KR20030053108A - Method for resizing images in block-DCT domain - Google Patents

Abstract

PURPOSE: A method for transforming the size of an image at a block discrete cosine transform domain is provided to randomly transform the size of the image and remarkably reduce the amount of calculation by simplifying window functions. CONSTITUTION: In the case of downsampling, 8xM samples are made by inserting M-1 zeros in the back of each sample of a DCT(Discrete Cosine Transform) block formed of 8 samples. The adjacent 8xM samples are symmetrically convoluted with DCT coefficients of M window functions. Upper 8 samples of the M results of the symmetrical convolution are added with each other to make 8-sample DCT. In the case of upsampling, 8xL samples are made by inserting (L-1)x8 zeros after each sample of a DCT block formed of 8 samples. 8xL samples are symmetrically convoluted with DCT coefficients of L window functions. Every L sample is collected from the 8xL sample result value of the symmetrical convolution to make L 8-sample DCT block.

Description

Image size conversion method in block discrete cosine transform domain {Method for resizing images in block-DCT domain}

The present invention relates to a method for reducing or increasing the size of an image using symmetric convolution in a block DCT region.

As digital images are widely used, there is a growing need for effective tools to process these images. Image size conversion is also a basic and important image processing tool. In particular, in order to support various image media with one digital image data, image size conversion necessarily follows. For example, video media that must be supported by a Video On Demand (VOD) service include video media of various sizes such as liquid crystal displays of mobile phones, in addition to general computer monitors, HDTVs, and general televisions. It is almost impossible to prepare and store all the digital image data of the size suitable for these image media. Therefore, one digital image data should be generated and stored, and only its size should be converted according to the image medium.

In general, in order to convert an image size, two operations, a change of a sampling rate and a low pass filtering, are required. To reduce the size of the image, lowpass filtering is performed on the image and then downsampling. In order to increase the size of the image, upsampling is performed on the image and then low pass filtering is performed. Typically this is done in the pixel region.

However, most still images and moving images are stored in a compressed form. Therefore, in order to convert the size of a compressed image, it has to be decompressed and then recompressed. In other words, in order to reduce the size of the image, it is necessary to go through three processes of decompression, image size conversion, and compression.

In order to solve this problem, many methods of directly converting the image size of a compressed image have been proposed. Since the compressed image is mainly Discrete Cosine Transform (DCT), the image size conversion for the compressed image means that the size conversion in the DCT region.

One such method is US Patent No. 5,708,732 (Fast DCT domain downsampling and inverse motion compensation). Here, 1 / n downsampling is realized by taking the average of n 8x8 DCT blocks and generating one 8x8 DCT block. However, according to this method, a reduction ratio such as 1 / n can be achieved, but there is a disadvantage that an arbitrary reduction ratio such as m / n cannot be achieved.

Another method is US Patent No. 5,845,015 (Method and apparatus for resizing images using the discrete cosine transform). In this case, the low pass filtering operation is performed by multiplying the DCT coefficients by the transform coefficients of the low pass filter, and then a 4 × 4 DCT block is generated by folding and subtracting the filtered coefficients. However, this method has a disadvantage in that the size of the generated DCT block is not 8x8 used in the general compression method, so that it cannot be used immediately in the DCT region.

SUMMARY OF THE INVENTION The present invention has been made in view of this point, and an object thereof is to provide a method for converting an image size in a DCT region which can be converted to an arbitrary size.

Another object of the present invention is to provide a method for converting an image size in a DCT region in which the size of the size-converted DCT block is 8x8 used in a general compression standard.

Another object of the present invention is to provide a method for converting an image size having a small amount of calculation.

1 is a conceptual diagram illustrating the concept of two-fold downsampling of the present invention.

2 is a block diagram of an apparatus for performing two fold downsampling of the present invention.

3 is a conceptual diagram illustrating the concept of two-fold upsampling of the present invention.

