Method and device for selecting optimal transform matrices for down-sampling DCT image
View Patent ↗Down-sampling of an image may be performed in the DCT domain. Transform matrices are obtained for down-sampling a DCT image of size M×N to a down-sampled DCT image of size I×J. The transform matrices may be used to down-sample the DCT image directly in the DCT domain. A spatial domain down-sampling method is selected and applied to the DCT image to produce a down-sampled DCT reference image. The transform matrices are selected by solving an optimization problem, leading to transform matrices which achieve a desired trade-off between the visual quality of images obtained using the transform matrices and the computational complexity associated with using the transform matrices. The visual quality is a measure of the difference between the down-sampled DCT image obtained using the transform matrices and the visual quality of the DCT reference image obtained using a spatial domain down-sampling method.
1. A method of selecting transform matrices for down-sampling in the discrete cosine transform (DCT) domain, the method comprising:
initializing the transform matrices;
obtaining at least one optimization parameter; and
selecting transform matrices to minimize an optimization expression, the optimization expression is a function of the at least one optimization parameter, wherein the at least one optimization parameter comprises a complexity trade-off parameter to balance the relative importance of a plurality of factors on the computational complexity of selecting transform matrices.
2. The method of claim 1 , wherein the at least one optimization parameter comprises a quality-and-complexity trade-off parameter to balance the relative importance of quality of an image down-sampled using the transform matrices and the computational complexity of selecting the transform matrices.
3. The method of claim 1 further comprising:
converting a DCT reference image into a spatial domain reference image;
applying a spatial domain down-sampling method to the spatial domain reference image to produce a spatial domain down-sampled reference image; and
converting the spatial domain down-sampled reference image to the DCT domain to produce a down-sampled DCT reference image, wherein the at least one optimization parameters comprises a quality-and-complexity trade-off parameter to adjust the trade-off between the error between a down-sampled image obtained using the transform matrices and the down-sampled DCT reference image.
4. The method of claim 3 , wherein selecting transform matrices includes determining the visual quality of the down-sampled DCT image obtained by applying the transform matrices to the DCT reference image relative to the visual quality of the down-sampled DCT reference image by calculating the mean squared error between the down-sampled DCT image obtained using the transform matrices and the down-sampled DCT reference image.
5. The method of claim 3 , wherein the transform matrices comprise a row-transform matrix and a column-transform matrix, and wherein selecting transform matrices includes determining the visual quality of down-sampled DCT images obtained by applying the row-transform matrix and the column-transform matrix to the DCT reference image, and determining the computational complexity associated with applying the row-transform matrix and the column-transform matrix to down-sample the DCT reference image.
6. The method of claim 3 , wherein the transform matrices comprise a row-transform matrix and a column-transform matrix, and wherein selecting transform matrices includes selecting transform matrices that satisfy the optimization expression:
min
D
IM
,
W
NJ
(
D
IM
·
C
MN
·
W
NJ
-
V
IJ
2
+
λ
·
r
g
)
,
where D IM is the row-transform matrix; W NJ is the column-transform matrix; C MN is the DCT image; D IM ·C MN ·W NJ is the down-sampled DCT image obtained using the transform matrices; V IJ is the down-sampled DCT reference image; r g is a measure of the computational complexity associated with using the transform matrices D IM , W NJ to down-sample an image C MN ; and λ is the quality-and-complexity trade-off parameter for balancing the trade-off between visual quality of the down-sampled DCT image and the computational complexity of obtaining the down-sampled DCT image.
7. The method of claim 1 , wherein the computational complexity is a function of the absolute values of elements in the transform matrices.
8. The method of claim 7 , further comprising calculating the summation of the absolute value of all elements in the transform matrices.
9. The method of claim 1 , wherein the at least one optimization parameter comprises a selective learning with forgetting threshold parameter and wherein the computational complexity is a function of the absolute values of all elements in the transform matrices below the selective learning with forgetting threshold parameter.
10. The method of claim 9 further comprising calculating the summation of the absolute values of all elements in the transform matrices below the selective learning with forgetting threshold parameter.
11. The method of claim 1 , wherein the computational complexity is a function of the number of non-zero elements in a binary representation of each element of the transform matrices.
12. An electronic device comprising:
a memory; and
a processor connected to the memory for obtaining transform matrices for down-sampling in the discrete cosine transform (DCT) domain, the processor being configured to:
initialize the transform matrices;
obtain at least one optimization parameter; and
select transform matrices to minimize an optimization expression, the optimization expression is a function of the at least one optimization parameter, wherein the at least one optimization parameter comprises a complexity trade-off parameter to balance the relative importance of a plurality of factors on the computational complexity.
13. The electronic device of claim 12 , wherein the at least one optimization parameter is retrieved from memory.
14. The electronic device of claim 12 , wherein the at least one optimization parameter comprises a quality-and-complexity trade-off parameter to balance the relative importance of quality of an image down-sampled using the transform matrices and the computational complexity of selecting the transform matrices.
15. The electronic device of claim 12 wherein the processor is further configured to:
convert a DCT reference image into a spatial domain reference image;
apply a spatial domain down-sampling method to the spatial domain reference image to produce a spatial domain down-sampled reference image; and
convert the spatial domain down-sampled reference image to the DCT domain to produce a down-sampled DCT reference image, wherein the at least one optimization parameter comprises a quality and complexity trade-off parameter to adjust the trade-off between the error between a down-sampled image obtained using the transform matrices and the down-sampled DCT reference image.
16. The electronic device of claim 15 , wherein selecting transform matrices includes determining the visual quality of the down-sampled DCT image obtained by applying the transform matrices to the DCT reference image relative to the visual quality of the down-sampled DCT reference image by calculating the mean squared error between the down-sampled DCT image obtained using the transform matrices and the down-sampled DCT reference image.
17. The electronic device of claim 15 wherein the transform matrices comprise a row-transform matrix and a column-transform matrix and wherein the optimization expression is:
min
D
IM
,
W
NJ
(
D
IM
·
C
MN
·
W
NJ
-
V
IJ
2
+
λ
·
r
g
)
,
where D IM is the row-transform matrix; W NJ is the column-transform matrix; C MN is the DCT image; D IM ·C MN ·W NJ is the down-sampled DCT image obtained using the transform matrices; V IJ is the down-sampled DCT reference image; r g is a measure of the computational complexity associated with using the transform matrices D IM , W NJ to down-sample an image C MN ; and λ is the quality-and-complexity trade-off parameter for balancing the trade-off between visual quality of the down-sampled DCT image and the computational complexity of obtaining the down-sampled DCT image.
18. The electronic device of claim 12 , wherein the at least one optimization parameter comprises a predetermined threshold parameter and wherein the processor is configured to ignore the computational complexity due to values in the transform matrices that are above the predetermined threshold parameter.