Image coding apparatus, image coding method, and storage media

1. An image coding apparatus that encodes an image into a bitstream by using a plurality of blocks including a first block of a P×Q array of pixels (P and Q are integers), the image coding apparatus comprising:

a transform unit configured to generate transform coefficients from prediction residuals by performing transform processing on the prediction residuals, the transform coefficients representing frequency components; and

a quantization unit configured to generate quantized transform coefficients by quantizing the transform coefficients by using a quantization matrix,

wherein, in a case where a target block is the first block,

(i) the transform unit is configured to derive a P×M array of intermediate values by performing multiplication of a P×Q array of prediction residuals and a matrix of a Q×M array, and to derive an N×M array of transform coefficients by performing multiplication of a matrix of an N×P array and the P×M array of intermediate values, wherein M is an integer satisfying M<Q, and N is an integer satisfying N<P, and

(ii) the quantization unit is configured to generate an N×M array of quantized transform coefficients by quantizing the N×M array of transform coefficients by using a quantization matrix of an N×M array of elements,

wherein, in a case where a target block is a second block smaller than the first block,

(i) the transform unit is configured to derive an array of transform coefficients a size of which is the same as a size of the second block by performing multiplication using at least an array of prediction residuals a size of which is the same as the size of the second block and a matrix a size of which is the same as the size of the second block, and

(ii) the quantization unit is configured to generate an array of quantized transform coefficients a size of which is the same as the size of the second block by quantizing the array of transform coefficients the size of which is the same as the size of the second block by using a quantization matrix a size of which is the same as the size of the second block.

2. The image coding apparatus according to claim 1 , wherein the first block is a square block.

3. The image coding apparatus according to claim 2 , wherein the P and the Q are 64, and the N and the M are 32.

4. The image coding apparatus according to claim 2 , wherein the P and the Q are 128, and the N and the M are 32.

5. The image coding apparatus according to claim 1 , wherein the second block is a block of an N×M array of pixels.

6. The image coding apparatus according to claim 1 , further comprising a generation unit configured to generate the bit stream indicating that quantized transform coefficients other than the N×M array of quantized transform coefficients and corresponding to the first block of the P×Q array of pixels are zero.

7. The image coding apparatus according to claim 1 , wherein the N×M array of the quantized transform coefficients correspond to transform coefficients in a predetermined range including direct current (DC) components in quantized transform coefficients corresponding to the first block of the P×Q array of pixels.

8. The image coding apparatus according to claim 7 , wherein quantized transform coefficients other than the N×M array of quantized transform coefficients and corresponding to the first block of the P×Q array of pixels correspond to frequency components higher than frequency components in the predetermined range.

9. The image coding apparatus according to claim 7 , wherein the predetermined range corresponds to an N×M array of transform coefficients including DC components in a P×Q array of the transform coefficients.

10. The image coding apparatus according to claim 1 , wherein the first block is a non-square block.

11. The image coding apparatus according to claim 1 , further comprising a prediction unit configured to derive the prediction residuals by using a prediction method in which an intra prediction method and an inter prediction method are combined.

12. An image coding method for encoding an image into a bitstream by using a plurality of blocks including a first block of a P×Q array of pixels (P and Q are integers), the image coding method comprising:

generating transform coefficients from prediction residuals by performing transform processing on the prediction residuals, the transform coefficients representing frequency components; and

generating quantized transform coefficients by quantizing the transform coefficients by using a quantization matrix,

wherein, in a case where a target block is the first block,

(i) a P×M array of intermediate values is derived by performing multiplication of a P×Q array of prediction residuals and a matrix of a Q×M array, and an N×M array of transform coefficients is derived by performing multiplication of a matrix of an N×P array and the P×M array of intermediate values, wherein M is an integer satisfying M<Q, and N is an integer satisfying N<P, and

(ii) an N×M array of quantized transform coefficients is generated by quantizing the N×M array of transform coefficients by using a quantization matrix of an N×M array of elements, and

wherein, in a case where a target block is a second block smaller than the first block,

(i) an array of transform coefficients a size of which is the same as a size of the second block is derived by performing multiplication using at least an array of prediction residuals a size of which is the same as the size of the second block and a matrix a size of which is the same as the size of the second block, and

(ii) an array of quantized transform coefficients a size of which is the same as the size of the second block is generated by quantizing the array of transform coefficients the size of which is the same as the size of the second block by using a quantization matrix a size of which is the same as the size of the second block.

13. The image coding method according to claim 12 , wherein the first block is a square block.

14. The image coding method according to claim 13 , wherein the P and the Q are 64, and the N and the M are 32.

15. The image coding method according to claim 13 , wherein the P and the Q are 128, and the N and the M are 32.

16. The image coding method according to claim 14 , wherein the second block is a block of an N×M array of pixels.

17. The image coding method according to claim 12 , further comprising generating the bit stream indicating that quantized transform coefficients other than the N×M array of quantized transform coefficients and corresponding to the first block of the P×Q array of pixels are zero.

18. The image coding method according to claim 12 , wherein the N×M array of quantized transform coefficients correspond to transform coefficients in a predetermined range including direct current (DC) components in quantized transform coefficients corresponding to the first block of the P×Q array of pixels.

