Image processing apparatus and method

1. An image processing apparatus comprising:

a decoding section configured to decode a bitstream to generate coefficient data in which a predicted residual of an image is orthogonally transformed;

a derivation section configured to derive, from a submatrix as part of a first transform matrix in a first size, a second transform matrix in a second size that is a size smaller than the first size; and

an inverse orthogonal transform section configured to use the second transform matrix derived by the derivation section, to apply an inverse orthogonal transform to the coefficient data generated by the decoding section,

wherein the derivation section is further configured to use the first transform matrix stored in a lookup table, to derive the second transform matrix, and

wherein the decoding section, the derivation section, and the inverse orthogonal transform section are each implemented via at least one processor.

2. The image processing apparatus according to claim 1 , wherein

the derivation section is further configured to derive, as the submatrix, a matrix obtained by sampling matrix elements of the first transform matrix.

3. The image processing apparatus according to claim 2 , wherein

the derivation section is further configured to derive, as the submatrix, an even low-order matrix including matrix elements in a left half of matrix elements of an even matrix including matrix elements of even rows of the first transform matrix.

4. The image processing apparatus according to claim 2 , wherein

the derivation section is further configured to derive, as the submatrix, an even high-order matrix including matrix elements in a right half of matrix elements of an even matrix including matrix elements of even rows of the first transform matrix.

5. The image processing apparatus according to claim 2 , wherein

the derivation section is further configured to derive, as the submatrix, an odd low-order matrix including matrix elements in a left half of matrix elements of an odd matrix including matrix elements of odd rows of the first transform matrix.

6. The image processing apparatus according to claim 2 , wherein

the derivation section is further configured to derive, as the submatrix, an odd high-order matrix including matrix elements in a right half of matrix elements of an odd matrix including matrix elements of odd rows of the first transform matrix.

7. The image processing apparatus according to claim 2 , wherein

the derivation section is further configured to apply an operation to matrix elements of the submatrix to derive the second transform matrix.

8. The image processing apparatus according to claim 7 , wherein

the derivation section is further configured to apply the operation for a plurality of times to derive the second transform matrix.

9. The image processing apparatus according to claim 7 , wherein

the derivation section is further configured to apply a replacement operation to the matrix elements of the submatrix to derive the second transform matrix.

10. The image processing apparatus according to claim 7 , wherein

the derivation section is further configured to apply a flip operation to the matrix elements of the submatrix to derive the second transform matrix.

11. The image processing apparatus according to claim 7 , wherein

the derivation section is further configured to apply a transposition operation to the matrix elements of the submatrix to derive the second transform matrix.

12. The image processing apparatus according to claim 7 , wherein

the derivation section is further configured to apply a sign inversion operation to the matrix elements of the submatrix to derive the second transform matrix.

13. The image processing apparatus according to claim 7 , wherein

the first size includes 2{circumflex over ( )}(N) x 2{circumflex over ( )}(N), and

the second size includes 2{circumflex over ( )}(N−1) x 2{circumflex over ( )}(N−1), where

N is an integer equal to or greater than 3, and {circumflex over ( )} is exponentiation.

14. The image processing apparatus according to claim 2 , wherein

the inverse orthogonal transform section is further configured

to apply an inverse secondary transform to the coefficient data and use the second transform matrix derived by the derivation section, to apply an inverse primary transform to a result of the inverse secondary transform.

15. The image processing apparatus according to claim 2 , wherein

the decoding section is further configured to use a Coding Unit (CU) of a Quad-Tree Block Structure or a Quad Tree Plus Binary Tree (QTBT) Block Structure as a unit of processing to decode the bitstream.

16. The image processing apparatus according to claim 2 , wherein

the inverse orthogonal transform section is further configured to use a Transform Unit (TU) of a Quad-Tree Block Structure or a Quad Tree Plus Binary Tree (QTBT) Block Structure as a unit of processing to apply the inverse orthogonal transform to the coefficient data.

17. The image processing apparatus according to claim 2 , wherein

the derivation section is further configured to derive, as the submatrix, the matrix obtained by sampling the matrix elements of the first transform matrix based on predetermined sampling parameters.

18. The image processing apparatus according to claim 17 , wherein

the first transform matrix includes a transform matrix in which a transform type trType includes DCT2, the first size includes a maximum size maxTbS of a transform block, and the second size includes a size nTbS of a one-dimensional transform.

19. The image processing apparatus according to claim 18 , wherein

the sampling parameters include

a sampling interval stepsize indicating a row interval in sampling,

a row offset offsetCol indicating an offset (row location) of sampling, and

a column offset offsetRow indicating an offset (column location) of sampling.

20. The image processing apparatus according to claim 19 , wherein

the derivation section is further configured to sample the first transform matrix, based on the sampling interval stepsize, the row offset offsetCol, and the column offset offsetRow derived as follows, to derive the second transform matrix in which the transform type trType includes DCT2:

stepsize=1<<(Log 2(maxTbS)−Log 2(nTbS)),

offsetCol=0, and

offsetRow=0.

