Method and apparatus for encoding and decoding image by using rotational transform

1. A method of encoding an image, the method comprising:

performing discrete cosine transform (DCT) on a current block to generate a first frequency coefficient matrix;

determining an angle parameter based on whether the current block is intra predicted;

performing a partial switch between at least one of rows and columns of the first frequency coefficient matrix based on the determined angle parameter to generate a second frequency coefficient matrix;

quantizing the second frequency coefficient matrix; and

entropy-encoding the second frequency coefficient matrix and information about the angle parameter,

wherein the angle parameter indicates a degree of the partial switch between at least one of the rows and the columns of the first frequency coefficient matrix, and

wherein the determining the angle parameter comprises determining the angle parameter based on an intra prediction direction of the current block.

2. The method of claim 1 , wherein the determining the angle parameter based on the intra prediction direction of the current block comprises selecting a first matrix for performing partial switching between the rows and selecting a second matrix for performing partial switching between the columns from among a plurality of matrices based on the intra prediction direction of the current block.

3. The method of claim 2 , wherein the generating the second frequency coefficient matrix comprises multiplying a left side of the first frequency coefficient matrix by the selected first matrix and multiplying a right side of the first frequency coefficient matrix by the selected second matrix.

4. The method of claim 1 , wherein the angle parameter is a parameter for Euler angles.

5. A method of decoding an image, the method comprising:

entropy-decoding a second frequency coefficient matrix and information about an angle parameter;

determining the angle parameter based on the entropy-decoded information about the angle parameter and whether a current block is intra predicted;

inverse quantizing the entropy-decoded second frequency coefficient matrix;

performing a partial switch between at least one of rows and columns of the second frequency coefficient matrix based on the determined angle parameter to generate a first frequency coefficient matrix; and

performing inverse discrete cosine transform (IDCT) on the first frequency coefficient matrix to restore the current block,

wherein the predetermined angle parameter indicates a degree of partial switching between the at least one of the rows and the columns of the second frequency coefficient matrix, and

wherein the determining the angle parameter comprises determining the angle parameter based on an intra prediction direction of the current block.

6. The method of claim 5 , wherein the determining the angle parameter based on the intra prediction direction of the current block comprises selecting a first matrix for performing partial switching between the rows and selecting a second matrix for performing partial switching between the columns from among a plurality of matrices based on the intra prediction direction of the current block.

7. The method of claim 6 , wherein the generating the second frequency coefficient matrix comprises multiplying a left side of the second frequency coefficient matrix by the selected first matrix and multiplying a right side of the second frequency coefficient matrix by the selected second matrix.

8. The method of claim 5 , wherein the angle parameter is a parameter for Euler angles.

9. An apparatus for encoding an image, the apparatus comprising:

a transformer which performs discrete cosine transform (DCT) on a current block to generate a first frequency coefficient matrix and which performs a partial switch between at least one of rows and columns of the first frequency coefficient matrix based on an angle parameter determined according to whether the current block is intra predicted to generate a second frequency coefficient matrix;

a quantizer which quantizes the second frequency coefficient matrix; and

an entropy encoder which entropy-encodes the second frequency coefficient matrix and information about the angle parameter,

wherein the angle parameter indicates a degree of partial switching between the at least one of the rows and the columns of the first frequency coefficient matrix, and

wherein the transformer determines the angle parameter based on an intra prediction direction of the current block.

10. The apparatus of claim 9 , wherein the transformer selects a first matrix for performing partial switching between the rows and selects a second matrix for performing partial switching between the columns from among a plurality of matrices based on the intra prediction direction of the current block.

11. The apparatus of claim 10 , wherein the transformer multiplies a left side of the first frequency coefficient matrix by the selected first matrix and multiplies a right side of the first frequency coefficient matrix by the selected second matrix.

12. The apparatus of claim 9 , wherein the angle parameter is a parameter for Euler angles.

13. An apparatus for decoding an image, the apparatus comprising:

an entropy decoder which entropy-decodes a second frequency coefficient matrix and information about an angle parameter;

an inverse quantizer which inverse quantizes the entropy-decoded second frequency coefficient matrix; and

an inverse transformer which performs a partial switch between at least one of rows and columns of the second frequency coefficient matrix based on the angle parameter to generate a first frequency coefficient matrix, the angle parameter determined according to the entropy-decoded information about the angle parameter and whether a current block is intra predicted, and which performs inverse discrete cosine transform (IDCT) on the first frequency coefficient matrix to restore the current block,

wherein the angle parameter indicates a degree of partial switching between the at least one of the rows and the columns of the first frequency coefficient matrix, and

wherein the inverse transformer determines the angle parameter based on an intra prediction direction of the current block.

14. The apparatus of claim 13 , wherein the inverse transformer selects a first matrix for performing partial switching between the rows and selects a second matrix for performing partial switching between the columns from among a plurality of matrices based on the intra prediction direction of the current block.

15. The apparatus of claim 14 , wherein the inverse transformer multiplies a left side of the second frequency coefficient matrix by the selected first matrix and multiplies a right side of the second frequency coefficient matrix by the selected second matrix.

16. The apparatus of claim 13 , wherein the angle parameter is a parameter for Euler angles.

17. A non-transitory computer readable recording medium having embodied thereon a computer program for executing the method of claim 1 .

18. A non-transitory computer readable recording medium having embodied thereon a computer program for executing the method of claim 5 .