JP2003283840A - Filtering processing apparatus and filtering processing method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To carry out convolution operation in a simple configuration and to simultaneously obtain both the integer type and real number type filtering process results. <P>SOLUTION: A multistage integer type reversible filtering apparatus representatively like wavelet operation to be used for JPEG 2000 or the like is composed of a filtering operation part 901 for performing filtering operation as a reversible real number type, a correction part 903 for correcting the arithmetic result of the filtering operation part 901 by using intermediate data to be used for the operation due to the relevant filtering operation part 901 and real number coefficients (r), (p) and (u) used for the operation, and an integer part 905 for making integral the result corrected by the correction part 903. <P>COPYRIGHT: (C)2004,JPO

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a filtering apparatus and method.

[0002]

2. Description of the Related Art Images, especially multi-valued images, contain a great deal of information, and there is a problem that the amount of data becomes enormous when storing and transmitting the images. Therefore, when storing and transmitting images, the redundancy of images is excluded.
Alternatively, high-efficiency coding is used in which the amount of data is reduced by changing the content of the image so that the deterioration of the image quality is difficult to visually recognize.

[0003] For example, in JPEG that is recommended by ISO and ITU-T as an international standard encoding method for still images, image data is converted into DCT coefficients for each block (8 pixels x 8 pixels) by discrete cosine transform (DCT). After that, each coefficient is quantized and further entropy coded to compress the image data. Since DCT and quantization are performed for each block, so-called block distortion may be noticeable at the boundary of each block of the decoded image.

On the other hand, JPEG2000 is being studied as a new international standard encoding method for still images.
In G2000, a wavelet (DWT) transform is proposed as one of pre-processing performed before quantization.
The wavelet transform has a feature that deterioration of a decoded image is hard to be visually recognized because input data is continuously processed instead of processing in a block unit unlike the current JPEG.

The discrete wavelet transform used in JPEG2000 is positioned as a filter process for dividing image data into low frequency components and high frequency components. Usually, the filtering process is performed by a convolution operation of a filter coefficient and image data. However, the following discrete wavelet transform used in JPEG2000 is not limited to the convolution operation, and the
The method based on the Ting Scheme can be applied.・ Daubecheis 9/7 Filter (hereinafter referred to as 9 × 7 filter) ・ 〃 5/3 Filter (hereinafter referred to as 5 × 3 filter) Hereinafter, the Lifting Scheme will be described.

<Explanation of Lifting Scheme>
FIG. 1 shows the basic structure of the lifting scheme in the forward direction, and FIG. 2 shows the basic structure of the lifting scheme in the reverse direction. P and u in the figure are called Lifting coefficients, and the filter coefficient of the 5 × 3 filter is shown in FIG.
Shows the Lifting coefficient of the 5 × 3 filter.

Lifting coefficient shown in FIG. p = (-1, -1) / 2 u = (1, 1) / 4 The operation of FIG. 1 will be described below with reference to FIG.

X is input image data, which is (X0, X1, X2, X3, X4, X5 ...) As shown in FIG. Even-numbered series pixel data and odd-numbered series pixel data are generated from the beginning of the input image.

Odd series of pixel data (X1, X3, X
5, X7. ． ． ), The thinning unit 105 thins out (downsamples) every other input image data from the beginning.

Pixel data of even series (X0, X2, X
4, X6. ． ． In (1), the delay unit 101 delays the image data by one pixel, and then the thinning unit 103 thins out (downsamples) every other image data after delaying by one pixel.

Since the two thinning units are operating at the same timing, the data delayed by one pixel by the delay unit 101 and the input image data not delayed are respectively thinned, so that the thinning phases of the two series differ from each other. Pixel data can be generated.

The multiplier 107 multiplies the even-numbered series pixel data by the Lifting coefficient p, and the addition result is added to the odd-numbered series pixel data by the adder 109 to obtain the high-frequency side conversion coefficient X '. o (X'1, X'3, X'5, X '
7. ． ． ) Is calculated.

The multiplication of the Lifting coefficient and the addition processing of the multiplication result are 1 in Lifting Scheme.
This is one unit of processing, and this is called a Lifting calculation step.

The Lifting coefficient p is vector data having two components. Two consecutive even-numbered pixel data are multiplied by each component (coefficient value), and the sum of the two multiplication results is multiplied by the Lifting coefficient p. Will result.

The multiplication of the Lifting coefficient u in the multiplier 111 is similarly performed. The object to be multiplied is the conversion coefficient X′o on the high frequency side that has just been calculated. The multiplication result is added to the even series of pixel data by the adder 113, and the conversion coefficient X'e (X'0, X'2, X'4, X'8 ...) On the low frequency side.
Ask for.

