Image encoding apparatus, image decoding apparatus, methods for the same, and non-transitory computer-readable storage medium

An image decoding apparatus comprising:

• a decoding unit configured to decode a first quantization matrix;
• and
• an inverse quantization unit configured to perform inverse quantization on residual coefficients, using the first quantization matrix,
• wherein the decoding unit decodes, from a scaling list data syntax structure in a bitstream, first information representing a mode of decoding the first quantization matrix,
• wherein (a) in a case where the first information decoded by the decoding unit represents that a first mode is used, the decoding unit decodes, from the scaling list data syntax structure, second information for specifying a second quantization matrix to be referenced and decodes the first quantization matrix by determining that the first quantization matrix is the same as the second quantization matrix specified based on the second information,
• (b) in a case where the first information decoded by the decoding unit represents that a second mode is used, the decoding unit decodes, from the scaling list data syntax structure, the second information for specifying the second quantization matrix and decodes the first quantization matrix by using a difference between an element of the first quantization matrix and an element of the second quantization matrix specified based on the second information, and
• (c) in a case where the first information decoded by the decoding unit represents that a third mode is used, the decoding unit decodes the first quantization matrix by using a difference between an element and another element within the first quantization matrix,
• wherein a code amount of the first information representing that the first mode is used is less than a code amount of the first information representing that the second mode is used,
• wherein the code amount of the first information representing that the first mode is used is not greater than a code amount of the first information representing that the third mode is used,
• wherein a size of the second quantization matrix can only be 2×2, 4×4, or 8×8, and
• wherein in a case where a size of the first quantization matrix to be decoded is 4×4, the size of the second quantization matrix is 4×4.

An encoding method comprising:

• quantizing transform coefficients in a block in an image, using a first quantization matrix;
• and
• encoding the first quantization matrix,
• wherein
• (a) in a case where a first mode is used to encode the first quantization matrix, the encoding encodes, into a scaling list data syntax structure, information indicating that the first quantization matrix is the same as a second quantization matrix to be referenced, and encodes, into the scaling list data syntax structure, information for specifying the second quantization matrix,
• (b) in a case where a second mode is used to encode the first quantization matrix, the encoding encodes, into the scaling list data syntax structure, the information for specifying the second quantization matrix, and encodes, into the scaling list data syntax structure, information for deriving a difference between an element of the first quantization matrix and an element of the second quantization matrix, and
• (c) in a case where a third mode is used to encode the first quantization matrix, the encoding encodes a difference between an element and another element within the first quantization matrix,
• wherein a code amount of information representing that the first mode is used is less than a code amount of information representing that the second mode is used,
• wherein the code amount of information representing that the first mode is used is not greater than a code amount of information representing that the third mode is used,
• wherein a size of the second quantization matrix can only be 2×2, 4×4, or 8×8, and
• wherein in a case where a size of the first quantization matrix to be encoded is 4×4, the size of the second quantization matrix is 4×4.

A decoding method comprising:

• decoding a first quantization matrix;
• and
• performing inverse quantization on residual coefficients, using the first quantization matrix,
• wherein the decoding decodes, from a scaling list data syntax structure in a bitstream, first information representing a mode of decoding the first quantization matrix,
• wherein (a) in a case where the first information decoded in the decoding represents that a first mode is used, the decoding decodes, from the scaling list data syntax structure, second information for specifying a second quantization matrix to be referenced and decodes the first quantization matrix by determining that the first quantization matrix is the same as the second quantization matrix specified based on the second information,
• (b) in a case where the first information decoded in the decoding represents that a second mode is used, the decoding decodes, from the scaling list data syntax structure, the second information for specifying the second quantization matrix and decodes the first quantization matrix by using a difference between an element of the first quantization matrix and an element of the second quantization matrix specified based on the second information, and
• (c) in a case where the first information decoded in the decoding represents that a third mode is used, the decoding decodes the first quantization matrix by using a difference between an element and another element within the first quantization matrix,
• wherein a code amount of the first information representing that the first mode is used is less than a code amount of the first information representing that the second mode is used,
• wherein the code amount of the first information representing that the first mode is used is not greater than a code amount of the first information representing that the third mode is used,
• wherein a size of the second quantization matrix can only be 2×2, 4×4, or 8×8, and
• wherein in a case where a size of the first quantization matrix to be decoded is 4×4, the size of the second quantization matrix is 4×4.