4 is a block diagram of an apparatus for performing two fold upsampling of the present invention.

5A and 5B are conceptual views for explaining a method of converting an image size at an arbitrary conversion rate.

In the downsampling method of the present invention, 0 is inserted after a sample of each block to perform symmetric convolution with DCT coefficients of M window functions. The convolution result of M adjacent blocks is added and then only the first 8 samples are taken for 1 / M downsampling. In the upsampling method, 8 samples of one block are padded with 8 samples of zero to perform symmetric convolution with DCT coefficients of L window functions. L-times upsampling by taking only even samples from the convolution results. After L times upsampling, 1 / M downsampling enables L / M size conversion. These calculations can also be obtained at once using determinants. In addition, the amount of computation can be significantly reduced by simplifying the window function.

First, the relation equations for multiplication-convolution properties in the DCT domain, which are used to implement filters used in downsampling and upsampling, will be described. The product-convolutional relationship in the DCT domain is described in S.A. Martucci's "Symmetric Convolution and the Discrete Sine and Cosine Transforms" (IEEE Trans.Signal Processing, vol. 42, No. 5, May 1994).

DCT, which is generally used for image compression, is type 2 among various forms, and its product-convolution characteristics are summarized as follows.

Type 2 DCT for a sequence x ( n ) having a size N is represented by Equation 1, and an inverse transform is represented by Equation 2.

Here, the weighting function u ( k ) is expressed by Equation 3 below.

In Equations 1 to 3, the product-convolution characteristic of DCT is defined as in Equation 4.

Here, w ( n ) is an arbitrary function, and in the present invention, it may be a filter function for upsampling / downsampling.

Meanwhile, Is a symmetric convolution, which is defined as in Equation 5.

X _e and W _e are anti-symmetric extensions of X ( k ) and W ( k ), respectively. For example, X ( k ) to X _e ( k ) are defined as in Equation 6.

Therefore, if one considers an arbitrary filter in the spatial domain, Equation 4 can be used to easily obtain a filter in the DCT domain.

Meanwhile, since DCT used in actual image compression is an orthogonal form of Type 2 DCT, a scaling factor in the entire calculation is required.

Orthogonal form and general type Type 2 DCT transformation relations are as follows.

Considering the orthogonal form, Equation 4 can be summarized as follows.

With this background, the image size conversion method of the present invention will be described.

1 is a conceptual diagram illustrating the concept of two-fold downsampling of the present invention. In FIG. 1, the left side is an example of a digital video signal in a spatial domain, and the right side is a coefficient after DCT of the same signal.

In (a) x ₁ ( n ) ₈ , x ₂ ( n ) ₈ are signals of 8 samples of adjacent blocks, and X ₁ ( k ) ₈ and X ₂ ( k ) ₈ are their DCT coefficients. in (b) , Is a symmetric extension of x ₁ ( n ) ₈ and x ₂ ( n ) ₈ in the spatial domain, respectively, which inserts 0 after the sample of each DCT coefficient in the DCT domain. , Corresponds to. (c) is a window function w ₁ ( n ) ₁₆ , w ₂ ( n ) ₁₆ and corresponding DCT coefficients W ₁ ( k ) ₁₆ , W ₂ for cutting out the desired portion of the signal of (b). ( k ) shows ₁₆ .

When the signal of (b) is multiplied by the window function in the spatial domain, a signal such as (d) appears, which corresponds to the symmetric convolution of the DCT coefficient of (b) and the DCT coefficient of the window function in the DCT domain.

As can be seen in (e), the sum x ( n ) ₁₆ of the two signals after windowing is equal to the original signal, i.e., the signal in (a). If this is expressed in the DCT domain, Equation 8 is given.

Therefore, since 16 samples of (e) are the same as DCT for all two adjacent blocks, two-fold downsampling can be realized by taking only 8 coefficients on the low frequency side.

A block diagram of an apparatus for implementing the above procedure is shown in FIG.