[0016] indicated by specific expression the above processes, (transform coefficients of the high-frequency _{side): X '2n + 1 =} X 2n + 1 + (- X 2n -X 2n + 2) / 2 (1) (Low-frequency-side conversion coefficient): _X'2n = _X2n + ( _X'2n-1 + _{X'2n + 1} ) / 4 (2).

The original image data is generally an integer value, but if the above filtering process is performed once, it becomes real number type data, and a fractional part generates 3 bits. In the two-dimensional filtering, once in the horizontal direction and once in the vertical direction, a total of 2
Since the above-described filtering process is performed once, if the rounding process of the decimal part is not performed in the middle, a decimal part of 6 bits is finally generated. Furthermore, if the filtering process is recursively repeated, the fractional part increases proportionally.

If the fractional part having 6 bits or more is left as it is, the amount of data increases, so that it is usually rounded, converted into an integer, and then saved. At the time of image data compression, integerization or quantization is performed to further reduce the data after filtering.

If the filtered result is rounded or quantized, information will be lost. Therefore, even if the filtering process is performed in the reverse direction, the original image data will not be restored. Above, the description of the forward filtering process is completed, and then the backward process is briefly described.

Reverse Lifting S shown in FIG.
The processing in the cheme is also similar to the forward processing. The processing content is expressed by an equation: (even-numbered series pixels): X _2n = X _2n − (X ′ _2n−1 + X ′ _{2n + 1} ) / 4 (3) (odd series pixels): X _{2n + 1} = _{X '2n + 1 - (-} X 2n -X 2n + 2) / 2 (4) and composed. The following three points are different from the forward processing.・ Lif used in two Lifting calculation steps
Reverse the order of the toning coefficients. -The result of multiplying Lifting coefficient is subtracted instead of addition.・ Instead of the thinning-out unit, replace the zero insertion unit with Li.
Used after the fting operation.

Units 209 and 213 in FIG. 2 are subtracters for performing the above subtraction, and units 203 and 205 are
Is the zero insertion unit. After that, in order to adjust the phase, the delay unit 201 delays the odd-sequence pixel data, which is zero-inserted, by one pixel. As a result, non-zero effective pixel data can be obtained alternately from the even series side and the odd series side. By combining them into one series, it is possible to obtain data obtained by subjecting the original image data to forward filter processing and backward filter processing.

If the tap number of the filter changes, Lift
The ing coefficient and the number of Lifting calculation steps change. For example, in the 9 × 7 filter, Lift
The number of ing calculation steps becomes four.

When the Lifting Scheme is used, the product-sum operation can be realized with a smaller number of times compared to the convolution operation processing, so that the implementation is made more efficient and the integer type reversible conversion described later becomes possible.

<Explanation of Reversible Transformation> Even if mathematically reversible, it is not always reversible when implemented. The details will be described below.

In the broad sense, the reversible transform is a transform in which transform coefficient data that has been filtered (transformed) in the forward direction can be completely restored to the original data by filtering it in the backward direction. This property of reversible transformation is called reversible or reversible. What is mathematically called a reversible transformation falls into this category. Specifically, a transform matrix represented by an orthonormal matrix such as DCT transform, or the above Liftin
There are filters and the like calculated by g Scheme. In a broad sense of reversible conversion, when the error in the real number operation is large, the error may not be restored even if the reverse conversion is performed because the error is accumulated in the iterative process. Therefore, it is necessary to consider the operation bit length. In order to compare the meaning with the integer type described below, the reversible conversion in a broad sense is referred to as a real number type reversible conversion below.

In the real number type reversible conversion, the total amount of data (the number of data × bit length) that must be held in order to maintain the reversibility increases. When the conversion is performed recursively many times, the amount of data increases many times as much as the original data. Therefore, when the conversion process is performed for the purpose of compressing data, it is general to perform lossy compression at the expense of losslessness. JPEG, H26 used for image data (still image, moving image) compression
1, MPEG1 / 2/4, etc. are representative.

On the other hand, in the integer type reversible conversion, the inverse conversion processing is performed while the data after the filtering is the same integer as the input data (the output may be the same fixed point data if the input is fixed point data). Is a conversion process for returning to the original data. The lossless conversion cannot be realized by simply rounding the result of the real number type lossless conversion and converting it into an integer.
This can be realized by performing rounding processing for integer conversion in the ng calculation step. This is called a reversible conversion in a narrow sense, and hereinafter, a reversible conversion (reversible filter) is simply a reversible conversion in a narrow sense, that is, an integer type reversible conversion.

