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

1. An image coding method for coding an image, the image coding method comprising:

selecting two or more transform components from among a plurality of transform components that include a translation component and a plurality of non-translation components, the two or more transform components indicating a transform relationship from a current block to be coded to a reference block of the current block, the current block being included in the image, and the reference block being included in a reference image different from the image;

generating a prediction image by using the selected two or more transform components;

coding the current block by using the prediction image;

coding selection information that identifies the selected two or more transform components; and

coding the two or more transform components of the current block by using two or more transform components of a coded block different from the current block.

2. The image coding method according to claim 1 , wherein the plurality of non-translation components include a rotation component, a scaling component, and a shearing component.

3. The image coding method according to claim 2 , wherein in the selecting, the two or more transform components are selected preferentially in a following order: the translation component, the rotation component, the scaling component and the shearing component.

4. The image coding method according to claim 1 , wherein the selection information includes a plurality of flags each of which corresponds to each of the plurality of transform components and indicates whether or not the corresponding transform component is selected.

5. The image coding method according to claim 1 , wherein

the selecting further includes

selecting one coding level from among a plurality of coding levels, the plurality of coding levels respectively indicating different combinations each of which includes some or all of the plurality of transform components; and

selecting the two or more transform components included in a combination indicated by the selected coding level which is indicated by the selection information.

6. The image coding method according to claim 1 , wherein the coding of the selection information further includes coding the selection information used in common for blocks in the image.

7. The image coding method according to claim 1 , wherein

in the selecting, the two or more transform components are selected based on a size of the current block, and

the selection information indicates the size of the current block.

8. The image coding method according to claim 7 , wherein

the plurality of non-translation components include a rotation component, a scaling component, and a shearing component, and

in the selecting, the shearing component is not selected in a case where the size of the current block is smaller than a threshold.

9. An image decoding method for decoding an image from a bitstream, the image decoding method comprising:

decoding, from the bitstream, selection information that identifies two or more transform components from among a plurality of transform components that include a translation component and a plurality of non-translation components;

selecting the two or more transform components identified by the decoded selection information, the two or more transform components indicating a transform relationship from a current block to be decoded to a reference block of the current block, the current block being included in the image, and the reference block being included in a reference image different from the image;

decoding, from the bitstream, the two or more transform components of the current block by using two or more transform components of a decoded block different from the current block;

generating a prediction image by using the two or more transform components of the current block; and

decoding, from the bitstream, the current block by using the prediction image.

10. The image decoding method according to claim 9 , wherein the plurality of non-translation components include a rotation component, a scaling component, and a shearing component.

11. The image decoding method according to claim 9 , wherein the selection information includes a plurality of flags each of which corresponds to each of the plurality of transform components and indicates whether or not the corresponding transform component is selected.

12. The image decoding method according to claim 9 , wherein

the selecting further includes

selecting one coding level from among a plurality of coding levels, the plurality of coding levels respectively indicating different combinations each of which includes some or all of the plurality of transform components; and

selecting the two or more transform components included in a combination indicated by the selected coding level which is indicated by the selection information.

13. The image decoding method according to claim 9 , wherein the decoding of the selection information further includes

decoding the selection information used in common for blocks in the image.

14. The image decoding method according to claim 9 , wherein

the selection information indicates a size of the current block, and

in the selecting, the two or more transform components are selected based on the size of the current block.

15. The image decoding method according to claim 14 , wherein

the plurality of non-translation components include a rotation component, a scaling component, and a shearing component, and

in the selecting, the shearing component is not selected in a case where the size of the current block is smaller than or equal to a threshold.

16. The image decoding method according to claim 14 , wherein

the plurality of non-translation components include a rotation component, a scaling component, and a shearing component, and

in the selecting, the two or more transform components are selected preferentially in a following order: the translation component, the rotation component, the scaling component, and the shearing component.

17. An image coding apparatus configured to code an image, the image coding apparatus comprising:

processing circuitry; and

storage coupled to the processing circuitry, wherein

the processing circuitry is configured to execute the image coding method according to claim 1 by using the storage.

18. An image decoding apparatus configured to decode an image from a bitstream, the image decoding apparatus comprising:

processing circuitry; and

storage coupled to the processing circuitry, wherein

the processing circuitry is configured to execute the image decoding method according to claim 9 by using the storage.

19. An image coding method for coding an image, the image coding method comprising:

selecting two or more transform components from among a plurality of transform components, the two or more transform components indicating transform relationship from a current block to be coded to a reference block of the current block, the current block being included in the image, and the reference block being included in a reference image different from the image;

generating a prediction image by using the selected two or more transform components;

coding the current block by using the prediction image;

coding selection information that identifies the selected two or more transform components; and

coding the selected two or more transform components of the current block by using two or more transform components of a coded block different from the current block.