The zero inserters 11 and 12 insert two zeros after two eight-sample signals X ₁ and X ₂ of the input adjacent block to output two 16-sample signals. Symmetric convolution operators 13 and 14 perform symmetric convolution on these two 16 sample signals for the window functions W ₁ and W ₂ , respectively. The adder 15 adds the outputs of the symmetric convolution operators 13 and 14 and outputs a result as shown in Equation (8). The first eight-sample extractor 17 takes the first eight samples, that is, the low-wavelength eight samples from the 16-sample signal resulting from Equation 8, and outputs a two-fold downsampled signal Z.

The window functions W ₁ ( k ) ₁₆ and W ₂ ( k ) ₁₆ can be obtained using Equation 1, and the results of the results are shown in Table 1 below.

Looking at Table 1, since the coefficients have a lot of zeros and the symmetry convolution has symmetry, we can arrange each of them as a matrix of 8x8 as follows.

In Equations 9 and 10, each matrix is as follows.

As a result, when downsampling ( z ^or ) is arranged in the form of a matrix, Equation 16 is used.

Here, F and G are scaling factors, which are represented by Equations 17 and 18, respectively.

As shown in Equation 16, symmetric convolution can be implemented in the form of a matrix to consider the zero coefficient, and part of {} in Equation 16 can be used in advance to calculate the actual amount of upsampling / downsampling. It can be greatly reduced than the method.

In the same way, three-fold downsampling can be obtained with three window functions for eight samples of three adjacent blocks. In this case, the first window function has 1 left 8 sample is 1, the remaining 16 samples are 0, the second window function has 1 middle 8 sample is 1, the remaining 16 samples is 0, the third window function is right 8 sample is 1 and the remaining 16 samples is 0. . The DCT coefficients of these window functions can be obtained from Equation 1.

By extending this approach, you can achieve 1 / M downsampling. That is, downsampling can be performed with the M window functions for 8 samples of adjacent M blocks through the same procedure.

This is described as follows. First, 8xM samples are made by inserting M-1 zero samples after each sample of the 8-sample DCT block. The 8xM samples of the adjacent M DCT blocks are symmetrically convolved with the DCT coefficients of the M window functions, respectively. When the upper eight samples of the M symmetric convolutions are added together to form one eight-sample DCT, 1 / M downsampling is completed. In this case, the M window functions are 8xM samples in size, and the nth window function is a function in which the nth 8th sample is 1 and the remaining samples are all 0.

To create one 8-sample DCT by adding each of the top 8 samples of the M symmetric convolutions, add the results of the M symmetric convolutions to each sample to create one 8xM sample, where the top 8 You can take a sample and make one 8-sample DCT block. Alternatively, the upper 8 samples may be taken from the result values of the M symmetric convolutions, and each sample may be added to form one 8-sample DCT block.

Next, the concept of two-fold upsampling of the present invention will be described with reference to FIG. In FIG. 3, the left side is an example of a digital video signal in a spatial domain, and the right side is a coefficient after DCT of the same signal.

In (a) x ( n ) ₈ is the signal of 8 samples of one block and X ( k ) ₈ is the DCT coefficient of x ( n ) ₈ . The signal Y ( k ) ₁₆ in (b) is a signal when 8 zeros are inserted into the high frequency side of X ( k ) ₈ , and y ( n ) ₁₆ is a signal appearing in the spatial domain at this time. It can be seen that the signal in the spatial domain is an upsampled 16-sample signal. (c) is a window function w ₁ ( n ) ₁₆ , w ₂ ( n ) ₁₆ and corresponding DCT coefficients W ₁ ( k ) ₁₆ , W ₂ for cutting out the desired portion of the signal of (b). ( k ) shows ₁₆ .