To show that a transformation is reversible,
It is necessary to show the reversible transformation in the forward direction and the corresponding reversible transformation in the reverse direction as a pair.

In order to realize the reversible filter processing using Lifting Scheme, as described above, each Li is used.
The rounding process is performed in the lifting operation step. More specifically, in each Lifting operation step, the rounding process is performed before the result after the Lifting coefficient multiplication is added or subtracted. In the following, a reversible conversion 5 × 3 filter (hereinafter, reversible 5 ×
The reversibility will be described with reference to an example of 3 filters). Therefore, FIG. 5 shows a processing system that immediately performs reverse lossless conversion after forward lossless conversion.

In the figure, 501, 503, 505,
507 is a floor function operation unit that extracts the maximum integer value that does not exceed the input data, and 502 and 504 are Lif.
It is an addition unit that adds 0.5 to the data multiplied by the toning coefficient. The other units are exactly the same as the same-numbered units used in FIGS. 1 and 2. Only integer data is input to the adder and subtractor in the figure, and the output is naturally integer data. Such a Lifting operation is called an integer-type Lifting operation, and is used to realize a reversible conversion.

Image data (integer value) input from the left side of FIG. 5 is processed by the forward filter processing unit 540 and then by the backward filter processing unit 550, and the result is exactly the same as the original input. By explaining this, it is shown that the filter processing (conversion processing) is reversible.

First, note that the inputs of the four adders and subtractors in FIG. 5 are all integer values, and their outputs are also integer values.

As a policy for explanation, the following property (a)
After explaining that (b) holds, the property (c) is used to show that the even pixel series and the odd pixel series before and after the filtering process are equal to each other. (A) The output of the floor function calculation unit 503 in the forward filter processing unit 540 and the backward filter processing unit 5
The output of the floor function operation unit 505 in 50 is equal. (B) The output of the floor function operation unit 501 in the forward filter processing unit 540 and the backward filter processing unit 5
The output of the floor function operation unit 507 in 50 is equal. (C) If the same value as the added value is subtracted, the original value before the addition is restored.

The multipliers 111 and 211 have the same Liftin.
The g coefficient u is multiplied, and the data series to be multiplied is also the same high-frequency side conversion coefficient X'o. Therefore, the outputs of the two multipliers are equal. The outputs are added by 0.5 in addition units 502 and 504, respectively, and flo is obtained.
The results obtained via the or function operation units 503 and 505 are naturally the same. It can be said that the property (a) is satisfied. If the property (c) is used for this, it can be said that the even pixel series Xe input to the adder 113 and the even pixel series output from the subtractor 213 are also equal.

Next, the multipliers 107 and 207 have the same Lif.
The toning coefficient p is multiplied, and the data series to be multiplied is also the above-mentioned even pixel series Xe. Therefore,
It can be said that the outputs of the two multipliers are also equal. Each of the outputs is a floor function operation unit 50 having the same function.
The results of processing 1 and 507 are naturally the same. It can be said that the property (b) is also satisfied. When the property (c) is used for this, the odd pixel series X input to the adder 109 is input.
It can be said that the odd pixel series output from the subtractor 209 are also equal to o. Therefore, it can be said that the forward filter processing unit 540 and the backward filter processing unit 550 shown in FIG. 5 are reversible.

Since the output of the forward filter processing section 540 is an integer value, rounding processing for integerization is unnecessary,
The output of the integer value can be directly input to the backward filter processing unit 550. If the quantization step is set to "1" in the quantization process used during data compression, information is not lost in the quantization process, so that reversible compression can be performed. On the other hand, if the quantization step is set to be larger than "1", information loss occurs, so that the compression rate increases but it is not reversible.

As described above, Lifting Sch
Reversible conversion becomes possible by using eme. Here, the following is a summary of the relationship between the types of filters and the arithmetic methods for realizing them. -Arbitrary filter processing can be realized by convolution calculation-Part of the filter processing is Lifting Scheme
Real-type filter that can be realized by Lifting Scheme can be reversibly converted.-In the above real-number-type reversible filter, integer-type reversible filter processing can be performed by converting Lifting operation to integer type. Can be realized.

Therefore, the arbitrary filter processing can be realized by the convolution operation, but the integer type reversible filter processing cannot be realized by the convolution operation. In this, Lift
If both functions of filter processing that cannot be realized by ing Scheme (only realized by convolution operation) and integer type reversible filter processing are required, separate processing units (circuits)
Must be realized in.

When performing the integer type reversible filter processing, since it is necessary to perform the integer type Lifting operation, the real number type filter processing cannot be performed at the same time, and both the integer type and the real number type are processed. It is not possible to obtain the filtering results at the same time.

