoded pixel located on a first line onto a second line to derive the one-dimensional array of the plurality of reference samples, the second line being perpendicular to the first line and including values of a plurality of second decoded pixels, and the plurality of reference samples of the one-dimensional array being located on the second line and including the value of the at least one first decoded pixel projected on the second line and the values of the plurality of second decoded pixels;
• after deriving the one-dimensional array of the plurality of reference samples, performing smoothing on the derived one-dimensional array of the plurality of reference samples;
• and
• after performing smoothing on the derived one-dimensional array of the plurality of reference samples, generating a prediction image using the plurality of reference samples upon which the smoothing has been performed,
• wherein the smoothing on the derived one-dimensional array of the plurality of reference samples is performed according to the following:
• smoothed_ref[x]=(ref[x−1]+2*ref[x]+ref[x+1])>>2,
• where ref[x] is a reference sample at index x from among the derived one-dimensional array of the plurality of reference samples not including the minimum value of the indexes of the derived one-dimensional array of the plurality of reference samples and the maximum value of the indexes of the derived one-dimensional array of the plurality of reference samples, and
• where smoothed_ref[x] is a smoothed reference sample at index x from among the plurality of reference samples upon which the smoothing has been performed.

A decoding method for decoding a video, the decoding method comprising:

• deriving a one-dimensional array of a plurality of reference samples for intra prediction by projecting a value of at least one first decoded pixel located on a first line onto a second line to derive the one-dimensional array of the plurality of reference samples, the second line being perpendicular to the first line and including values of a plurality of second decoded pixels, and the plurality of reference samples of the one-dimensional array being located on the second line and including the value of the at least one first decoded pixel projected on the second line and the values of the plurality of second decoded pixels;
• after deriving the one-dimensional array of the plurality of reference samples, performing smoothing on the derived one-dimensional array of the plurality of reference samples;
• and
• after performing smoothing on the derived one-dimensional array of the plurality of reference samples, generating a prediction image using the plurality of reference samples upon which the smoothing has been performed,
• wherein the smoothing on the derived one-dimensional array of the plurality of reference samples is performed according to the following:
• smoothed_ref[x]=(ref[x−1]+2*ref[x]+ref[x+1])>>2,
• where ref[x] is a reference sample at index x from among the derived one-dimensional array of the plurality of reference samples not including the minimum value of the indexes of the derived one-dimensional array of the plurality of reference samples and the maximum value of the indexes of the derived one-dimensional array of the plurality of reference samples, and
• where smoothed_ref[x] is a smoothed reference sample at index x from among the plurality of reference samples upon which the smoothing has been performed.