When the signal of (b) is multiplied by the window function in the spatial domain, a signal such as (d) appears, which corresponds to the symmetric convolution of the DCT coefficient of (b) and the DCT coefficient of the window function in the DCT domain. Here, it can be seen that the window function used in upsampling is the same as that used in downsampling. in (d) Taking the first eight samples of Taking the last 8 samples of, we can obtain the signals y ₁ ( n ) ₈ and y ₂ ( n ) ₈ obtained by double-folding up x ( n ) ₈ as shown in (e). This is equivalent to taking even samples in the signal of (d) in the DCT region.

A block diagram of an apparatus for implementing the above procedure is shown in FIG.

In the eight-sample signal X in one block, zero is inserted into eight samples of the high frequency region by the zero padding unit 21 so that a signal of 16 samples is output. This signal is subjected to symmetric convolution operations with the window functions W ₁ and W ₂ by the symmetric convolution operators 23 and 24, respectively. The even sample extractors 25 and 26 extract only the even samples from the outputs from the symmetric convolution operators 23 and 24 and output two eight-sample signals Y ₁ and Y ₂ to complete two-fold upsampling.

When the upsampling procedure is expressed in the form of a matrix, Equations 19 and 20 are used.

From here, , Are the results of each upsampled eight samples, and the other matrices are the same as for downsampling.

In the same way, three-fold upsampling can be obtained with three different window functions for eight samples of a block, as in three-fold downsampling.

The generalized description is as follows. First, an 8xL sample is made by inserting (L-1) x8 zero samples after 8 samples of a DCT block of 8 samples. The 8xL sample is then symmetrically convolved with the DCT coefficients of the L window functions. This produces L symmetric convolution results of 8xL samples. L-fold upsampling is achieved by taking every L-th sample from each of them to make L 8-sample DCT blocks. In this case, the L window functions are 8xL samples, and the nth window function is a function in which the nth 8th sample is 1 and the remaining samples are all 0.

When performing the convolution in the DCT domain, the DCT coefficients of the window function and the image contain 0, and since the convolution in the DCT is symmetric convolution, it can be expressed simply in matrix form, and the window function is also in the range that image quality is allowed. It can be further simplified within.

For example, when using the window function of downsampling by replacing some coefficients with 0, a matrix such as Equation 21 can be obtained.

When a simple matrix such as Equation 21 is used, the amount of calculation can be reduced to about 60% compared to the case of using the Equations 11 and 12.

Next, a description will be given of a method for implementing image ratio conversion of any ratio.

For example, in the case of converting the image size of L / M times, the image size conversion of the desired ratio is realized by performing M times downsampling after performing L times upsampling using the method described above. An example of this is shown in FIG. 5A. In this case, Equations 16, 19, and 20 may be easily transformed into a form of upsampling / downsampling of an arbitrary size, and a window function according to the present invention may also be easily obtained.

5b shows a case of converting an image size of 3/2 times, that is, 1.5 times. In FIG. 5B, an eight-sample signal is first upsampled into three eight-sample signals, and two eight-sample signals are downsampled into one eight-sample signal to achieve a 3 / 2-fold image size conversion.

The generalized description is as follows. First, an 8xL sample is made by inserting (L-1) x8 zero samples after 8 samples of a DCT block of 8 samples. The 8xL samples are then symmetrically convolved with the DCT coefficients of the L window functions. This produces L symmetric convolution results of 8xL samples. Each Lth sample is taken from each of them to make L 8 sample DCT blocks to achieve L times upsampling. Then, after each sample of the upsampled 8-sample DCT block, M-1 zero-inserted samples are inserted to make 8xM samples. The 8xM samples of the adjacent M DCT blocks are symmetrically convolved with the DCT coefficients of the M window functions, respectively. The result of M symmetric convolutions is then generated. L / M times size conversion is completed by generating one 8-sample DCT by adding each of the upper 8 samples of the result.

In this case, the L window functions are 8xL samples, and the nth window function is a function in which the nth 8th sample is 1 and the remaining samples are all 0. In addition, the M window functions are 8xM samples in size, and the mth window function is a function in which the mth 8th sample is 1 and the remaining samples are all 0.