[0040]

As described above, since the reversible filter processing could not be realized by the convolution operation, when both the filter processing and the reversible filter processing function which can be realized only by the convolution operation are required, they are separated. However, there is a problem in that the filter processing apparatus cannot be constructed at a low cost because the size of the filter processing apparatus becomes large.

Further, the integer type reversible filter processing and the real number type filter processing cannot be performed at the same time, and thus both the integer type and real number type filter processing results cannot be obtained at the same time.

The present invention has been made in view of the above points, and can execute a convolution operation with a simple structure.
An object of the present invention is to provide a filter processing device and method capable of simultaneously obtaining both integer type and real number type filter processing results.

[0043]

In order to solve such a problem, the filter processing apparatus of the present invention has the following configuration.
That is, data D that is spatially continuous and is represented by an integer
₀ , D ₁ , D ₂ , D ₃ , ... Are input and odd data D ₁ , D ₃ ,
D ₅ ... and, even data _{D 0, D 2, D 4} , divided into ... and, ± t / 2
^{When the} real number coefficient represented by ^q is P ₁ , P ₂ , P _3, ...
Operation in at least three stages, X1 _2n = D _2n + P ₁ × (D _2n-1 + D _{2n + 1} ) (i) X2 _{2n + 1} = D _{2n + 1} + P ₂ × (X1 _2n + X1 _{2n + 2} ) ( ii) X3 _2n = X1 _2n + P ₃ × (X2 _2n-1 + X2 _{2n + 1} ) (iii): Reversible conversion of integer type that processes and outputs Xm _2n and Xm _{2n + 1} at the final stage as integer values Is a filter processing device for image data, wherein the processing device performs a filter operation on the operation expression as a reversible real number type, and intermediate data used in the operation of the filter operation means, Using the real number coefficients P1, P2, P3 ... Used in the calculation, the correction means for correcting the calculation result of the filter calculation means and the integerization means for converting the correction result by the correction means into integers are separated. Filtering device for featured image data.

[0044]

DETAILED DESCRIPTION OF THE INVENTION Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

<First Embodiment> The applicant of the present application has already
As Japanese Patent Application No. 2001-335185, two-stage integer type Li
Integer type reversible filter processing consisting of
Real-type operation that can perform reversible conversion (This is Lifting
It has already been proposed as a method of realizing the calculation by either the calculation or the convolution calculation) and the process of converting the calculation result real number data into an integer.

In the present embodiment, by further developing such a proposal, an integer type reversible filter process consisting of three stages of integer type Lifting operations is realized by a real number type operation capable of reversible conversion and an integerization process. Is.

FIG. 6 (a) shows the configuration of only the Lifting operation unit excluding the delay unit and the decimation unit by increasing the number of Lifting operation stages of the forward filter processing unit 540 shown in FIG. 5 from 2 stages to 3 stages.

Lifting coefficient multiplier 601, flo
The first-stage Lifting arithmetic unit including three units of the or function arithmetic unit 603 and the adder 605 is newly added, and the second and third Lifting arithmetic units have the same configuration as in FIG.

Lift in the first-stage Lifting operation
The toning coefficient r has the following value.

R = (1,1) / 2 From FIG. 6A, floor function operation units 603, 5
When 01 and 503 and the addition unit 502 are moved from the input side to the output side of the adder 605, the subtractor 109, and the adder 113, respectively, the result is as shown in FIG. 6B. In the figure, 611 is a Celing function operation unit that outputs a minimum integer value equal to or greater than the input data.

The following relational expressions are used in the conversion from FIG. 6 (a) to FIG. 6 (b). N + floor (R) = floor (N + R) (5) N-floor (R) = ceiling (N-R) (6) N + floor (R + 0.5) = floor (N + R + 0.5) (7) In the above formula, N is an integer Numerical values and R are real values. (5)
Both of the expressions (6) and (7) are self-explanatory.

Since the element of the Lifting calculation coefficient r in the first stage is 1/2, the actual real value in the above equation (5) has only one bit after the decimal point. Therefore, the data input to the floor functions on both the left and right sides is either an integer value or an integer value + 0.5. When the input data is an integer value, the input data is the output data as it is, and when the input data is an integer value + 0.5, the value obtained by cutting 0.5 from the input data is the output data.

The element of the Lifting calculation coefficient p in the second stage is -1/2, but fl on the left side in the above equation (6) is used.
The data input to the oor function operation unit is either an integer value or an integer value + 0.5. Fraction 0.5
Is rounded down and subtracted, resulting in the addition of the fractional part 0.5. Therefore, in the expression on the right side where the subtraction is performed first, round up the fractional part 0.5 to
Calculation is performed using the ng function.

