Image coding apparatus, image coding method, image decoding apparatus, image decoding method, and storage medium

1. An image coding apparatus comprising:

a processor; and

a memory;

wherein the processor performs prediction for an input image stored in the memory to generate prediction errors;

wherein the processor performs orthogonal transform to the prediction errors to generate transform coefficients;

wherein the processor quantizes the transform coefficients using a quantization matrix to generate quantization coefficients;

wherein the processor codes a difference value between a first coefficient and a second coefficient, the first coefficient and the second coefficient are two of a plurality of coefficients in the quantization matrix;

wherein the processor codes the difference value into a code with less number of bits in case where the difference value is a positive value than a number of bits in case where the difference value has the same absolute value as the absolute value of the positive value while the difference value is a negative value; and

wherein the processor stores the difference value using the code in the memory.

2. The image coding apparatus according to claim 1 , wherein the processor determines, when a first difference value between coefficients included in the quantization matrix is coded and the first difference value is different from the difference value between the first coefficient and the second coefficient, whether the coding method using a code with equal or less number of bits when the first difference value is a positive value than a code when the first difference value is a negative value and the first difference value has the same absolute value as the absolute value of the positive value or a different coding method is to be used, and

wherein the processor codes the first difference value based on the determined coding method.

3. The image coding apparatus according to claim 2 , wherein the processor codes the first difference value using:

the coding method using a plus-minus asymmetry table of codes corresponding to a pair of positive and negative values having the same absolute value, the table including a shorter code length for the positive value than a code length for the negative value having the same absolute value as the positive value; or

the different coding method using a plus-minus symmetry table of codes corresponding to a pair of positive and negative values having the same absolute value, the table always providing the same code length for any combination of the positive value and the negative value having the same absolute value.

4. The image coding apparatus according to claim 2 , wherein the processor generates an identifier indicating the determined coding method,

wherein the processor codes the first difference value based on the generated identifier.

5. The image coding apparatus according to claim 1 , wherein the processor codes a first difference value between coefficients included in the quantization matrix, the first difference value being different from the difference value between the first coefficient and the second coefficient, using a code with equal or less number of bits in case where the first difference value is a positive value than a number of bits in case where the first difference value has the same absolute value as the absolute value of the positive value while the first difference value is a negative value.

6. The image coding apparatus according to claim 1 , wherein the processor scans the coefficients in the quantization matrix, and codes the difference value between the first coefficient and the second coefficient adjacent to the first coefficient in an order of scanning.

7. The image coding apparatus according to claim 1 , wherein the processor codes the difference value using a parameter corresponding to a value subjected to coding.

8. The image coding apparatus according to claim 1 , wherein the processor codes, a difference value between an initial coefficient in a scanning order among the coefficients in the quantization matrix and a predetermined value, or the initial coefficient.

9. The image coding apparatus according to claim 1 , wherein

in a case of coding the difference value between the first coefficient and the second coefficient, the processor performs mapping of the difference value to an index having a positive value, and codes the index, and

in a case where the difference value is a negative value, at least one index smaller than the index of mapping of the difference value is mapped to a positive value having an absolute value larger than the negative value.

10. The image coding apparatus according to claim 9 , wherein

in the case of coding the difference value between the first coefficient and the second coefficient, the processor performs mapping of the difference value tc the index having the positive value using a selected table among a plurality of tables for mapping a value subjected to coding to the index having the positive value, and codes information representing the index and the selected table, and

in at least one table among the tables, an index corresponding to a negative value having the same absolute value as the absolute value of the positive value is always greater than an index corresponding to the positive value, and the table includes at least one positive value greater than an absolute value of the negative value corresponding to an index having a smaller value than an index corresponding to an arbitrary negative value.

11. The image coding apparatus according to claim 10 , wherein the processor codes information representing a difference value between an index corresponding to a positive value first occurring and an index corresponding to a negative value first occurring in an order of indices on the table in the table.

12. A non-transitory computer-readable storage medium storing a program that causes a computer to function as the image coding apparatus the program comprising:

instructions for performing a prediction for an input image to generate prediction errors;

instructions for performing orthogonal transform to the prediction errors to generate transform coefficients;

instructions for quantizing the transform coefficients using a quantization matrix to generate quantization coefficients;

instructions for coding a difference value between a first coefficient and a second coefficient, the first coefficient and the second coefficient are two of a plurality of coefficients in the quantization matrix;

wherein the difference value uses a code with less number of bits in case where the difference value is a positive value than a number of bits in case where the difference value has the same absolute value as the absolute value of the positive value while the difference value is a negative value; and

instructions for storing the difference value using the code in memory.