19. The image coding method according to claim 18 , wherein quantized transform coefficients other than the N×M array of quantized transform coefficients and corresponding to the first block of the P×Q array of pixels correspond to frequency components higher than frequency components in the predetermined range.

20. The image coding method according to claim 18 , wherein the predetermined range corresponds to an N×M array of transform coefficients including DC components in a P×Q array of transform coefficients.

21. The image coding method according to claim 12 , wherein the first block is a non-square block.

22. The image coding method according to claim 12 , further comprising deriving the prediction residuals by using a prediction method in which an intra prediction method and an inter prediction method are combined.

23. A non-transitory computer readable storage medium storing a program for causing a computer to function as each unit of the image coding apparatus according to claim 1 .

24. An image decoding apparatus that decodes, from a bit stream, an image using a plurality of blocks including a first block of a P×Q array of pixels (P and Q are integers), the image decoding apparatus comprising:

a decoding unit configured to decode data corresponding to quantized transform coefficients from the bitstream;

an inverse quantization unit configured to derive transform coefficients from the quantized transform coefficients by using a quantization matrix, the transform coefficients representing frequency components;

an inverse transform unit configured to derive prediction residuals from the transform coefficients by performing inverse transform processing on the transform coefficients; and

a reconstruction unit configured to derive a predicted image by using a prediction method in which an intra prediction method and an inter prediction method are combined, and to reconstruct image data by using the predicted image and the prediction residuals,

wherein, in a case where a target block is the first block,

(i) the inverse quantization unit is configured to derive an N×M array of transform coefficients from an N×M array of quantized transform coefficients by using a quantization matrix of an N×M array of elements, wherein N is an integer satisfying N<P, and M is an integer satisfying M<Q, and

(ii) the inverse transform unit is configured to derive an N×Q array of intermediate values by performing multiplication of the N×M array of transform coefficients and a matrix of a M×Q array, and to derive a P×Q array of prediction residuals for the first block by performing multiplication of a matrix of a P×N array and the N×Q array of intermediate values, and wherein, in a case where a target block is a second block smaller than the first block,

(i) the inverse quantization unit is configured to derive an array of transform coefficients for the second block from an array of quantized transform coefficients for the second block by using a quantization matrix for the second block, wherein a size of the array of transform coefficients for the second block, a size of the array of quantized transform coefficients for the second block, and a size of the quantization matrix for the second block are the same as a size of the second block, and

(ii) the inverse transform unit is configured to derive an array of prediction residuals a size of which is the same as the size of the second block by performing multiplication using at least the array of transform coefficients for the second block and a matrix a size of which is the same as the size of the second block.

25. The image decoding apparatus according to claim 24 , wherein the first block is a square block.

26. The image decoding apparatus according to claim 25 , wherein the P and the Q are 64, and the N and the M are 32.

27. The image decoding apparatus according to claim 25 , wherein the P and the Q are 128, and the N and the M are 32.

28. The image decoding apparatus according to claim 24 , wherein the second block is a block of an N×M array of pixels.

29. The image decoding apparatus according to claim 24 , wherein the first block is a non-square block.

30. An image decoding method for decoding, from a bit stream, an image using a plurality of blocks including a first block of a P×Q array of pixels (P and Q are integers), the image decoding method comprising:

decoding data corresponding to quantized transform coefficients, from the bitstream;

deriving transform coefficients from the quantized transform coefficients by using a quantization matrix, the transform coefficients representing frequency components;

deriving prediction residuals from the transform coefficients by performing inverse transform processing on the transform coefficients; and

deriving a predicted image by using a prediction method in which an intra prediction method and an inter prediction method are combined, and reconstructing image data by using the predicted image and the prediction residuals,

wherein, in a case where a target block is the first block,

(i) an N×M array of transform coefficients is derived from an N×M array of quantized transform coefficients by using a quantization matrix of an N×M array of elements, wherein N is an integer satisfying N<P, and M is an integer satisfying M<Q, and

(ii) an N×Q array of intermediate values is derived by performing multiplication of the N×M array of transform coefficients and a matrix of a M×Q array, and a P×Q array of prediction residuals for the first block is derived by performing multiplication of a matrix of a P×N array and the N×Q array of intermediate values, and

wherein, in a case where a target block is a second block smaller than the first block,

(i) an array of transform coefficients for the second block is derived from an array of quantized transform coefficients for the second block by using a quantization matrix for the second block, wherein a size of the array of transform coefficients for the second block, a size of the array of quantized transform coefficients for the second block, and a size of the quantization matrix for the second block are the same as a size of the second block, and

(ii) an array of prediction residuals a size of which is the same as the size of the second block is derived by performing multiplication using at least the array of transform coefficients for the second block and a matrix a size of which is the same as the size of the second block.

31. The image decoding method according to claim 30 , wherein the first block is a square block.

32. The image decoding method according to claim 31 , wherein the P and the Q are 64, and the N and the M are 32.

33. The image decoding method according to claim 31 , wherein the P and the Q are 128, and the N and the M are 32.

34. The image decoding method according to claim 30 , wherein the second block is a block of an N×M array of pixels.

35. The image decoding method according to claim 30 , wherein the first block is a non-square block.

36. A non-transitory computer readable storage medium storing a program for causing a computer to function as each unit of the image decoding apparatus according to claim 24 .