Since the element of the Lifting calculation coefficient u in the third stage is ¼, the fractional part of the input real value of the floor function is 0, 0.25, 0.5 or 0.75. The expression on the left side that rounds down the fractional part and then adds an integer and the expression on the right side that adds up the integer value N and then rounds down the decimal part have the same result.

Next, FIG. 6 (b) is modified as shown in FIG. 6 (c). In FIG. 6C, 613 is an adder 605.
From the output data of the
It is a 1-bit subtractor that subtracts only the first decimal point bit (referred to as SB). Since the multiplier 107 multiplies the addition result by the Lifting coefficient, the distribution law relating to the four arithmetic operations is applied here, and FIG.
It can be transformed as shown in (a).

By applying the distribution law, a new multiplier 701 and a new adder 703 are required. These multiplier and adder perform Lifting operation only on the LSB of the output data of the adder 605.

Since the LSB of the output data of the adder 605 depends only on the LSB of the even-numbered series data Xo, the LSB of the Xo is directly calculated in the configuration of FIG. 7B. After this, the LS of the output data of the adder 605
1-bit data equivalent to B is expressed as LSB_A and used.

In FIG. 7B, two adders 615 and 703 are present in the preceding stage of the multiplier 111. By applying the distributive law again to this multiplication and addition operation,
FIG. 7B can be modified as shown in FIG. The application of the distribution rule requires new multipliers 803 and 805 and adders 813 and 815. These multipliers and adders lift the Lift bit for each of the 2-bit data added by the adder 703 and the LSB data added by the adder 615.
The ing operation is performed.

The subtractor 613 and the adder 113 shown in FIG.
9 is obtained by replacing the arrangement (the order of operations) of FIG. 9 and replacing the addition processing of the first decimal place (LSB_B) in the adder 615 with the addition operation of 0.5 and the floor function operation.
The configuration shown in FIG. 3 is a specific example of the first embodiment.

In FIG. 9, 901 is a real type Lift.
A Lifting operation unit that performs an ing operation, a data correction unit 903 that generates correction data based on bit information of a part of the input data, and adds and subtracts the correction data.

In FIG. 9, a real type Lifting operation unit 901, a data correction unit 903, and an integer processing unit 905.
And are clearly separated. Since the output of the real number type Lifting operation unit is not rounded at all during the operation, the original data can be restored by performing the inverse conversion.
That is, there is reversibility. The data correction unit and the integerization processing unit in the subsequent stage perform integer conversion without losing the reversibility.

The separated real number type Lifting operation unit 901 can also be realized by a convolution operation generally used in filter operation processing. One example of the configuration is shown in FIG. A normal filter coefficient is required in the convolution operation. The filter coefficient is shown in FIG.

In FIG. 10, the data to be filtered is input to the terminal indicated by □ (which can be composed of a latch), and
By adding input data with each other by the adder shown by, multiplying the filter coefficient by the multiplier shown by Δ, and finally adding them, the same result as the filter processing result obtained by the real type Lifting operation unit 901 is obtained. Can be obtained. Since the convolution operation is a known technique, detailed description will be omitted.

Therefore, by providing the data correction unit 903 and the integer conversion calculation unit 905 of FIG. 9 in the subsequent stage of the convolution calculation processing unit 1001 shown in FIG. 10, it is possible to realize a function equivalent to the configuration shown in FIG. Is. Of course, FIG.
Needless to say, it is equivalent to the function of (a). This configuration is also a modification of the present invention.

In the above-described first embodiment, all three Lifting operation coefficients are ± 1 / 2q.
It may be ± t / 2q (t is a natural number).

There is no problem because the real number type filter operation unit may faithfully perform the operation based on the set coefficient and the integer processing unit may also perform the predetermined rounding process.

The data correction unit seems to have the most problem, but it is sufficient to extract only the fractional part from the output of the Lifting multiplier at the first stage, whatever the coefficient value. Depending on the coefficient value, the fractional part to be extracted may be 2 bits or more. (In the above embodiment, LSB_A
The extracted fractional part is input to the subtractor 613 in the data correction unit 903 in FIG. 9 and also to the Lifting multiplier 701, and all bit information of the multiplication result is added to the adder 703. And Lifting
Input to the multiplier 803. All the multiplication results are also input to the adder 813.

Similarly, the fractional part output from the adder 703 is taken out and input to the Lifting multiplier 805 regardless of the value of the Lifting coefficient p in the second stage.
All bit information of the multiplication result is input to the adder 815.