As described above, according to the present invention, since the size of the size-converted DCT block is 8x8 used in a general compression standard, there is an effect that there is no need for inverse DCT transformation.

In addition, by performing L-sampling upsampling and M-folding downsampling, there is an effect that it can be converted to an arbitrary size such as L / M times.

In addition, there is an effect that the amount of calculation can be significantly reduced by simplifying the window function.

Claims (11)

A first step of creating an 8xM sample by inserting M-1 zero samples after each sample of an 8-sample DCT block, Performing a symmetric convolution of 8xM samples of adjacent M DCT blocks with DCT coefficients of M window functions, respectively; A third step of adding one of the eight upper samples of the M symmetric convolution results to create one eight-sample DCT, The M window functions are 8xM samples in size, and the nth window function is a function in which the nth 8th sample is 1 and the remaining samples are all 0. The method of claim 1, wherein the third step Adding the results of the M symmetric convolutions to each sample to produce one 8xM sample; and And taking one upper eight sample from the one 8xM sample to create one eight-sample DCT block. The method of claim 1, wherein the third step Taking a top eight samples from the results of the M symmetric convolutions, And adding eight M samples to each sample to create one eight-sample DCT block. Creating 8xL samples by inserting (L-1) x8 zero-samples after 8 samples of a DCT block of 8 samples, Symmetric convolution of the 8xL samples with the DCT coefficients of the L window functions, Taking every Lth sample from the 8xL sample results of the L symmetric convolutions to produce L 8 sample DCT blocks, The L window functions are 8 × L samples, and the n th window function is a function in which the n th 8 sample is 1 and the remaining samples are all 0. The first step of inserting (L-1) x8 zero samples after 8 samples of a DCT block of 8 samples to make 8xL samples, Performing a symmetric convolution of the 8xL samples with the DCT coefficients of the L window functions, A third step of taking every Lth sample from the 8xL sample results of the L symmetric convolutions to produce L 8 sample DCT blocks, A fourth step of making 8xM samples by inserting M-1 zero samples after each sample of the eight-sample DCT block of the third step; A fifth step of symmetrically convolving 8xM samples of adjacent M DCT blocks with DCT coefficients of M window functions, A sixth step of adding one of the eight upper samples of the M symmetric convolution results to create one eight-sample DCT, The L window functions are 8xL samples in size, the nth window function is a function in which the nth 8th sample is 1 and the remaining samples are all 0. The M window functions are 8xM samples in size, and the m th window function is a function in which the m