Method and apparatus for encoding/decoding residual data based on a plurality of transformations

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

obtaining residual coefficients of a current block;

performing inverse-quantization for the residual coefficients;

performing a secondary inverse-transform for the current block; and

performing a primary inverse-transform on a result of performing the secondary inverse-transform,

wherein the secondary inverse-transform is performed for inverse-quantized residual coefficients, resultant from the invers-quantization, included in a partial region of the current block,

wherein the secondary inverse-transform is performed by using an inverse-transform matrix and an input matrix, the input matrix being generated by arranging the inverse quantized residual coefficients of a two-dimensional form in the partial region in a one-dimensional form, and

wherein a number of rows or columns of the inverse-transform matrix is greater than a number of the inverse-quantized residual coefficients included in the partial region.

2. The method of claim 1 , wherein a size of the partial region is adaptively determined based on a size of the current block.

3. The method of claim 1 , wherein a transform type for the primary inverse transform is determined based on index information signaled through a bitstream.

4. The method of claim 3 , wherein the index information specifies any one of a plurality of transform sets,

wherein a first transform type candidate included in the transform set is determined as a horizontal directional transform type of the current block, and

wherein a second transform type candidate included in the transform set is determined as a vertical directional transform type of the current block.

5. The method of claim 1 , wherein a transform type for the primary inverse transform is determined by comparing a width of the current block or a height of the current block with a threshold value.

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

performing a primary transform on residual samples in a current block;

performing a secondary transform for the current block;

quantizing transform coefficients generated as a result of the secondary transform; and

encoding the quantized transform coefficients,

wherein the secondary transform is performed for intermediate transform coefficients, resultant from the primary transform, included in a partial region of the current block,

wherein the secondary transform is performed by using a transform matrix and an input matrix, the input matrix being generated by arranging the intermediate transform coefficients of a two-dimensional form in a one-dimensional form, and

wherein a number of rows or columns of the transform matrix is less than a number of the intermediate transform coefficients included in the partial region.

7. The method of claim 6 , wherein a size of the partial region is adaptively determined based on a size of the current block.

8. The method of claim 6 , wherein index information indicating a transform type for the primary transform is encoded in a bitstream.

9. The method of claim 8 , wherein the index information specifies any one of a plurality of transform sets,

wherein a first transform type candidate included in the transform set is determined as a horizontal directional transform type of the current block, and

wherein a second transform type candidate included in the transform set is determined as a vertical directional transform type of the current block.

10. The method of claim 6 , wherein a transform type for the primary transform is determined by comparing a width of the current block or a height of the current block with a threshold value.

11. A non-statutory computer-readable medium for storing compressed video data, the compressed video data comprising:

information on residual coefficients of a current block,

wherein an inverse-quantization is performed for the residual coefficients,

wherein a secondary inverse-transform is performed for inverse-quantized residual coefficients, resultant from the invers-quantization, included in a partial region of the current block,

wherein a primary inverse-transform is performed on a result of performing the secondary inverse-transform,

wherein the secondary inverse-transform is performed by using an inverse-transform matrix and an input matrix, the input matrix being generated by arranging the inverse quantized residual coefficients of a two-dimensional form in the partial region in a one-dimensional form, and

wherein a number of rows or columns of the inverse-transform matrix is greater than a number of the inverse-quantized residual coefficients included in the partial region.