Through the above processing, all values that change due to the integer multiplication of the Lifting multiplication result can be reflected in the output. That is, the real type Liftin
It is possible to correct the g operation result to an integer type Lifting operation result.

<Second Embodiment> In the first embodiment, the correction data is generated by using a part of bit information of the input data. The second embodiment shows a configuration in which the correction data is generated from the output data of the real number type Lifting operation unit 901, not from the input data. Therefore, the real number type Lifting operation unit 901 and the integer conversion processing unit 905 use the same ones used in the first embodiment as they are, and only the data correction unit has a new configuration.

Here, the real number type Lifting operation unit 90
Let us take a closer look at the data below the decimal point in the output data of 1. While there are three stages of Lifting calculation processing, the first stage Lifting calculation coefficient r is (1
/ 2, 1/2), the number of bits after the decimal point in the output of the adder 605 is 1 bit (only 1 bit after the decimal point has meaning).

The Lifting operation coefficient p of the second stage is also (1/2, 1/2), and the coefficient is the adder 60.
Since the output of 5 is multiplied, the number of bits after the decimal point in the outputs of the multiplier 107 and the subtractor 109 is 2 bits.

The Lifting calculation coefficient u of the third stage, which is the final stage, is (1/4, 1/4). Since the coefficient is multiplied by the output of the subtractor 109, the number of bits after the decimal point in the outputs of the multiplier 111 and the adder 113 is 2+.
2 = 4 bits.

Therefore, the real number type Lifting operation unit 90
The number of bits below the decimal point in the output data of 1 is 4 bits on the upper side and 2 bits on the lower side.

Therefore, in order to perform the operation of 4 bits which is the maximum bit width of the decimal part, only the bit data below the decimal point is taken out from the upper side, and the integer part 2 bits and the 2 bits below the decimal point are taken out from the lower side. And between them L
Performs ifting calculation. In the following, description will be given with reference to FIG.

The Lifting coefficient multiplier 1203 applies Lifti to the 4-bit data sequence extracted from the lower side.
The ng operation coefficient u = (1/4, 1/4) is multiplied. When the multiplication result is input to the subtractor 1205 and subtracted from the 4-bit data series extracted from the upper side, the subtraction result (4 bits) is a real number type Lifting based on the principle described in <Description of lossless conversion>. It becomes the same as the bit data after the decimal point in the output of the adder 605 in the arithmetic unit 901.

That is, of the 4 bits of the subtraction result, the lower 3
All bits become zero and the most significant 1 bit (MSB)
Is 1 bit after the decimal point of the output of the adder 605, that is, the same as the above-mentioned LSB_A.

After LSB_A is obtained, the correction data can be generated and the addition / subtraction calculation can be performed after that, similarly to the data correction unit 903.

In FIG. 12, bit data below the decimal point is separated from two input data sequences, and L is set between the bit data.
The LSB_A data is generated by performing the ifing operation, the other two correction data are generated from the LSB_A, and the LSB_A and the two correction data are added / subtracted to / from the input data. The reversible filter processing apparatus is configured by using the data correction unit 1201 shown in FIG. 12, the real number type filter operation unit (either Lifting operation or convolution operation can be used), and the integer processing unit 905 to configure the reversible filter processing device. In this embodiment, which is the second embodiment, 3
A smart configuration is possible in which two processing units are simply cascade-connected.

<Third Embodiment (Software Processing)> The first and second embodiments relate to a filter processing device using hardware. Hereinafter, an embodiment relating to a filter processing method by software will be described.

Conventionally, in order to realize the integer type reversible filter calculation process, it was necessary to use the integer type Lifting calculation. In the third embodiment, an integer type Lift
An integer type reversible filter process is realized by using a fixed-point type filter calculation process and an integer rounding calculation process without using the ing calculation.

The flowchart shown in FIG. 13 uses a convolution operation as the fixed-point type filter operation processing, and the data to be processed are X ₀ , X _1, ..., X _M-2 , X _M-1.
Data of M (even number).

In the figure, padding processing is performed in step 1301. The padding process is X _-3 , X _-2 , X _-1 or X _M , X _{M + 1} with no data (undefined).
Is a process of substituting certain data into a variable such as.

In a generally performed method, data at both ends of all data is simply copied to expand the data, thereby generating data at coordinate positions necessary for calculation. As a slightly devised method, there is also a method in which the data is folded back and copied at the boundaries of both ends of the data.

In step 1303, n = 0 in the initialization process.
Set to. LSB_X ₁ required in step 1309 in the first loop processing described later, step 13
In step 1305, the LSB_A ₀ required in step 11, the three data T ₋₁ required in step 1313, and the data required to calculate the data are calculated in advance.