th eighth sample is 1 and the remaining samples are all zero. The method of claim 5, wherein the sixth step Adding the results of the M symmetric convolutions to each sample to produce one 8xM sample; and And taking one upper eight sample from the one 8xM sample to create one eight-sample DCT block. The method of claim 5, wherein the sixth step Taking a top eight samples from the results of the M symmetric convolutions, And adding eight M samples to each sample to create one eight-sample DCT block. Two 8-sample DCT blocks x ₁ = [ X ₁ (0) ₈ X ₁ (1) ₈ X ₁ (2) ₈ X ₁ (3) ₈ X ₁ (4) ₈ X ₁ (5) ₈ X ₁ (6 ) ₈ X ₁ (7) ₈ ] ^T and x ₂ = [ X ₂ (0) ₈ X ₂ (1) ₈ X ₂ (2) ₈ X ₂ (3) ₈ X ₂ (4) ₈ X ₂ (5) ₈ X ₂ (6) ₈ X ₂ (7) ₈ ] One 8 sample DCT block from ^T z = [ Z (0) ₈ Z (1) ₈ Z (2) ₈ Z (3) ₈ Z (4) ₈ Z (5) ₈ Z (6) ₈ Z (7) ₈ ] In the method of downsampling to ^T to convert the size of an image, Z is the following determinant Saved by From here , , , , W ₁ ( k ) ₁₆ = [16.0000, 10.2023, 0, -3.4449, 0, 2.1214, 0, -1.5763, 0, 1.2936, 0, -1.1339, 0, 1.0450, 0, -1.0048] Image size conversion method characterized in that. Two 8-sample DCT blocks x ₁ = [ X ₁ (0) ₈ X ₁ (1) ₈ X ₁ (2) ₈ X ₁ (3) ₈ X ₁ (4) ₈ X ₁ (5) ₈ X ₁ (6 ) ₈ X ₁ (7) ₈ ] ^T and x ₂ = [ X ₂ (0) ₈ X ₂ (1) ₈ X ₂ (2) ₈ X ₂ (3) ₈ X ₂ (4) ₈ X ₂ (5) ₈ X ₂ (6) ₈ X ₂ (7) ₈ ] One 8 sample DCT block from ^T z = [ Z (0) ₈ Z (1) ₈ Z (2) ₈ Z (3) ₈ Z (4) ₈ Z (5) ₈ Z (6) ₈ Z (7) ₈ ] In the method of downsampling to ^T to convert the size of an image, Z is the following determinant Saved by From here , , , , W ₁ ( k ) ₁₆ = [16.0000, 10.2023, 0, -3.4449, 0, 2.1214, 0, -1.5763, 0, 1.2936, 0, -1.1339, 0, 1.0450, 0, -1.0048] Image size conversion method characterized in that. One 8-sample DCT block x = [ X (0) ₈ X (1) ₈ X (2) ₈ X (3) ₈ X (4) ₈ X (5) ₈ X (6) ₈ X (7) ₈ ] Two 8-sample DCT blocks from ^T y ₁ = [ Y ₁ (0) ₈ Y ₁ (1) ₈ Y ₁ (2) ₈ Y ₁ (3) ₈ Y ₁ (4) ₈ Y ₁ (5) ₈ Y ₁ (6) ₈ Y ₁ (7) ₈ ] ^T and y ₂ = [ Y ₂ (0) ₈ Y ₂ (1) ₈ Y ₂ (2) ₈ Y ₂ (3) ₈ Y ₂ (4) ₈ Y ₂ ( 5) ₈ Y ₂ (6) ₈ Y ₂ (7) ₈ ] In the method of converting the size of an image by upsampling to ^T , Y ₁ and y ₂ are the following determinants . Saved by From here , , , , W ₁ ( k ) ₁₆ = [16.0000, 10.2023, 0, -3.4449, 0, 2.1214, 0, -1.5763, 0, 1.2936, 0, -1.1339, 0, 1.0450, 0, -1.0048] Image size conversion method characterized in that. One 8-sample DCT block x = [ X (0) ₈ X (1) ₈ X (2) ₈ X (3) ₈ X (4) ₈ X (5) ₈ X (6) ₈ X (7) ₈ ] Two 8-sample DCT blocks from ^T y ₁ = [ Y ₁ (0) ₈ Y ₁ (1) ₈ Y ₁ (2) ₈ Y ₁ (3) ₈ Y ₁ (4) ₈ Y ₁ (5) ₈ Y ₁ (6) ₈ Y ₁ (7) ₈ ] ^T and y ₂ = [ Y ₂ (0) ₈ Y ₂ (1) ₈ Y ₂ (2) ₈ Y ₂ (3) ₈ Y ₂ (4) ₈ Y ₂ ( 5) ₈ Y ₂ (6) ₈ Y ₂ (7) ₈ ] In the method of converting the size of an image by upsampling to ^T , Y ₁ and y ₂ are the following determinants . Saved by From here , , , , W ₁ ( k ) ₁₆ = [16.0000, 10.2023, 0, -3.4449, 0, 2.1214, 0, -1.5763, 0, 1.2936, 0, -1.1339, 0, 1.0450, 0, -1.0048] Image size conversion method characterized in that.