21. The image processing apparatus according to claim 20 , wherein

the derivation section is further configured to apply a flip operation of each column to the matrix elements of the submatrix obtained by sampling the first transform matrix and perform a sign inversion operation of odd columns, to derive the second transform matrix in which the transform type trType includes DST2.

22. The image processing apparatus according to claim 19 , wherein

the derivation section is further configured to sample the first transform matrix, based on the sampling interval stepsize, the row offset offsetCol, and the column offset offsetRow derived as follows, to derive the second transform matrix in which the transform type trType includes DCT4:

stepsize=1<<(Log 2(maxTbS)−Log 2(nTbS)),

offsetCol=stepsize<<1, and

offsetRow=0.

23. The image processing apparatus according to claim 22 , wherein

the derivation section is further configured to apply a flip operation of each row to the matrix elements of the submatrix obtained by sampling the first transform matrix, to derive the second transform matrix in which the transform type trType includes FlipDCT4.

24. The image processing apparatus according to claim 23 , wherein

the derivation section is further configured to apply a sign inversion operation of odd rows to the matrix elements of the submatrix subjected to the flip operation, to derive the second transform matrix in which the transform type trType includes DST4.

25. The image processing apparatus according to claim 19 , wherein

the derivation section is further configured to sample the first transform matrix, based on the sampling interval stepsize, the row offset offsetCol, and the column offset offsetRow derived as follows, multiples matrix elements of even rows of an obtained submatrix by a base sign baseSign derived based on the row offset offsetCol as follows, and multiplies matrix elements of odd rows of the submatrix by an opposite sign −baseSign of the base sign, to derive the second transform matrix in which the transform type trType includes DST4:

stepsize=1<<(Log 2−(maxTbS)−Log 2(nTbS)),

offsetCol=stepsize>>1,

offsetRow=maxTbS−nTbS, and

baseSign=(offsetCol %2==0)? 1:−1.

26. The image processing apparatus according to claim 1 , wherein

the decoding section includes

an arithmetic decoding section configured to arithmetically decode the bitstream to generate quantization data, and

an inverse quantization section configured to apply inverse quantization to the quantization data generated by the arithmetic decoding section, to generate the coefficient data,

the inverse orthogonal transform section is further configured to apply an inverse orthogonal transform to the coefficient data generated by the inverse quantization section, and

the arithmetic decoding section and the inverse quantization section are each implemented via at least one processor.

27. The image processing apparatus according to claim 1 , wherein

each element of the first transform matrix is scaled and approximated to an integer.

28. An image processing method comprising:

decoding a bitstream to generate coefficient data in which a predicted residual of an image is orthogonally transformed;

deriving, from a submatrix as part of a first transform matrix in a first size, a second transform matrix in a second size that is a size smaller than the first size;

using the derived second transform matrix to apply an inverse orthogonal transform to the generated coefficient data; and

using the first transform matrix stored in a lookup table, to derive the second transform matrix.

29. An image processing apparatus comprising:

a derivation section configured to derive, from a submatrix as part of a first transform matrix in a first size, a second transform matrix in a second size that is a size smaller than the first size;

an orthogonal transform section configured to use the second transform matrix derived by the derivation section, to orthogonally transform a predicted residual of an image and generate coefficient data; and

an encoding section configured to encode the coefficient data generated by the orthogonal transform section, to generate a bitstream,

wherein the derivation section is further configured to use the first transform matrix stored in a lookup table, to derive the second transform matrix, and

wherein the derivation section, the orthogonal transform section, and the encoding section are each implemented via at least one processor.

30. An image processing method comprising:

deriving, from a submatrix as part of a first transform matrix in a first size, a second transform matrix in a second size that is a size smaller than the first size;

using the derived second transform matrix to orthogonally transform a predicted residual of an image and generate coefficient data;

encoding the generated coefficient data to generate a bitstream; and

using the first transform matrix stored in a lookup table, to derive the second transform matrix.

31. A non-transitory computer-readable medium having embodied thereon a program, which when executed by a computer causes the computer to execute an image processing method, the method comprising:

decoding a bitstream to generate coefficient data in which a predicted residual of an image is orthogonally transformed;

deriving, from a submatrix as part of a first transform matrix in a first size, a second transform matrix in a second size that is a size smaller than the first size;

using the derived second transform matrix to apply an inverse orthogonal transform to the generated coefficient data; and

using the first transform matrix stored in a lookup table, to derive the second transform matrix.

32. A non-transitory computer-readable medium having embodied thereon a program, which when executed by a computer causes the computer to execute an image processing method, the method comprising:

deriving, from a submatrix as part of a first transform matrix in a first size, a second transform matrix in a second size that is a size smaller than the first size;

using the derived second transform matrix to orthogonally transform a predicted residual of an image and generate coefficient data;

encoding the generated coefficient data to generate a bitstream; and

using the first transform matrix stored in a lookup table, to derive the second transform matrix.