Steps 1307, 1309, 2111,
N loop processing consisting of 2113, 2115, and 2117
It starts from = 0 and is performed while satisfying n <M / 2.

At step 1307, the arithmetic processing of the two types of filters H0 and G0 shown in FIG. 11 is performed by fixed point arithmetic. The weight of LSB in the calculation result of the even series is 1 /
16 and the weight of the LSB in the operation result of the odd series is 1/4.

Step 1309 calculates two types of LSB data (LSB_X, LSB_A).

In step 1311, the correction data (T _n ) is calculated to the odd-numbered series of conversion coefficients and the first decimal point data is extracted (the result is F _n ), and the correction data (T _n ) is obtained as the filter calculation result. The correction data addition processing for adding to, and the bit shift operation for cutting off the decimal part are performed. Here, since the weight of LSB is 1/4, 2-bit shift is performed.

In step 1313, correction data addition processing to the even-numbered series of conversion coefficients and bit shift operation for cutting off the decimal part are performed. Since the weight of LSB is 1/16, 4-bit shift is performed.

At step 1315, it is determined whether or not the loop processing is continued. If it is determined to continue, in step 1317, the value of n is incremented by 1 to be updated, and the process returns to step 1307.

Since the contents of the above correction data are the same as those described in the first embodiment, the description thereof will be omitted.

The integer even-numbered sequence conversion coefficient and odd-numbered sequence conversion coefficient obtained by the above calculation are outputs of the integer type reversible filter processing.

The flowchart of FIG. 13 is a processing flow in the case where there is no restriction on the padding processing. When the data is folded around the boundary input data X0 as the padding process, that is, when the condition of X−n = Xn is added, the process of step 1305 can be simplified as step 1405 in the flowchart shown in FIG. . Steps 1309 and 1311 in the loop processing,
Only the three data needed at 1313 need be calculated directly.

LSB_A ₀ is the LSB_X _-1 and LSB_
Although it is the least significant 1 bit of the value obtained by adding X ₁ , the two LSB_X have the same value under the above conditions, so the added value is an even number and the least significant bit is always zero. This result also affects the next calculation of T ₋₁ , and T ₋₁ = LSB_A ₀ +
LSB_A ₋₂ = LSB_A ₂ (because all the negative subscript data are equal to the positive subscript data of the same value due to the mirror image relationship).

In the above embodiment, in order to make the contents of the operation known accurately, the floating-point operation is not used, but the fixed-point operation is described. However, these fixed-point operation can be replaced by the floating-point decimal operation. It's easy to imagine being there. In general, floating-point arithmetic operations are worried about conversion errors that occur when converting data represented by decimal decimals into binary notation and accumulation of the errors due to repeated operations. In the above-described embodiment, since such a conversion error does not occur, the same result as the fixed point arithmetic can be obtained.

Although the various filter processing apparatuses and filter processing methods described above are the processing for one-dimensional data, the processing is performed twice for the two-dimensional image data in the horizontal direction and the vertical direction. Therefore, a filter processing apparatus and a filter processing method for performing two-dimensional filter processing naturally belong to the scope of the present invention.

As described above, according to this embodiment,
An integer type reversible filter process having a filter processing means for performing a real number type filter operation capable of reversible conversion, a data correction means for generating correction data and adding / subtracting it, and a rounding means for converting the operation result into an integer. The device can be realized, and at the same time, the real number type filter calculation result and the integer type reversible filter calculation result can be obtained at the same time.

Further, by having a filter processing step of performing a real number type filter operation capable of reversible conversion, a data correction step of generating and adding / subtracting correction data, and a rounding processing step of performing integer conversion, an integer type The reversible filter processing method can be realized, and at the same time, the real number type filter operation result and the integer type reversible filter operation result can be obtained at the same time.

As is apparent from the description of the third embodiment, the present invention can be realized by software. As an implementation target of such software, not only can it be applied to DWT operations such as JPEG2000, but it can also be applied to various image processing filters. Also,
Usually, in order to execute a computer program on a general-purpose information processing device such as a personal computer, a portable computer-readable medium such as a flexible magnetic disk disk or a CD-ROM is set in the device and copied or installed in the system. Therefore, it is obvious that the present invention also includes such a computer-readable storage medium in its category.

[0101]

As described above, according to the present invention, the convolution operation can be executed with a simple structure, and both integer type and real number type filter processing results can be obtained at the same time.

[Brief description of drawings]

FIG. 1 is a diagram expressing a Lifting Scheme in a forward direction.

FIG. 2 is a diagram showing a lifting scheme in the reverse direction.

FIG. 3 is a diagram showing coefficients of a 5 × 3 filter.

FIG. 4 is a diagram showing Lifting coefficients of a 5 × 3 filter.

FIG. 5 is a diagram showing configurations of a reversible forward filter processing unit and a reversible filter processing unit.

FIG. 6 is a diagram showing a configuration of a filter processing unit including a three-stage Lifting operation and a modification equivalent to the configuration.

FIG. 7 is a diagram showing a modified example equivalent to FIG.

FIG. 8 is a diagram showing a modified example equivalent to FIG.

FIG. 9 is a diagram showing a configuration of a first exemplary embodiment of the present invention.

FIG. 10 is a diagram showing a configuration for performing filter processing by a convolution operation.

FIG. 11 is a diagram showing filter coefficients of a forward filter and a backward filter.

FIG. 12 is a diagram showing a configuration of a second exemplary embodiment of the present invention.

FIG. 13 is a diagram showing a flowchart of a filter processing method according to a third embodiment of the present invention.

FIG. 14 is a diagram showing a modification of the third embodiment of the present invention.

Claims (10)

[Claims] 1. Data D ₀ , D ₁ , D ₂ , D ₃ , ... Which are spatially continuous and are expressed by integers are input, and odd data D ₁ ,
D _3, D ₅ ... and, even data _{D 0, D 2, D 4} , divided into ... and,
When the real number coefficient represented by ± t / 2 ^q is P ₁ , P ₂ , P _3, ..., At least three-stage calculation: X1 _2n = D _2n + P ₁ × (D _2n-1 + D _{2n + 1} ) (i) X2 _{2n + 1} = D _{2n + 1} + P ₂ × (X1 _2n + X1 _{2n + 2} ) (ii) X3 _2n = X1 _2n + P ₃ × (X2 _2n-1 + X2 _{2n + 1} ) (iii): Is a filter processing device for image data capable of performing integer reversible conversion by processing Xm _2n and Xm _{2n + 1} at the final stage as integer values, and the processing device is capable of reversing the arithmetic expression. Filter operation means for performing filter operation as a real number type, intermediate data used for operation of the filter operation means,
Using the real number coefficients P1, P2, P3 ... Used in the calculation, the correction means for correcting the calculation result of the filter calculation means and the integerization means for converting the correction result by the correction means into integers are separated. Filtering device for featured image data. 2. The filter processing apparatus according to claim 1, wherein the filter calculation means uses a convolution calculation. 3. The filter calculation means comprises Lifti
The filter processing device according to claim 1, wherein an ng operation is used. 4. The correction means generates correction data based on predetermined bit information of a calculation result and a calculation result, and adds the correction data to Xm _2n and Xm _{2n + 1} immediately before being converted into an integer. 4. The filter processing device according to any one of 1 to 3. 5. Data D ₀ , D ₁ , D ₂ , D ₃ , ... Which are spatially continuous and are expressed by integers are input, and odd data D ₁ ,
D _3, D ₅ ... and, even data _{D 0, D 2, D 4} , divided into ... and,
When the real number coefficient represented by ± t / 2 ^q is P ₁ , P ₂ , P _3, ..., At least three-stage calculation: X1 _2n = D _2n + P ₁ × (D _2n-1 + D _{2n + 1} ) (i) X2 _{2n + 1} = D _{2n + 1} + P ₂ × (X1 _2n + X1 _{2n + 2} ) (ii) X3 _2n = X1 _2n + P ₃ × (X2 _2n-1 + X2 _{2n + 1} ) (iii): Is a filter processing method for image data capable of performing integer reversible conversion in which Xm _2n and Xm _{2n + 1} at the final stage are output as integer values. Possible real number type or fixed point type filter calculation step, intermediate data used in the calculation of the filter calculation step,
Using the real number coefficients P1, P2, P3 ... Used in the calculation, the correction step for correcting the calculation result of the filter calculation step and the integerization step for converting the correction result by the correction step into integers are separated. Filtering method for featured image data. 6. The filter processing method according to claim 5, wherein a convolution operation is used in the filter operation step. 7. In the filter calculation step, Lifti
The filter processing method according to claim 5, wherein an ng operation is used. 8. The correction step is to generate correction data based on predetermined bit information of a calculation result and a calculation result, and add the correction data to Xm _2n and Xm _{2n + 1} immediately before being converted into an integer. The filtering method according to any one of 5 to 7. 9. A computer program that executes the steps according to any one of claims 5 to 8. 10. A computer-readable storage medium storing the computer program according to claim 9.